On-machine metrology is particularly important for diamond turning and grinding as it is difficult to remount and align a part if it does not meet off-line inspection criteria. There is also the issue of tool wear; a process that started well may fail part way through the cut, and if tool replacement is needed, it is vital to know that before removing the part. A means of rapid, noncontact, in situ profiling and roughness measurement could improve the productivity of diamond tool machining.
Recently we first showed that diamond turning machines are sufficiently isolated that steady fringes can be obtained by simply setting a Point Source Microscope [1,2] equipped with an interferometric Mirau objective on the cross slide of a machine. Further, we demonstrated that the machine can be precisely driven to get temporally shifted fringes so that common algorithms can be used to obtain area based surface roughness measurements. This led to the question of whether essentially the same hardware could be used to rapidly profile diamond turned parts. We show via simulation that the answer is yes and that the approach can be implemented rather simply.
We first describe the PSM and its configuration as a Microfinish Topographer (MFT) by using interferometric data reduction software. Then we describe how this hardware is changed into a profiler by changing the light source and camera. Finally, we show how this hardware that we call a Non-Contact Profiler [3] (NCP) is used on a diamond turning machine to profile turned or ground parts in situ.
MICROROUGHNESS TOPOGRAPHER (MFT)
The Point Source Microscope [1] has been described previously while the MicroFinish Topographer [2] (MFT) is the same hardware where the LED illumination channel is used as the light source and a Mirau interference objective replaces the standard infinite conjugate objective as shown in Fig. 1.
The red LED source has sufficient coherence to obtain interference fringes within about ±8 μm of the reflection from the reference mirror in a 10x Mirau objective. This is more than enough coherence to get surface roughness data over a 1 x 0.75 mm area with a 10x objective as long as the objective reference mirror is within about 1° of the normal to the surface. Higher magnification objectives have proportionally smaller fields of view but can accommodate greater tilt between surface and reference.
Commercially available software drives a PZT behind the objective to shift the fringes to produce roughness data. Alternatively, machine control based software can step the MFT in ¼ fringe intervals to capture 4 or more interferograms, and reduce the data to provide surface roughness information.
WHITE FRINGE LOCATION
Quite separately from our work on roughness metrology we found that by using a white light LED and a color camera, it is easy to obtain three fringe intensity patterns, one for each color as shown in Fig. 2. When the phases of all three fringe intensity patterns are aligned we get a white or black fringe depending on whether the surface is a dielectric or metal, respectively, indicating that the surface and reference mirror in the objective are precisely conjugate, or the same distance from the beamsplitter. In white light scanning interferometry this is done by looking for a peak in fringe contrast. With the 3 distinct wavelengths in a white LED there are 3 distinct fringe intensity patterns captured by the color camera. On the left of Fig. 2 is the white LED fringe pattern as seen using a 10x Mirau objective and a color camera, while on the right is a plot of the three intensities from one row of the data. The phases of all three sinusoidal intensity patterns from a row of data align at the location of the white fringe as indicated by the black line tying the figures together.
The realization that we could easily recognize the white fringe using the same hardware as the MFT led directly to the idea that the same device used for roughness measurement could be used as an indicator, or sensor, to profile based on the location of the white fringe in the frame of data. We call the MFT used in this way to profile the Non-Contact Profiler (NCP).
INFORMATION IN THE WHITE FRINGE
The information for contouring comes out of the algorithm used to find where the phases align. A sine wave is fit to each of the three intensities in the form I = A*sin(B*x + C). The amplitude A is of no interest while B is proportional to the number of fringes in a frame of data, or the tilt between the reference mirror and the patch of surface observed. For a given frame of fringes, B is also inversely proportional to the wavelength being fit because there will be more fringes for a shorter wavelength. The white fringe is at the value of x (in pixels) where the argument (B*x+C) is equal Nπ/2 for odd integral N. Once B and C are found for each row (or column) of intensity data, the y value (or x value), in pixels, is known for the position where the reference mirror and surface are conjugate, or the same distance from the beamsplitter in absolute terms.
Fig. 3 shows an example of a 2 μinch (50 nm) rms surface from a GAR surface roughness standard artifact [4] with the x,y locations of the center of the white fringe indicated with a row of dots. The scale in the Figure was set by the 10x objective; the optical path difference between fringes for the blue wavelength is about 240 nm and in this example there are about 100 pixels between fringes. Once the fitting is done to find the white fringe, and assuming there are no big jumps from row to row of data, the center of the fringe can be found with a simple algorithm that takes less than 1 ms per row. This means surfaces can be profiled with 1 μm spatial resolution at a rate of 1 mm/sec and proportionally faster at lower spatial resolutions and with height resolutions of a few nm rms.
One mode of using the NCP is as an optical micrometer. For example, in Fig. 3 if one wanted to know how far to move the NCP in z to bring the center of the white fringe to the cross, the column of data containing the cross would be fit to find B and C. The C coefficient tells how far to move in nm scaled by the fringe spacing B in pixels per nm.
This mode could be used to find spindle growth by laterally positioning the cross at the vertex of a part and then moving in z to set the white fringe on the vertex. After running the spindle for a time, the movement of the white fringe from the cross gives the spindle growth. Similarly, in the indicator mode, parts could be squared with the face plate.
The usefulness of this mode is that the height or angle of a particular feature in the field of view can be compared to another to a few nm rms or a few seconds of arc for nm or second differences. The sensitivity is proportionally less the greater the difference in feature height or angle unless the diamond turning machine is used to re-position the NCP. If the NCP is repositioned to have just a few fringes in the field of view, the sensitivity is again in the few nm or second regime. Said in another way, the NCP has high sensitivity when used in a null detector mode but features of interest can be selected on a μm scale spatially.
USING THE NCP AS A PROFILER
Using the NCP as a profiler on a diamond turning machine for near flat surfaces means mounting the NCP on the x slide with set and forget adjustments to center the field of view on the spindle axis and a few minutes of arc off normal so there are a few near vertical fringes across the detector. As long as the angle between reference mirror and surface is no more than about 1° for a 10x objective, the white fringe can be kept in its initial position as the x axis is scanned by using the value of C as a feedback signal to the z axis. A safer and more practical mode would be to run the theoretical part curve and record C as a function of the x axis position to create a contour error map.
For parts with a steep enough radius to have normals greater than 1° when using a 10x objective, the NCP must be mounted on a B axis rotary table and the B axis used to keep the NCP near normal to the surface as it is scanned in x and z as illustrated in Fig. 4. Again, the most practical method of contouring is to run the part contour path and watch for changes in the white fringe location as the indication of errors in the part.
The distance between the objective focus with the white fringe in the middle of the display and the B axis is the “tool radius” used in calculating the measurement profile. To go from cutting the part to measuring is a matter of changing from the “tool radius” to the “measurement radius” where the measurement radius is pre-calibrated and stored in the machine control software as a new “tool radius”. Clearly, errors in the measurement of the tool radius will lead to errors in the measured contour. However, calibrating the tool radius for measurement purposes is easily done by contouring a good grade steel ball.
Radial errors in the B axis will contribute directly to errors in the measurement of the part contour. However, the oil hydrostatic B axis bearing can be compensated to under 20 nm. Errors in all three angular degrees of freedom in the B axis rotation and axial translation of the B axis make only second order contributions to measurement errors.
Although we have not yet profiled a part on a diamond turning machine, we have simulated real fringe data by thermally changing the optical path between a diamond turned part and the objective reference mirror and shown that the white fringe center can be tracked at 30 frames per second. We have also shown that fringe centers within each frame of data can be found at least as fast as 1 msecond per pixel row or column of data in the frame. This translates to a spatial resolution of 1 μm on the surface using a 10x Mirau objective.
FUTURE WORK
Clearly, our next move is to mount the NCP on a machine and profile a known part. We hope to do this in the next couple of months to obtain data showing in situ profiling performance. In addition, we want to profile a non-rotationally symmetric part. If, using a 10x objective, the normal in the y direction is less than 1°, we can do this profiling with the setup just as described including profiling while the part is rotating on the spindle at low rpm.
Further, surface roughness measurements can be made at any point in the process of profiling by moving in steps normal to the surface. Roughness data can be obtained at angles as great as 1° for a 10x objective as well since the diamond turning machine is well isolated and there is little danger of fringe print through. If the normals are greater than 1° we can go to higher power objectives to get up to 5° off normal with a 50x objective and smaller field of view.
For still greater angles we will have to add an A axis of rotation and use the white fringe position from both row and column data to produce profiles in both the radial and tangential directions. In this case the initial tilt of the NCP to the surface under test would be set to produce fringes at roughly 45° to the machine coordinate system. Further, the profiling could be done on a spiral basis to give areal coverage of non-symmetric and free-form parts.
CONCLUSIONS We have described a simple method of performing in situ, non-contact profiling of diamond turned parts using a well proven sensor head with a pseudo-white light source and a color camera instead of the normally used red LED and monochrome camera. The color source and camera provide a means of unambiguously isolating the white, or black, fringe that shows precise conjugation of the reference with the surface under test. This permits making profile measurements with a precision of a few nm rms and a spatial resolution of a few μm while taking data at a contouring speed of about 10 mm/second.
For surfaces that depart from plane by 1° or less, all that is required for profiling is a PSM with a Mirau objective, a white light LED source and fairly simple algorithms. This same mode of operation works for angles up to 5° by using a 50x objective although proportionally smaller fields of view are seen.
For symmetric surfaces with larger slopes, the sensor head must be mounted on a B axis to keep the number of fringes from becoming to great to resolve. For steep non-symmetric surfaces, an A axis must also be added. In addition to this profiling capability, there is the
simultaneous ability to measure surface roughness by stopping the scan and obtaining 4 or more interferograms at the desired location. No additional alignment is necessary because the NCP is already near normal to the surface, and the machine motion control can do the phase stepping.
REFERENCES
Parks, R. E., “Versatile Autostigmatic Microscope”, Proceedings of SPIE Vol. 6289, 62890J, (2006).
Parks, R. E., “Micro-Finish Topographer: surface finish metrology for large and small optics”, Proceedings of SPIE Vol. 8126, 8126- 11, (2011).
An autostigmatic microscope is described and its uses explained. Then an adaptation of the original instrument is described that uses current technological advances in laser diodes and video displays to turn an old workhorse into a versatile optical test and alignment device. This paper illustrates applications that make use of the capabilities of the modern autostigmatic microscope outside the field of aligning optical systems such as using it as an electronic autocollimator, a check on the centration of the axes of molded optics and the measurement of the runout and wobble of precision spindles such as air bearings.
1. INTRODUCTION
First we will describe what an autostigmatic microscope (ASM) is and how it has traditionally been used. Then we will describe the features that make this modern realization of an autostigmatic microscope have applications far wider than the traditional ones. Finally we give examples of the use of this modern adaptation to demonstrate the versatility and practicality of the instrument outside the areas strictly concerned with alignment.
2. DESCRIPTION OF AN AUTOSTIGMATIC MICROSCOPE
2.1 Definition of an autostigmatic microscope
We all know what a microscope is; an optical instrument with an objective lens designed to produce images of objects located a short distance from the objective at a high magnification, or at large image distances. This means there is a fast f/number cone of light on the object side of the objective lens and a slow cone on the image side. “Stigmatic” means that the objective lens images well.1 A point source of light at one conjugate of the objective forms a cone of light at the other conjugate where all the rays cross at a single point, particularly on axis.
This leaves the word “auto”. The autostigmatic microscope (ASM) is analogous to an autocollimator except that instead of sending out a perfectly collimated beam of light and having a means of detecting the angle of the return light beam, the microscope sends out a perfectly focused cone of light and has the means of detecting the lateral position and focus of the return spot or stigma of the cone of light. Fig. 1 shows the necessary components of a simple ASM microscope. A point source of light is reflected from a beamsplitter into a microscope objective that forms a perfect axial focus and the light diverges to the right. Perfectly focused light converging from the right to the objective focus would be stigmatically imaged at the center of the eyepiece object plane at the left.
2.2 Traditional uses of an autostigmatic microscope
To understand the traditional uses of an ASM it is again helpful to think of an autocollimator. An autocollimator is an instrument that measures the angles of plane surfaces using the light reflected off of them at near normal incidence and is helpful in seeing what the angular relationship of one surface is to another. The ASM is an instrument that measures the location of the center of curvature of a spherical surface using light reflected off the surface at, or near, normal incidence, and is helpful in relating the position, in three dimensions simultaneously, of one center of curvature to another. Since the alignment of optical systems is really about placing centers of curvature where an optical design specifies they should be, an ASM is useful for the alignment of optical systems.2,3
2.3 The utility of an autostigmatic microscope
Even this very simple autostigmatic microscope is more useful than an autocollimator in that it can also measure the radius of curvature of a spherical surface when attached to a linear scale. Fig. 2 shows two examples of this, one for the more familiar case of a concave spherical surface and the other for a convex surface. The reason the ASM can measure the radius of curvature is that when the focus of the objective is coincident with a surface, a Cat’s eye reflection is produced off the surface. This is illustrated in the right hand side of Fig. 2 in the plane of the page where light coming out of the top of the objective aperture is reflected off the surface. The angle of incidence equals the angle of reflection and so the light returns into the bottom of the objective aperture. Obviously the same thing happens symmetrically around the objective aperture but is not shown for clarity.
The axial distance the microscope is moved between the positions where the return spot in the eyepiece object plane is in sharp focus is the radius of curvature of the spherical surface. If the radius of the convex surface is larger than the working distance of the objective, an auxiliary positive lens with a object distance longer than the radius must be used to relay the center of curvature. Although this measurement looks like simplicity itself, making the measurement accurately to better than 1 part in 1000 is not easy without attention to detail that has little to do with the ASM itself.4,5
Returning to the discussion of the Cat’s eye reflection, notice that the light coming out of the objective at an angle α with respect to the axis of the objective returns at -α independently of the tilt of the surface until the tilt is so great no light gets back into the objective, or is completely vignetted. This means the center of the return spot will always be in the same position in the eyepiece object plane regardless of the tip or tilt of the surface. Because of this feature of a Cat’s eye reflection no information is known about the tilt of the surface, only whether the surface is in focus as evidenced by the smallest possible spot diameter as seen in the eyepiece or a CCD camera located at the long conjugate of the objective. For this reason the Cat’s eye lateral location is a perfect “zero” lateral reference.
2.4 Relative scarcity of autostigmatic microscopes
It is clear from the brief discussion above that ASM’s are useful and, in fact, are used in most optical shops for measuring the radii of optical surfaces. Most of these ASM’s were built before laser diodes were common and use either a projected reticule illuminated by an incandescent bulb or a bulb filament as the light source, both of which are extended sources, not very bright and not particularly good for centering. They are fine instruments for finding focus at centers of curvature (once you find the dim return spot) and surfaces.
One of the things that has happened since most of these ASM’s were put in service is that there are now virtually perfect light sources for ASM’s, namely single mode, fiber pigtailed, laser diodes. These are bright (many mW’s), nearly monochromatic, visible (635 nm), small Gaussian spots (~4.5 μm single mode field diameter) with a divergence of about f/5 at the beam waist. In addition the laser diodes are relatively inexpensive, they last forever and their intensity is easily controlled remotely. The small size of the single mode fiber source means that the focused spot exiting the objective will be diffraction limited for any decent microscope objective (assuming the rest of the optics in the microscope are high quality).
Another thing that has happened relatively recently is that there are small, digital, CCD cameras available at a reasonable price that can be easily interfaced with computer displays. This is particularly advantageous when using a laptop computer because the display can be located close to the ASM so what would ordinarily be viewed through an eyepiece can now be viewed in a much more ergonomic fashion right along side the instrument being tested or aligned. This also aids hand/eye feedback while making alignment adjustments.
In addition, someone had to take these new devices and package them along with custom software to drive the laser diodes and control the camera. Our company, Optical Perspectives Group, and principally, Bill Kuhn,6 has done just that. Optical Perspectives Group7 markets this new ASM as the Point Source Microscope or PSM.
3. DESCRIPTION OF THE POINT SOURCE MICROSCOPE (PSM)
3.1 Optical design rationale for the PSM
First, if one is going to use a relatively expensive, long working distance (so convex surfaces can be accessed) microscope objective to produce a diffraction limited, focused spot it would be useful if the microscope also imaged as well as a professional reflected light (or metallurgical) microscope. Of course this requires a completely different illumination (Kohler) method than the ASM so this extra illuminator was added to the PSM. However, it was undesirable to have a big, hot bulb hanging off our ASM (along with its big, heavy transformer) so we used red LED’s in the Kohler illuminator and a second beamsplitter to make the PSM a practical, reflected light, imaging microscope as well as shown in Fig. 3 (left).
Another advantage of the solid state illumination is that the whole microscope weighs a fraction of what a reflecting microscope weighs and there is a corresponding reduction in volume. (To be fair the PSM requires an external three axis stage to locate it whereas the stage is an integral part of a reflecting microscope.) Fig. 3 (right) shows a photograph of the PSM with the CCD camera8 on the rear and a Nikon long working distance objective on the front.
A Firewire cable is the power to and video signal from the camera while another cable controls the illumination. The scale of the PSM is obvious from the fiber connector and the Nikon objective and the weight is 600 gm as pictured.
3.2 Additional features of the PSM
Modern microscopes use infinite conjugate objective lenses. The PSM was similarly designed to take advantage of this and add versatility. The use of infinite conjugate optics means that when the objective is removed a collimated beam exits. In this configuration the PSM can be used as an electronic autocollimator.
Speaking of autocollimators, anyone who has used one knows the frustration of getting the light back into the autocollimator aperture and eyepiece. The field of view of an autocollimator that is sensitive to a second of arc has a total capture range of a little more than ±one minute of arc. Often it is necessary to completely darken the lab and then use a flashlight projected into the eyepiece to get a bright enough patch of light back to capture the reflection off the surface under test, particularly if it is an uncoated surface.
The PSM takes care of this problem with a “bright” setting on the laser diode. Slightly less than 1 mW of light comes out the front of the PSM and this is bright enough to see with the room lights on. This makes it easy to find either the return collimated beam, or the focused spot if using the PSM with an objective, under normal lighting conditions. Once even a small fraction of the return light enters the PSM aperture the laser diode can be turned down to the lower setting (which is so dim it is not visible) so the CCD camera is not saturated.
Another feature that makes the PSM very convenient to use is that it is coupled to a computer and that the computer can multi-task. This means that one can take notes of the experiment they are doing while taking data. Settings and video data can be pasted directly into Word or WordPad documents used for tracking experimental conditions. This makes an integrated report that is essentially finished when the experiment is over.
3.3 Simple tests using the PSM
The PSM will do all those tests that one would think an ASM might be good for. We have already mentioned radius of curvature measurement. While the ASM is at the center of curvature of a surface it also measures the optical quality of that surface as in a Star test9. Unless the surface is near perfect, eighth wave or better peak-to-valley, the ASM will show a lack of symmetry in the return spot and the software will give a quantitative analysis of the low order aberrations present. This makes the PSM a good way to do in-coming inspection on optical components for shops that do not have an interferometer.
In an approach similar to measuring the radius of curvature, the PSM can be used as a non-contact way of measuring the center thickness of lenses and windows. For lenses, the curvature of the side being looked through must be taken into account as well as the index of refraction of the material. Then the distance the PSM is moved between the Cat’s eye reflection from the upper surface and the Cat’s eye from the back of the lower surface will give the thickness. This is easily modeled in an optical design program such as Zemax10.
In a similar vein, microscopes are often used to examine surfaces for scratches or other surfaces defects. Yet if a surface is well polished it is very difficult to focus on because it is featureless and has no features with sufficient contrast on which to focus. The PSM solves this problem with the point source because there will always be a Cat’s eye reflection when the PSM is focused on the surface. Once the Cat’s eye reflection is in good focus the sample can be moved laterally until a feature of interest is found because the surface is now in the focal plane of the microscope.
4. APPLICATIONS OF THE POINT SOURCE MICROSCOPE
Now that it has been shown what an ASM is and how the addition of a second illumination path and the infinite conjugates optics make the PSM a very versatile and practical ASM, some of the uses of the PSM will be described. The very first example I saw of an ASM at work was at Frank Cooke, Inc. where Ray Boyd used it for checking the concentricity of hemispherical domes. By placing the focus of the ASM at the center of curvature of one surface of the dome a reflection would return from that surface and also from the second surface. Using a filar eyepiece the lateral separation of the two surfaces could be measured. Noting the axial motion of the ASM in focus between the centers of curvature the separation in the axial direction is measured as well as shown in Fig. 4. The apparent separation of the centers of curvature is half the actual separation because of the angular doubling in reflection. It was this simple example that convinced me of the power of the technique of using an ASM.
4.1 Use of the PSM for alignment
Subsequently I have used crude versions of ASMs to align optical systems including off-axis mirrors. The real start of the present PSM was the need to align a catadioptric laser scanning system that included spherical and toroidal lenses and spherical concave and convex mirrors. The centers of curvature of all of the surfaces had to lie on a line that was the optical axis of the system. In this case the PSM was mounted on the ram of a coordinate measuring machine (CMM). The ram was held so the focus of the PSM objective was at the desired height of the optical axis above the CMM table. Using the spacings from the optical design of the system it was then possible to position one lens or mirror after the other so that its center(s) of curvature lay on the optical axis. Use of the PSM reduced the assembly and alignment time of the system from two weeks to one morning and the system aligned using the PSM gave substantially better performance. Other examples of the uses of the PSM for alignment including off-axis aspheres are given in the references2,3.
4.2 Use of the PSM as an electronic autocollimator
A collimated beam of light exits the PSM when the objective lens is removed. When this beam is reflected from a plane mirror at near normal incidence the light returns to the PSM and is focused on the CCD detector by the 100 mm efl tube lens. Since the camera has pixels that are 4.65 μm square and the software centroids to 0.1 pixels the PSM is sensitive to angle changes of 4.65 μradians (0.96 arc seconds) or changes in tilt of the mirror of 2.33 μradians (0.48 arc seconds). Almost all autocollimators read out in the change in angle of the mirror being interrogated rather than the angular change in the light entering the collimator.
Since the detector in the PSM has 1024 pixels in the horizontal direction it has a total range of ±1.4º of mirror tilt and ±1.0º in the vertical. This gives a dynamic range of ±5040:1 in the horizontal. A combination of the sensitivity and total range compare favorably with other commercially available autocollimators, both visual and electronic. Again, because of the packaging, the PSM is a fraction the volume and mass of most autocollimators.
4.3 Use in measuring the centration of plastic molded aspheres
Molded plastic lenses such as those used in cell phone cameras and DVD read heads generally have aspheric surfaces on both sides because the use of aspheres helps eliminate optically active surfaces in a lens design and mold inserts are easily made by diamond turning. The real challenge is to make sure the two sides of the mold line up during the molding process. Misalignment in terms of the decentration and tilt of the two aspheric surfaces will degrade the performance of the lens even though both aspheres have a perfect figure or shape. The PSM is the only instrument we know of that can directly measure the alignment of the aspheric surfaces because it can both image the surface to locate the vertex of the surface and find the center of curvature of that surface to establish the axis of the asphere. The optical axis of the surface is the line joining the vertex and center of curvature of the surface.
4.3.1 Definition of lens centering
Before demonstrating the process of measurement we must digress a moment to define what alignment means. Whether a lens has spherical or aspheric surfaces the optical axis of the lens is the line joining the centers of curvature of the two surfaces. The lens must be installed in a cell so the lens optical axis is coincident with the axial ray which should also be the axis of the cell. Only in this way does the axial ray strike both lens surfaces at normal incidence and go through the lens undeviated in either displacement or angle. Fig. 5 shows a lens centered in a cell.
4.3.2 The optical axis of an aspheric surface
The axis of an aspheric surface is the line joining the vertex and the center of curvature of the surface. On a polished surface there is usually no mark that distinguishes the vertex but on molded plastic lenses the inserts are generally diamond turned and the diamond turning pattern is replicated in the molded lens. This makes it easy to locate the vertex of the surface by imaging on the surface. Fig. 6 shows the diamond turning marks on a precision molded, commercially available acrylic lens listed in the Zemax10 catalog of lens designs.
For a lens with two aspheric surfaces, as is the case for most molded lenses, there are two surface axes and for the lens to be perfectly centered these axes should be coaxial. In this case the optical axis will then be coincident with the two axes of the surfaces. Fig. 7 shows the case of misalignment (left) and perfect alignment (right). Notice that the alignment of the axes of the two surfaces is a part of the lens, or is intrinsic to the lens, and has nothing to do with the centering the lens in a cell, a separate operation.
In Fig. 7 the aspheric lens is “centered” as we have defined centering, that is, the optical axis is aligned so an axial ray will strike both surfaces at normal incidence and not be deviated. However, the axes of the two surfaces are not aligned with each other or the optical axis of the lens in the left of Fig. 7. On the right all the axes are coincident and the lens is perfectly aligned, both the surfaces to each other and with the optical axis.
4.3.3 Measurement of the misalignment of the aspheric surfaces
The measurement of the misalignment is quite straightforward. Referring to Fig. 7, the PSM is first focused at the center of curvature of the weak or right-hand surface and the x-y-z coordinates of the center of curvature noted. Then the microscope is focused farther to the right on the surface of the steep or left-hand side of the lens and the xy- z coordinates of the vertex noted. Focusing farther to the right the vertex of the weak side comes into focus as viewed through the steep side and its location noted. Finally the center of curvature of the steep side comes into focus and its location is noted.
Using this set of four x-y-z locations and a spreadsheet, the coordinate system of the points is translated and rotated in two directions until the two points representing the ends of the optical axis of the lens lie along the z axis of the analysis coordinate system with one center of curvature at the origin. This has the effect of putting the center of curvature of each aspheric surface on the z-axis and now it is only necessary to read out the locations of the vertices of the two surfaces in the analysis coordinate system to tell the misalignment. Obviously, if the lens is held in a fixture that locates its mounting surfaces relative to how the lens is held in its cell, the centering of the lens in the cell can also be determined. This whole measurement sequence is easy because the PSM can simultaneously locate both vertices by imaging and the centers of curvature with the autostigmatic feature of the point source.
4.4 A mechanical application – checking a spindle bearing accuracy
By using the PSM and a thoughtfully designed fixture the PSM can be used to measure rotary spindle runout and wobble. The fixture is shown in Fig. 8 (left) and consists of a baseplate that sits on the spindle. On the baseplate are three steel balls that touch each other and form a kinematic support for the two very round (blue) balls separated by a rod. The fixture is slightly easier to use if the balls are magnetized so the rod part of the fixture is more stable.
The PSM is focused on the center of the lower ball attached to the rod and as the spindle is turned the ball center will drift horizontally on the PSM laptop display and go in and out of focus. As the baseplate is translated so it is more centered on the spindle axis the drift will be reduced. The best centering is indicated by the minimum displacement of the spot on the display and will have a sensitivity of 50 nm using a 10x objective. Once the lower ball is centered the PSM is moved so it is focused on the center of the upper ball as in the right side of Fig. 8. Now the upper ball can be gently tapped to align the center of the ball with the spindle axis. Because the upper ball pivots about the center of the lower ball the lower ball centering is not disturbed by aligning the upper ball.
By noting the maximum excursions of the centers of the two balls as a function of the spindle rotation the runout and tilt of the spindle axis can be quantified. In addition, vertical motion of either ball indicates axial motion of the spindle. Thus the PSM and a simple fixture can be used to completely specify spindle accuracy to the level of 50 nm in runout and 1 μradian in wobble assuming a fixture ball center spacing of 50 mm.
This measurement could be done as well or better using capacitance gauges but those instruments would be comparable in price to the PSM and the PSM has many other capabilities that the capacitance gauges do not have. Comparable accuracies could also be obtained with air bearing LVDT electronic indicators but the measurement would be more difficult because these are contact devices and might have sufficient force to displace the balls during measurement. Again, costs would be comparable.
5. CONCLUSION
We have described what an autostigmatic microscope is, how it works and why it is a useful optical instrument for aligning and testing optical components and assemblies. We have further described a modern implementation of an ASM with an additional illumination path and greater control over the brightness of illumination that makes the Point Source Microscope a practical, versatile and commercially available adaptation of an ASM. We have illustrated the versatility of the PSM with several examples ranging from an electronic autocollimator to a strictly mechanical application. These are in addition to uses in the alignment and testing of optical systems that have been described in other publications7.
In every application the PSM compares favorably in performance and cost with other specialized optical alignment and test instruments yet because the PSM can do multiple separate functions that it has a value far greater than any one of the separate instruments. In fact, we had one client who claimed he would be hard pressed to think of how he would do certain alignment functions without the aid of a PSM. Also the combination of solid state illumination and small digital CCD camera make the PSM small and light enough to mount on a simple three axis stage so that it may be brought to the optics rather than the other way around. Finally, the PSM Align software produces flexible and quantitative output for residual misalignment and image characteristics at frame rates.
REFERENCES
1. M. Born and E. Wolf, Principles of Optics, 2nd. ed., Macmillan (1964) pp. 149 and 197.
2. R. E. Parks and W. P. Kuhn, “Optical alignment using the Point Source Microscope”, Proc. SPIE, 58770B (2005).
3. R. E. Parks, “Alignment of Optical Systems”, International Optical Design Conference (2006) in publication.
4. T. L. Schmitz, A. Davies, and C. J. Evans, “Uncertainties in interferometric measurements of radius of curvature”, Proc. SPIE, 4451, pp. 432-47, (2001).
5. A. Davies and T. L. Schmitz, “Defining the measurand in radius of curvature measurements”, Proc. SPIE, 5190, pp. 134-45, (2003).
We give an example of a Point Source Microscope (PSM) and describe its uses as an aid in the alignment of optical systems including the referencing of optical to mechanical datums. The PSM is a small package (about 100x150x30 mm), including a point source of light, beam splitter, microscope objective and digital CCD camera to detect the reflected light spot. A software package in conjunction with a computer video display locates the return image in three degrees of freedom relative to an electronic spatial reference point. The PSM also includes a Köhler illumination source so it may be used as a portable microscope for ordinary imaging and the microscope can be zoomed under computer control. For added convenience, the laser diode point source can be made quite bright to facilitate initial alignment under typical laboratory lighting conditions. The PSM is particularly useful in aligning optical systems that do not have circular symmetry or are distributed in space such as off-axis systems. The PSM is also useful for referencing the centers of curvatures of optical surfaces to mechanical datums of the structure in which the optics are mounted. By removing the microscope objective the PSM can be used as an electronic autocollimator because of the infinite conjugate optical design.
1. INTRODUCTION
In the last decade or two the optics community has seen huge strides made in the improvement of optical image quality due to the widespread availability of phase-measuring quantitative-interferometry. Surface topography data from phase measuring interferometers is now commonly used by fine figuring processes such as ion milling1, MRF2 and other computer controlled polishing methods to produce optical surfaces accurate to a few nanometers peak-to-valley. A few decades ago one would have asked “Why do you want surface figure this good?” With the luxury of hindsight we see that some of the applications for highly precise figure include the optics that corrected the error in the Hubble Space Telescope and the ever increasing demands of the semiconductor industry.
With an eye on the past it is clear that if another significant improvement in overall optical quality could be made in optical systems there would be applications waiting for those improvements. However, it is probably unrealistic to assume that the optical figure quality of surfaces can be made much better, or at least better at an affordable cost. On the other hand there is an area where significant improvements can be made; the alignment of the surfaces within an optical system to one another. The same sorts of optical performance improvement that have been made in figure can be achieved by the alignment of optical components to tighter tolerances. What is needed to accomplish this are the tools, and a new way of thinking about achieving better alignment.
There are at least three reasons to think that improvements could be made in alignment. The majority of optical systems are getting smaller which means the absolute tolerances are getting tighter. As the optical tolerances get tighter, the tolerances on mating features of cell and lens get tighter and become prohibitively expensive to manufacture. Finally, using the periphery and seat of an optical element to control centering is operating at the optically insensitive end of the optical lever arm. Optics should be centered based on aligning their centers of curvature directly, again for at least two reasons. The edges and seats of lenses and cells have a poor finish relative to the optical surfaces and it is difficult to impossible to control a tolerance to better than the finish of the part. An optical surface is fabricated well enough to produce a return spot a few microns in diameter at its center of curvature. These spots can be located to a small fraction of their diameter in space and provide the information to align centers of curvature coaxially, or in three dimensional space, to a micron or so.
In this paper we will describe the Point Source Microscope (PSM) 3, an instrument for locating the centers of curvature of optical surfaces to micron accuracy for alignment of optical elements that is analogous to the use of a phase measuring interferometer to provide information used to guide the figuring of optical components. Once the location of the center of curvature of an optical surface is known it is easy to position that center on the optical axis of the system in analogy to what ion milling or MRF can do for surface figure.
2.1 PSM hardware The PSM is a video metallographic, or reflected illumination, microscope with a Köhler light source to provide uniform illumination over the field of view. In addition, the PSM has a point source of illumination produced by the end of a fiber pigtailed laser diode that is conjugate to the microscope object surface as shown in Fig. 1 below.
Both sources can be used simultaneously as shown in the right-hand image in Fig. 2. Because the point source produces a retro-reflection, its centroid will always appear in the same pixel location on the video screen but its size (and shape, if the surface is rough) will vary depending on how well the microscope is focused on the surface. A crosshair (Fig. 2, middle) can be aligned to the retro-reflected spot so that if the point source is turned off the location in the image plane where it would appear is known. The PSM could be used with an external fiber source to illuminate a particular pixel location on a surface with an alternative wavelength of light if this were useful. The point source is also useful when trying to image a transparent surface with virtually no defects on which to focus. When the surface is in focus there will be a bright return from the point source retro-reflection even though no other surface detail may be visible in the image.
3.1 Alignment of the PSM with a sphere We have described how the PSM produces a retro-reflected spot when focused on a surface. When the PSM objective focus is at the center of curvature of a concave sphere, light will be reflected from the sphere at normal incidence and produce a focused spot at the PSM objective focus. The same is true for a convex sphere whose radius of curvature is limited by the working distance of the objective. The PSM then relays this spot back to the CCD detector as shown in Fig. 4. The difference between this point image and the retro-reflected spot is that the spot image from the center of curvature is sensitive to the lateral alignment of the PSM to the center of curvature as well as to focus.
The PSM can equally well be used with convex spheres, the only requirement is that the radius of the sphere is less than the working distance of the objective, or that an auxiliary lens is used to create a long working distance as will be illustrated in the example of the doublet below. Because the PSM can be used with convex spheres and cylinders many kinds of mechanical tooling hardware become practical and useful optical alignment tooling. Some examples of this tooling are shown in Fig. 5. Surprisingly, these mechanical spheres and cylinders are very accurate figure-wise and are inexpensive compared to most optical hardware. CERBEC™ silicon nitride balls8 are rounder and have better finish than the best chrome steel balls plus are opaque and approximately match the reflectivity of bare glass.
Finally, it should be noted that the PSM also works as an electronic autocollimator when the objective is removed and that is why we have shown the gauge block target mirror among the tooling in Fig. 5. A collimated 6.5 mm diameter Gaussian beam exits the PSM with no objective, is reflected by a plane specular surface and is focused on the CCD detector by the internal tube lens. In the autocollimator mode the angular sensitivity is better than 5 seconds.
3.2 Alignment of a simple doublet lens This example is given to show how the PSM can be used for alignment in cementing a simple doublet. The optical parameters of this example are such that adequate performance does not require precision alignment; however it is a convenient example to illustrate some of the principles of the PSM. The technique also shows the power of using rotary tables for centering systems with rotational symmetry.
Mindful of the background in Sec. 3.1 on using the PSM at the center of curvature, consider cementing an f/5 doublet objective. Assume the flint is sitting on a cup on a precision rotary table, the surface to be cemented facing up as shown in Fig. 6 (left). This element has been centered with the PSM so that the reflected images from both surfaces are stationary as the table is rotated. The rear (flatter) surface is viewed through the upper surface via an auxiliary lens to converge the light enough to get convergence of the reflected light, in other words, to give the PSM a long working distance to get at the apparent center of curvature. A lens design program is used to find the correct conjugates and, in general, there will be spherical aberration in the return image. If the spherical aberration is objectionably large, the aperture of the lens can be stopped down to the limit where diffraction begins to make the spot larger rather than smaller. The upper surface can be viewed directly at its center of curvature.
Mindful of the background in Sec. 3.1 on using the PSM at the center of curvature, consider cementing an f/5 doublet objective. Assume the flint is sitting on a cup on a precision rotary table, the surface to be cemented facing up as shown in Fig. 6 (left). This element has been centered with the PSM so that the reflected images from both surfaces are stationary as the table is rotated. The rear (flatter) surface is viewed through the upper surface via an auxiliary lens to converge the light enough to get convergence of the reflected light, in other words, to give the PSM a long working distance to get at the apparent center of curvature. A lens design program is used to find the correct conjugates and, in general, there will be spherical aberration in the return image. If the spherical aberration is objectionably large, the aperture of the lens can be stopped down to the limit where diffraction begins to make the spot larger rather than smaller. The upper surface can be viewed directly at its center of curvature.
With the flint centered, a drop of cement is placed in the concavity and the mating crown element set in place. Once the cement has been reduced to an appropriate thickness, the crown element may be centered by either of two methods, see Fig. 6 (right). The auxiliary lens may be used to view the center of curvature of the convex surface directly or the PSM can view the reflection off the rear of the flint as seen through the crown. Both methods have similar sensitivity using the parameters of this example but looking directly at the center of curvature is most sensitive. In either case, a 0.01º tilt of the front surface produces a 15 μm or more decenter of the spot that is doubled by rotating the table. If one were to use a contact indicator at the edge of the upper surface, this same tilt would register a 5 μm total indicated runout.
As was explained at the beginning of this section, this example illustrates how to use the PSM for cementing a doublet even though the optical parameters do not warrant this degree of precision and accuracy. There are cases not substantially different from this example for wide field of view projection systems or very fast imaging lenses used in the visible where these sort of centering tolerances are necessary to obtain the desired lens performance. The next example is one where the alignment accuracy is definitely needed.
3.3 Alignment of an Offner relay mirror system In an example where the need for micron alignment is truly required, consider the Offner9 relay shown below in Fig 8a. Because this is an all reflective system it can be used at a 13.5 nm wavelength in the soft X-ray region and now precision alignment becomes a necessity. The question is how to assemble the two spherical mirrors as well as possible to the mechanical hardware that position the relay optics relative to the rest of the lithography system.
In the example Offner relay used, the total field is about 90 μm in width, the distance from the object plane to the primary is 250 mm and the object is 40 mm off the axis of symmetry. Given this design, Fig. 7 shows the effect decentering or despacing have on performance. Not unexpectedly, performance at the edge of the field is worse than the center but also the image plane is tilted. Knowing the tilt would allow compensating or correcting for the error. Clearly the biggest loss in performance is despace but this can also be corrected by an axial shift in the image plane.
The PSM is particularly useful if some thought to alignment has been made in the initial system opto-mechanical design by incorporating features such as tooling balls to locate critical datums. Assuming critical datums have been defined mechanically, we start the alignment by placing a ball where the two mirrors have their common centers of curvature.
Next, using an auxiliary lens with a focal length slightly longer than the radius of curvature of the secondary mirror, align the PSM focus conjugate with the center of the ball in three directions so that the return image is centered and in focus in the PSM image. Then insert the secondary mirror and align it to the PSM image using the reflection from the secondary convex surface that is conjugate to its center of curvature as in Fig. 8b.
Move the PSM so it faces the primary mirror and align the PSM focus to the center of the ball as in Fig. 8c. Remove the ball and align the primary to the PSM focus so light reflected from the primary is centered on the PSM image and is in focus. Now the two mirrors are concentric and located precisely to the optical bench datum indicated by the ball.
Once the Offner relay is aligned optically and located precisely to its mechanical structure via the tooling ball, light from an object on one side of the system axis of symmetry will be nearly perfectly imaged on the other side of the axis. The relay will have been optimized for a particular object distance off the axis but this distance is not highly critical to the relay performance. It is important to know exactly where the input is imaged on the other side of the axis. If a tooling ball is placed so that its center is at the center of the object field, the PSM can precisely determine where the image will be located by using the relay in double pass, see Fig. 8d. Light from the point source in the PSM is brought to focus by the PSM objective and sent on through the relay until it reflects off the center of the ball located with its center at the object plane of the relay. The light then retraces itself exactly back to the PSM focus where it is imaged by the CCD and its location shown on the video monitor. When the return spot is centered in the reference cross hair and is at best focus, the PSM focus is in focus at the center of the relay image plane. This check of object and image location also permits a double check that the alignment was done correctly, something that is always useful when the tolerances are tight.
We conclude this example by saying the Offner 1:1 relay is the simplest sort of all reflecting, ring field microlithography optical systems. The all reflective systems that will be used to make future IC chips will contain six or more mirrors with their centers of curvature located along a common optical axis.10 If these systems are to meet their theoretical optical design performance, they will have to be assembled so their centers of curvature truly lie on the optical axis to 1 μm or better tolerances. Variations on the method described here will make this possible and avoid the inevitable tolerance stack up when optics are centered mechanically by their edges and seats.
3.4 Alignment of an off-axis telescope system In this example we will describe two other modes of using the PSM for optical alignment and alignment of optics to mechanical datums. In practice, though not often thought of this way, all optical alignment deals with positioning optical surfaces in a particular relationship to mechanical datums as in the case of centering a single lens element. The optical axis is the line joining the centers of curvature of the two optical surfaces. Edging a lens is bringing its periphery, a mechanical datum, into concentricity with the optical axis. In this example, the telescope system is similar to the single element with the telescope itself being like one optical surface, the backend of the system like the second surface and the mounting plate for the system like the periphery of the lens. In this case, the periphery was established first and the two halves of the optical system each brought into alignment with the periphery or mounting plate. Figure 9 shows a simplified outline of the telescope system.
The telescope on the left of the mounting plate is an off-axis Ritchey-Chretien with an f/11 output as shown in Figure 9. The telescope and the prism housing are attached to the mounting plate by a three ball and groove kinematic mounting scheme, one coupling of which is shown in Fig. 10. Drilled balls fit into conical countersunk recesses in the telescope frame and prism housing. The two halves are pulled together by a screw through the center of the balls and are located by a pair of pins forming a double sided “V” groove in the mounting plate. In this way the two halves of the telescope are precisely located relative to each other and flexing of the mounting plate (by which the telescope assembly is held in its housing) will not disturb the alignment of the telescope system. Test fixtures for both sides of the telescope system used the same mounting scheme to accurately locate the halves during individual assembly and test.
3.4.1 Alignment of the telescope By design the optical axis of the telescope was precisely defined relative to the telescope frame. The telescope frame, in turn, was precisely located relative to the optical table on which the telescope was aligned by means of a fixture incorporating the three ball kinematic mounting scheme as shown in Fig. 11. Two ends of the temporary long screws can be seen in the upper kinematic locators clamping the telescope frame to the test fixture.
Prior to aligning the telescope, the telescope alignment test fixture was adjusted in four degrees of freedom relative to the collimator; two degrees of tilt to make it square to the collimated beam and two degrees in translation to center the apertures. Then two balls were placed on the table relative to the test fixture and table so as to provide reference positions accessible to the PSM at the short focus of the hyperbolic primary and at the system focus. The line joining the centers of these balls defined the optical axis of the telescope mechanically
The telescope mirrors were then aligned in two steps against a collimator, first the primary alone and then the combination of primary and secondary. Initially the PSM was positioned so that it was looking into the center of the primary with its focus at the center of the ball at the primary focus. The collimator was then de-focused to produce a focus far behind the primary at the long focus of the hyperbolic primary. The source in the collimator also had to be raised precisely because the optical axis of the collimator and telescope were at known but different heights.
Once the PSM was aligned with the ball defining the location of the primary short focus, the ball was removed so the PSM could view the light from the collimator and focused by the primary. It was necessary to adjust the primary in five degrees of freedom, three to correctly position the focus and two to remove the aberrations caused by the primary optical axis not lying on the collimator axis. First the primary was adjusted so that light from the collimator and reflected by the primary was in focus and centered on the PSM crosshairs and in the computer monitor. This process aligned the first three degrees of freedom but the image showed substantial astigmatism, exactly what would be expected from a misaligned off-axis hyperbola.11 (It should be noted that since this was an off-axis telescope the aberration was largely astigmatism with a little coma and the two aberrations decreased together as the primary was aligned. Had this been a symmetrical telescope the only aberration seen due to misalignment would have been coma.)
The next step was to adjust the primary tilt and decenter to maintain the image centration and focus on the PSM crosshairs and to reduce the astigmatism. The most straight forward method of doing this is tilt and decenter sideways to straighten the astigmatic image so it is perpendicular to the optical table. Then adjust vertically relative to the table to reduce the length of the image until it is round and symmetrical. This procedure worked in a quick, directed fashion. The images observed with the PSM corresponded to the images in reference 11. Further, the PSM had sufficient magnification to view the “star” image to reduce the astigmatism to at least the tenth wave level. The star test is very sensitive to symmetry in the image and by going through focus the least astigmatism is very apparent.
Once the primary was adjusted so that it focused in the correct location and was free of aberrations indicating that its optical axis and the mechanical optical axis were coincident and parallel to the collimator axis, the PSM was mounted looking into the telescope centered on the secondary mirror aperture with its focus centered on the ball defining the system focus. Alignment of the secondary followed the same sequence as the primary but now the collimator was set at infinity focus with its source on axis. Fig. 12 shows this phase of the alignment with the PSM barely visible behind the telescope while the monitor shows the image from the telescope in the crosshair. The kinematic base at which the ball screwdriver is pointing accepts the posts (lying on their sides) that hold the balls that define the locations of the primary and secondary foci.
First the secondary mirror was adjusted in tilt and decenter so that the image was centered on the PSM crosshairs and was focused as well as could be determined given the residual astigmatism. Then the secondary was adjusted using a combination of tilt and decenter to reduce the astigmatism to give a well focused, symmetrical image while keeping the image centered on the PSM display crosshairs. Once this alignment had been performed we knew that the telescope focus was located the correct distance behind the test fixture and that the optical axis of the telescope as defined by the line between the primary focus and the telescope of secondary focus was perpendicular to the test fixture and correctly positioned relative to the three kinematic mounting locations on the test fixture.
The main difference between this telescope alignment technique and those described previously is that by using aberrations as well as locations, the PSM can monitor alignment in five degrees of freedom, something that would be impossible using an alignment telescope. Further, because the PSM operates with a relatively fast cone of light it is much less confusing than an alignment telescope in terms of selecting the reflection from the surface of interest. The alignment of telescope took less than a day and the secondary, which had more refined adjustments on the mount, took less than ½ hour including PSM setup time.
3.4.2 Alignment of the prisms in the prism housing There were numerous prisms and fold mirrors in the prism housing to direct light from the telescope to various sensors as well as a path to direct light into the telescope and a path to couple a display into the eyepiece. All of these paths had to be boresighted so that as the operator changed from one mode of operation to another an object in the center of the field for one sensor remained centered for another. Further, it was desired that the prism housing and sensors be interchangeable with the telescopes so the center of the field had to be defined relative to a mechanical datum, namely the mounting plate coupling the telescope to the prism housing. To align these various paths two fixtures were used, a projector that produced a converging cone of light that matched the telescopes f/11 focus and a mounting fixture for the prism housing that exactly simulated the mounting plate. This approach is shown schematically in Fig. 13 where the ball in the foreground represents the projector source; the joined base of the cones represents a positive lens to produce the f/11 cone that ends with the far ball at the conjugate focus.
The three balls in the prism housing mate with the test fixture to hold the prism housing correctly in five degrees of freedom. Three degrees of freedom are controlled by the ball at the projector focus. The other two degrees of freedom control the location of the optical axis of the projector relative to the three balls defining the prism housing location. This is exactly the same condition that applied to the telescope so that when the two halves of the system are mated the telescope will focus at the far ball location and the telescope optical axis will be co-axial with the projector axis.
Figure 14 shows the prisms in the housing and the paths into which the prisms direct the beams. These beams need to be correctly positioned to a few pixels on each detector so the final alignment can be accomplished by a very slight lateral adjustment of the sensors themselves. To accomplish this, the test fixture that held the prism housing was drilled and bushings inserted directly beneath the foci of the various paths and rods of the correct lengths were cut to hold balls at the foci as shown in Fig. 15, a picture of the actual fixture set up for locating one of the paths.
Figure 15 is instructive in that it shows almost all of the elements of the alignment discussed to this point. The f/11 light cone is coming in from the left and going through the prism visible in the prism housing that is attached to the test fixture via the three kinematic locators clearly visible on the back of the fixture. A metering rod is located in one of the bushings and has a ball sitting on its top. The PSM is aligned pointing down the diverted beam path and the PSM objective focus is aligned to the center of the ball. The PSM is supported by a substantial x-y-z stage to facilitate its alignment with the ball center. The PSM tilt adjustments are relaxed because they only control vignetting.
The next step in the alignment of this beam path was to remove the ball and metering rod so light diverted by the prism could be viewed by the PSM. Crude adjustment of the prism was made with the projector source set at maximum intensity. The focus of the projected beam was easily visible on a card in front of the objective and the prism was tapped lightly to tilt the prism and bring the beam focus in front of the objective. Once the beam entered the objective the source intensity was reduced and the beam position monitored on the computer display. The real-time visual feedback of spot location and focus made positioning the prism straightforward and rapid. Another feature of the PSM allows left/right and up/down image flips so the displayed image always had the expected or natural orientation independent of mirror flips of the beam. This ergonomic feature make alignment easier because adjustments appear to work in the direction expected instead of the way they actually move.
Once the prism had been adjusted so the spot of light was positioned within tolerance, UV cement was carefully applied to several places along the edges of the prism and the prism tacked in place with a UV source. Once tacked and still properly aligned, epoxy cement was applied and allowed to cure slowly. The next prism in the chain was added, the proper metering rod located in the next bushed hole and the procedure repeated for the remaining prisms in the paths. The procedure for alignment of the six paths in the prism housing was so efficient that all the paths could be aligned in two hours. In addition to the time savings, the mechanical tolerances on the prisms and their holders did not have to be very tight. Ledges to guide the initial prism placement were all that was required. The balance of the alignment was done by slight taps and shimming to correctly position the prisms.
3.4.3 Alignment using the PSM mounted on a CMM It should be noted that there is an analogous approach to aligning the prisms that has been very successfully used OPG on another off-axis optical system, that is to mount the PSM on the ram of a coordinate measuring machine (CMM) and use the CMM to position the PSM at the end of each path rather than use the fixture as we have just described12, 13. Generally the CMM approach is more effective when there are either only a few prototype systems or a variety of systems to align while the fixture method is more suited to production. The geometry and complexity of the system may influence the decision as to which approach would be best as well as the availability of a CMM.
Using the CMM eliminates two aspects of the fixture. Using the example of the prisms above, a source projector is still required but the location of the source focus and the position of the optical axis can be determined using the PSM and stored in the CMM. To accomplish this, the first step is to mount the PSM on the CMM ram in place of a touch tip probe and set the probe tip radius set to zero in the CMM software. Next the PSM objective is focused at the center of the CMM master ball and the coordinate system zeroed in all three directions simultaneously. Then the PSM is moved to the projector source and the PSM focus made coincident with the source focus. The coordinates of the source are noted. Then the PSM is moved to the image of the source and that location noted. This defines the five degrees of freedom of the source location as shown in Fig. 16, four degrees define the axis and one is the axial location of the focus.
Now the PSM would be rotated 180 degrees about a vertical axis and the PSM focus zeroed again on the master ball. Then the locations of the three balls defining the location of the prism holder can be found, see Fig. 16. The telescope mechanical design defines where these three balls must be relative to the optical axis and focus of the source projector to be aligned. Using COTS alignment stages the prism housing can be brought into alignment with those three positions to locate it correctly relative to the source projector. Once the housing is correctly positioned, the PSM can be rotated to look down the first path to be aligned, zeroed again on the master ball and moved to the first path focus ready to sense the position of the first beam. The CMM software displays the global coordinates of PSM objective focus after each zeroing on the master ball. All that is necessary is to read from the design where the next focus is and move the PSM to that location and lock the CMM axis motions until the prism is aligned. Once the concept of using a CMM as an assembly tool is understood, the implementation is straight forward, and the CMM takes on added value as an assembly tool in addition to its traditional use as an inspection tool through use of the PSM.
Another way of aligning an optical system with powered elements on a CMM is to place the optical bench onto which the elements will be mounted on the CMM bed. Assuming provisions have been made in the opto-mechanical design, after zeroing the PSM on the CMM master ball, pick up three known tooling ball locations on the optical bench. Since these locations will be known by design relative to the optical axis and centers of curvature of the various optical elements, the PSM objective focus can be located precisely as each element is added. By picking up the three tooling balls on the optical bench, the CMM software establishes a coordinate system in the optical bench space and displays x-y-z coordinates in this space. When the first optical element is introduced the PSM can be located at the centers of curvature (or apparent centers of curvature) of the two surfaces. The element is then adjusted by tapping or shimming until it is correctly located within the given tolerances. Again, neither the element nor the holder need to be machined to tight tolerances because the element location can be adjusted far better using its optical axis, which is the line joining its centers of curvature. This alignment method largely eliminates tolerance stack up because the usual glass-metal (or optical-mechanical) interface features are not used to define optical alignment.
4. COMPARISON OF THE PSM WITH OTHER OPTICAL ALIGNMENT TOOLING
Now that various methods of using the PSM for the alignment of complex optical systems has been explained, we compare the features of the PSM with other more familiar optical alignment tooling. First, it should be said that the PSM is a compliment to existing tooling, not a replacement for it. For example, in Figs. 12 and 15 an alignment telescope is clearly visible. At the same time, there are other situations where it is very handy to have more than one PSM available.
4.1 Autocollimators Although no examples have been given of the PSM used as an autocollimator, it is one if the objective is removed because the microscope is based on infinite conjugate optics. With the 100 mm tube lens and tenth pixel sensitivity, the PSM has angular sensitivity of about 5 seconds in reflection over a 6 mm beam diameter. While this is almost an order of magnitude worse than what can be achieved with a Davidson14 or Nikon15 autocollimator, there are situations where this electronic autocollimating capability is very useful, particularly in cramped locations and for use in conjunction with a CMM to move the PSM without pitch or yaw from interrogating one plane surface to another for parallelism.
An ergonomic feature of the PSM in this mode is the display on a computer monitor as opposed to looking through an eyepiece that might not be conveniently located. A very practical advantage of the PSM used as an autocollimator is that it is easy to align initially under normal lab lighting because of the bright laser source. With the more traditional autocollimators it is often difficult to find the return beam initially even if the lab lights are turned off.
4.2 Alignment telescopes The PSM is probably most analogous to an alignment telescope in terms of what it does best but direct comparisons are difficult. A typical alignment telescope locates a line of sight to about 1 part in 800 of the full field at the object distance that the telescope is focused. This works out to roughly 5 seconds, the same as the PSM used as an autocollimator. The PSM has a minimum of 760 pixels across the field and is sensitive to 0.1 pixels when centered on a spherical surface and is thus about an order of magnitude more sensitive than the alignment telescope. The alignment telescope can bring objects on that line of sight into focus one after another as the focus is changed from near (about 16”) to infinity. This is very convenient when all the objects are in a line because no part of the test setup needs to be moved during the alignment. On the other hand, the alignment telescope is nearly useless if the objects needing alignment are in a three dimensional space such as the paths in the prism housing example or in aligning the components of a spectrometer.
The PSM is perhaps best thought of as a null or end point detector in three dimensions and it does this to about 1 μm laterally and a few μm axially. The ideal way to use the PSM is either mounted on the ram of a CMM where it can locate spherical and cylindrical features to better than the accuracy of most CMM’s over any reasonable distance, or in conjunction with a fixture like that described for aligning the prisms. In both cases, the PSM can locate centers of curvature and axes of cylinders to as well as or better than the mechanics of the CMM, or fixtures can establish the desired mechanical datums in three dimensional space. In this sense the PSM has a sensitivity of at least an order of magnitude better than an alignment telescope. Coupled with its small size, light weight, ability to be used as an autocollimator and ergonomically convenient to use display, the PSM can turn tedious assembly and alignment operations into rapid, accurate and easily documented procedures.
5. CONCLUSIONS
We have described the Point Source Microscope and illustrated its usefulness in the alignment of various optical systems by accurately linking mechanical datums to optically functional surfaces and these surfaces to each other. In comparison with other optical tooling, the PSM is a flexible compliment to, rather than replacement for, traditional autocollimators and alignment telescopes. A combination of the PSM’s accuracy and its use aligning the optically significant features of an opto-mechanical system make it possible to achieve higher alignment accuracy than attempting alignment via strictly mechanical features. This leads to systems with better optical performance than can presently be achieved at a reasonable cost.
With insight as to how the PSM works it is clear that the PSM, in a very practical sense, makes many alignment operations easier and quicker to perform to a higher level of accuracy, particularly for optical systems that are distributed in three, rather than two, dimensions, or do not have circular symmetry. Although difficult to document specifically, we have seen the time taken to align complex optical systems drop by a factor of ten while achieving better alignment than more traditional methods. Furthermore, by aligning using the optically functional surfaces of a system, both tolerance build up and the expense of precisely made parts can be largely eliminated.
6. ACKNOWLEDGEMENTS
The telescope referred to in Sec. 3.4 was a team effort of Breault Research Organization, Inc (BRO)16 and Optical Perspectives Group, LLC (OPG). The lead optical engineer on the project was Matthew Dubin of BRO who had many insightful and useful comments regarding the use of the PSM. OPG’s primary responsibility was assembly and test of the system that was performed at BRO with the able assistance of Joe Barcelo. The optical design of the telescope and sensor optics was performed by Richard Buchroeder of Optical Design Service under contract to BRO. The mechanical design of the telescope was done by Kris Tvedt of BRO. The details of the kinematic location features were due to Bryan Loucks, an opto-mechanical design consultant working with OPG.
7. REFERENCES
1 See www.rcopticalsystems.com/ionmill.html, for example 2 www.qedmrf.com/technology/tech.shtml 3 US Patent pending 4 www.optiper.com 5 www.nikon-instruments.jp/eng/page/products/list11.aspx 6 www.ptgrey.com/products/flea/index.html 7 sine.ni.com/nips/cds/view/p/lang/en/nid/12892 8 www.cerbec.com/TechInfo/TechSpec.asp 9 A. Offner, US Patent 3,748,015 10 D. M. Williamson, “Evolution of ring field systems in microlithography”, Proc. SPIE, 3482, 369-76, (1998). 11 R. E. Parks, “Alignment of off-axis conic mirrors”, Optical Fabrication and Testing Workshop Technical Notebook, OSA, Falmouth, MA Sept. 1980, pp. 139-45. Revised reprint available at www.optiper.com/Documents/Alignment%20of%20Off-axis%20Conic%20Mirrors.pdf www.optiper.com. 12 R. E. Parks and W. P. Kuhn, “Using a CMM for optical system assembly and alignment”, ASPE Proceedings Spring Topical Meeting on Coordinate Measuring Machines, 29, 3-8, (2003) 13 US Patent Application 20020054296 14 www.davidsonoptronics.com/catalog.htm 15 www.nikonusa.com/template.php?cat=3&grp=30&productNr=6B6D 16 www.breault.com/consulting/consulting-overview.php
As optical systems become more complex and packaging requirements more severe and multi-dimensional, proper alignment becomes more challenging. Yet with current improvements in the manufacture and measurement of optical surfaces to nm levels, alignment is one of the few remaining opto-mechanical aspects of optical system manufacture and assembly where improvement in optical performance can be made. There are four approaches to aligning optical systems. These will be described and the advocated method illustrated by examples.
The preferred alignment method overcomes most of the difficulties of traditional methods but requires a new way of thinking about alignment. The method also requires alignment considerations must be studied immediately after the optical design is complete so that the necessary opto-mechanical datums can be incorporated into the mechanical design of the optical system cell, chassis or lens bench.
2. Methods of alignment
While one could argue with these definitions of alignment methods, they illustrate the point to be made. First is “snap together” or drop the elements into a cell which is the method traditionally used from the beginnings of centered optical systems. A cell and lenses are manufactured to tolerances governed by cost and performance considerations and then the lenses are set in the cell against their seats and held down by retainers. One then lives with the assembled performance of the system that is well modeled by Monte Carlo analysis. Since there will be a spectrum of performance outcomes in keeping with the model, optimum system performance will be achieved in only a few of these systems. However, this is the only economical method of assembling large volumes of optical systems.
Another method used on limited quantity, high performance, high cost systems is to assemble lenses into their seats while measuring each lens at its periphery for centration and vertex for spacing, and then testing the performance against a go/no go standard. If the performance falls below the acceptance criteria, the system is taken apart and reassembled as carefully as possible according to the design and tested again. This is a very tedious and costly procedure that exposes the optical components to many sources of damage through dis- and re-assembly.
A third method is a more systematic approach similar to the second but where the performance of the system is measured quantitatively in the pupil plane, possibly at a number of field points. If the system does not perform to an acceptable level optical design software is used to figure out what spacings and misalignments are causing the less than optimum performance, these adjustments are made and the system is tested again. Sometimes a second round of adjustments is necessary as changes in alignment affect performance non-linearly. While this method is more systematic it is still tedious and requires substantial careful testing and analysis of the test results.
The fourth method that this paper advocates for high end, modest production systems is to locate the centers of curvature of each powered optical element at the exact design nominal location, or “true position” in mechanical engineering terms, and each plane mirror tilted and spaced so the beam focuses at the design nominal position after the fold. For centered systems this is most easily done by centering a datum seat in the cell on a rotary table and then checking that the light from the centers (or apparent centers) of curvature of the elements as they are assembled, one by one, do not nutate as the table is rotated as shown in Fig. 1.
This example shows the cementing of a double where the flint element is placed in a centering cup and the cup centered until the reflection of a point source of light conjugate to the convex surface center of curvature (C of C) does not nutate. An auxiliary positive lens is needed to reach the apparent C of C but its focal length is not critical. The flint is then slid in the cup about the convex surface until the reflection of a point source of light at the C of C of the concave side remains still. The flint is then considered centered meaning that the line joining the centers of curvature of the two surfaces (the optical axis) is coincident with the axis of the rotary table. Then the lens is lightly clamped.
A drop of cement is placed in the concave well of the flint and the crown element is set in place. The concave surface of the flint now acts as an aligned centering cup so all that is needed is to make the reflection from the upper crown convex surface remain stationary. Again an auxiliary positive lens is required to access the C of C of the crown. The right hand side of Fig. 1 also shows how the apparent C of C of the flint has moved toward the lens due to the refraction of the crown.
In this example we have referred to placing a point source of light at the C of C of a surface and then watching the behavior of the reflected image. The best way of doing this is with an autostigmatic microscope (ASM), a reflecting microscope with a beamsplitter behind objective and a point source of light produced by a single mode fiber located at the long conjugate of the objective. The return image can be viewed through an eyepiece or via a CCD camera. Fig. 2 shows a schematic illustration of the optical paths in a commercially available autostigmatic microscope.1
3. Aligning two and three dimensional systems
Centered systems are a trivial case of locating C of C’s according to an optical design. Of far greater interest are two and three dimensional systems where the chief ray moves over a plane or in three dimensions. Since three dimensional systems are difficult to diagram successfully on paper, a two dimensional example will be given that amply illustrates the three dimensional nature of the problem. An imaging spectrometer from US Patent 6,288,781 by D. R. Lobb with powered prismatic elements is shown to scale in Fig. 3. Light enters a slit on the face of a plane prism at the upper left of Fig. 3. It passes through a prism with power on both the entrance and exit faces and proceeds on to an arrangement of three spherical mirrors similar to an Offner relay. The light exits through another prism with power on both surfaces to the detector plane.
Fig. 4 shows the spectrometer in perspective and traces the chief ray from the entrance slit through the system to the middle of the detector plane. The line joining the entrance slit and detector plane is the axis of the spectrometer in an alignment, or opto-mechanical, sense just as the optical axis of a single refractive element is the line joining the C’s of C of the two surfaces. This axis defines five degrees of freedom of the spectrometer, three translations and two angles. We define the sixth degree of freedom in that we want the centers of all the elements to be the same height above a mounting plane.
It is obvious that the edging tolerances and mount fabrication for the dispersing elements is going to be difficult as they will have to be located precisely and unambiguously in all six degrees of freedom relative to the spectrometer axis as defined by the slits. Of course the three mirrors also have to be properly aligned but this is a relatively simple matter compared to the prisms.
In order to accomplish this alignment we suggest that the next diagram to draw is the one in Fig. 5 where the C’s of C and axes of all the elements are located relative to the entrance slit and center of the detector, all in the plane of the paper. The centers of curvature of the three Offner relay mirrors are clustered together between the entrance and exits slits. Because the two centers of curvature of the dispersive elements each define three degrees of freedom, all six are defined for each element so they may be located precisely and unambiguously without reference to their edges. To illustrate where the dispersive elements lie relative to their axes we show the full elements in Fig. 6. This also illustrates why these elements would be difficult to fabricate without understanding their geometry. Once the geometry is understood the generating and polishing of the surfaces is not much more difficult than the surfaces of any lens.
4. Alignment of the system
In order to align the system a fixture is made either by drilling holes in the optical bench to which the elements of the spectrometer are mounted or in a fixture to which the optical bench is located by pins. In the holes a precision rod is placed with a conical hole in the upper end to serve as a mount for a bearing ball about 10 mm in diameter. A collar on the rod is used to locate the center of the ball to the height of the plane of centers of curvature. The rod and ball can be moved from hole to hole as one element is aligned after the other.
For the three convex surfaces, an auxiliary positive lens is needed to make the C’s of C accessible as already illustrated in Fig. 1. Holes and rods are also needed to support these auxiliary lenses but their locations need not be very precise as long as the lenses are centered on a normal to the convex surface that is roughly in the center of the surface.
The short conjugate of the objective of an autostigmatic microscope is focused and centered on the center of the ball defining the C of C and pointing toward the element of interest. The ball is removed and the element adjusted until its center of curvature is focused and centered on the autostigmatic microscope display. Fig. 7 illustrates first aligning the autostigmatic microscope to the ball that defines the mechanical location of the C of C, removing the ball and aligning the mirror to the microscope. The microscope acts as the transfer device between the mechanical datum at the C of C and the optical surface. In the case of the refractive elements, having two microscopes makes this procedure much easier because both centers of curvature can be viewed simultaneously, one through the auxiliary lens. The order of alignment is governed only by avoiding the obstruction of the line of sight to the next surface.
When the alignment is complete a point source placed at the entrance slit will be well imaged at the detector. There can be no source of error unless the radii of the elements are substantially out of spec or the wrong glass was used. Since a good autostigmatic microscope can locate centers of curvature to < 1 μm, the translational errors of element locations can be held to about the same level and angular errors to a few seconds of arc (although the scale of the angular error will scale with the system size). The alignment is completely deterministic and does not depend on the type of optical system or even any knowledge of how the system will form an image because light is never put through the system the way it will be used during the alignment.
Alignment of folded systems with plane mirrors
Fold mirrors are plane mirrors used to change the direction of a beam of light and are useful in systems that must be made compact. If a light beam is focused it is defined by three degrees of freedom, the x,y,z coordinates of the focus. Since a plane is also defined by three points we have just enough degrees of freedom with two angles and one translation to change the beam direction and keep the distance from the last powered element to the focus constant. This does not count the two translational degrees of freedom needed to keep the beam centered on the plane mirror but these are not critical adjustments.
While we have been talking about folded systems the example we will use to illustrate the alignment of the plane mirrors was chosen to illustrate not only this section but the next concerning using aberration reduction as an alignment tool. Assume we want to put a deformable plane mirror in a telescope system for atmospheric error correction. This amounts to taking the beam of light coming toward the telescope focal plane and diverting it into a black box that corrects the wavefront and then spits the light back out so it focuses in the same place on the focal plane as it would have without the correction system. Whether the black box is in the system or not should be invisible to the detector. How do we align the fold mirrors to get the light in and out of the black box? A generic adaptive optical system (AOS) is shown in Fig. 8.
The AOS consists of a fold mirror to bend the beam headed toward the telescope focus to the entrance focus of the AOS, an off-axis parabola to collimate the beam, a deformable mirror to correct the wavefront, a second off-axis parabola to re-focus the beam and a final plane mirror to direct the output of the AOS to the telescope focus. If the whole optical bench were moved out of the way the focal plane would be none the wiser except the AOS decreases the f/number of the final beam somewhat. Just as in the imaging spectrometer we have identified an axis of the system with the sixth degree of freedom being the arbitrary angle about the axis.
For alignment purposes, the two plane mirrors must be precisely located so that the AOS does not appear to be in the telescope at all. To do this we first place a concave spherical mirror beyond the first fold mirror (mirror at top of Fig. 9) aligned so its center of curvature coincides with the telescope focus using an autostigmatic microscope (ASM) or similar device. Then we move the ASM so that it is focused at the center of the ball locating the exit focus of the AOS and is pointing toward the right. A second concave sphere is aligned to the microscope in tilt and focus.
Then the microscope is moved back to the telescope focus as now defined by the concave sphere at the top and the plane mirror that folds the beam downward is inserted and adjusted in tilt and translation normal to its surface until the reflection from the concave sphere to the right is aligned on itself in the microscope. Now the microscope is focused on the ball at the entrance focus and is set to point toward the left. The entrance plane mirror is inserted and adjusted in three degrees of freedom until the return image from the concave mirror at the top is re-imaged on itself in tilt and focus. Now the plane mirrors are aligned to the telescope focus and the entrance and exit foci of the AOS. It now remains to align the powered optics of the AOS to the entrance and exit foci.
One aspect of this is to note that the alignment steps must be ordered so that no previously aligned optic interferes with the light path to another optic that needs aligning. This is why we had to use two concave spheres as tooling to align the two plane mirrors. Another aspect to note is that if the distances from the mirror to the foci are not equal it will not be possible to adjust the fold mirror so the chief ray follows the angle given in the design but will be incorrect by some angle dependent on the error in distances. This could come about in the design in Fig. 8 if the lens bench were incorrectly located too close or far from the focal plane. Then the exit fold mirror could still be adjusted so the output focus fell on the telescope focus but the chief ray of the AOS output would not be parallel to the chief ray from the telescope. In most cases a small error will not matter but it is something to be aware of.
Alignment using aberrations
Alignment using aberrations is very useful for locating optical elements with axes, particularly aspheric mirrors either symmetric or off-axis. While we will return to the AOS example momentarily, we give an example of where alignment using aberrations is sometimes seen in optical fabrication shops. The optician will want to test an objective lens with an interferometer for the transmitted wavefront quality. The test is so obvious that many fail to realize how sensitive the test can be to aberrations in the field and are surprised to see astigmatism and/or coma.
As an example, take a 25 mm diameter, f/4 cemented doublet. It can be tested interferometrically in either of two ways, collimated light in or focused light in against a flat, as shown in Fig. 10. Although it is not obvious without very careful examination the doublet is tilted 1º about an axis perpendicular to the page relative to the collimated beam from the interferometer (upper) or the return plane mirror (lower). Yet this misalignment that is not obvious without taking great care in the set up of the test yields substantial transmitted wavefront error that is not intrinsic to the doublet but rather due to its incorrect test. Contour maps of the wavefront aberrations are shown in Fig. 11.
This example is a simple demonstration of the importance of proper alignment to achieve full optical system design performance. Small alignment errors can have disastrous consequences on system performance yet be imperceptible without careful monitoring. This leads to the more interesting example of using aberrations for alignment. We will examine two cases, the alignment of a symmetric parabola to a flat (or collimated source) and the same example with an off-axis parabola to show there is fundamentally no difference in the approach.
Assume we have a symmetric parabola with a central hole for the light to pass through. In this case a common test is to locate the test device focus at the mechanical center of the hole, let the out going light reflect off a flat placed at approximately half the focal distance from the parabola so the light fills the parabola and reflects back to the flat nearly collimated as shown in Fig. 12. The light then retraces itself back to the source when everything is aligned. The optical axis of the test setup is the line joining object and image and this we have located as soon as the image lies on top of the object, something easily seen with an ASM or when there are no tilt fringes in an interferometer.
The optical axis of the test set up must be aligned to the optical axis of the parabola for there to be no aberrations. The first step is to move the plane mirror longitudinally to focus the image and tilt the plane mirror until the object and image are coincident. If there is no coma then the parabola is perfectly aligned to the flat. In general this will not be the case. To finish the alignment the ASM focus (or the parabola) must be decentered in a direction to reduce the coma while the flat is tilted to keep object and image coincident. Moving the microscope in the direction of the point of the coma pattern will decrease the coma. Continue the decentering until the image is symmetrical. The location of the focus defines three degrees of freedom while the two tilts of the flat make up the balance of the five degrees of freedom needed for proper alignment. In this example with a 50 mm diameter, f/2 parabola just 23 μm of decenter (equivalent to 23 seconds in the field) will produce 0.1 waves of coma. This may be acceptable for viewing stars but is totally unacceptable for doing lithography.
Going back now to the AOS where we talked about the positioning of the fold mirrors, there are also two off-axis parabolas that need aligning, see Fig. 8. The location of the focus of each has already been used in the fold mirror alignment. The vertices and C of C’s of these mirrors is also indicated in the Figure. If there is no indication of where the optical axis is on the off-axis mirrors the best approach is to put an ASM at the design location of the C of C of one of the mirrors and adjust the mirror to return the light into the ASM objective. As the mirror is moved longitudinally the combination of astigmatism and coma will produce an image that looks somewhat like a fish as shown in Fig. 13. The tail of the fish points toward the vertex of the off-axis segment.
Once the off-axis mirror is located approximately correctly based on the location of its C of C an ASM is located at the design location of its focus and a plane mirror is used to reflect the nearly collimated light back into the off-axis mirror and ASM objective. The plane mirror should be used exclusively to get the light back into the ASM objective and centered on the display. Typical images might look like the through focus images in Fig. 14.
Adjustments should be made simultaneously to the off-axis parabola and the plane mirror to hold the image centered in the ASM and to orient the largely astigmatic image with the coordinate system, that is, make the astigmatism either horizontal or vertical. Once this is done tilt and decenter of the off-axis parabola and tilt of the mirror are only needed in one direction to shrink the image to a symmetrical, well focused image.2 As the image approaches symmetry it may be necessary to touch up the alignment in the other direction as the astigmatism may rotate as the image symmetry and focus improve due to better alignment.
For the final example5 we take the single pass alignment of a convex secondary in an off-axis Ritchey-Chretien telescope as shown in Fig. 15. In this case we had already aligned the primary mirror and had collimated light entering the telescope parallel with the primary optical axis. The design indicated precisely where the system should focus relative to the primary vertex. The line between the primary focus and the system focus defined the optical axis of the telescope. The secondary axis had to be aligned to this axis in five degrees of freedom to eliminate any aberrations.
With collimated light entering from the right in Fig. 15 the primary and secondary mirrors brought the light to focus in the vicinity of the autostigmatic microscope objective focus. The microscope objective focus had been located via mechanical tooling (see Fig. 7) and does not move once located mechanically. The secondary is then adjusted in focus and either tilt or decenter until the focused light enters the objective and the badly aberrated spot is roughly centered on the viewing screen. When reasonably well focused light is centered in the microscope objective the secondary has been adjusted in three of the five necessary degrees of freedom.
It is then necessary to use a combination of tilt and decenter plus focus to hold the focused spot centered in the objective and to reduce the aberrations, now a combination of focus, astigmatism and coma. The procedure is exactly as described previously above. If the secondary mirror has five adjustment screws and a minimum of backlash it is possible to do the alignment in a matter of minutes.
Determining aberrations from images
It has been suggested that the alignment described in the above sections of the papers can be performed with an ASM or an interferometer. Except for one embodiment of a commercial interferometer (Fisba), interferometers are too large to conveniently adjust accurately and stably in five degrees of freedom, three degrees of translation with high resolution and two degrees of tilt to be sure apertures are approximately uniformly filled with light. Not only is an ASM easier to move conveniently and accurately adjust to the locations necessary for alignment, but the adjustments needed on the optics being aligned are easier to interpret from the image shapes than from interference fringes. Granted that low order aberration quantities can be read off the interferometer monitor and these used to guide adjustments, the hand/eye human interface using the image shapes tend to be more efficient. The only downside to using the image is that it doesn’t give quantitative results as to the aberrations although an ASM is sensitive to wavefront errors of less that λ/8. In this last section we will describe a simple means of extracting pseudo low order aberration content from the images viewed with an ASM.
Two dimensional images have five symmetries; there is a part of the image that does not vary with azimuth and this part corresponds to all the rotationally symmetric parts of an image such as focus, third order spherical and all the higher order spherical aberrations. There remain four symmetries that describe how the image changes when it is flipped left-to-right, top-to-bottom and both left-right and top-bottom3,4. These are even-even and correspond to 3rd order and higher astigmatisms at 0º, odd-odd that are related to astigmatism at 45º, odd-even that are related to 3rd order and higher comas at 0º and even-odd relating to comas at 90 º.
As an example take the image in Fig.16 where the pixels are 4.5 μm square and the image was magnified by a factor of 5 by the ASM. Because the region of interest around the image comprises relatively few pixels it is a quick calculation to find the even-even part of the image and then extract the rotationally symmetric part from that.
Once the rotationally symmetric part of the image is removed the image is further processed simply by flipping and adding or subtracting the flipped images to make four linear combinations of the original to form the four symmetry groups. Fig. 17 shows the four symmetries derived from the image in Fig. 16 after the rotationally symmetric part was removed. As is clear the four images bear a close resemblance to the two orientations of astigmatism and the two orientations of coma. While there are probably a number of ways to derive quantitative information on how big the proportions are of each symmetry type, we simply used the root sum square of the values at each pixel as the criterion.
Now as the alignment of an optical system becomes relatively good the pseudo aberrations derived from the symmetry of the image can be used to help determine the final adjustments of the alignment. Notice that this approach does not carry a sign for the pseudo aberration; all that can be done is to minimize each of the four aberrations. Also, some of the symmetry in the image will depend on how uniformly the pupil of the system is illuminated. Care should be exercised to make sure the ASM axis is well centered on the pupil of the system being aligned. The simplicity of the calculations makes it possible to update the results at TV frame rates.
5. Conclusions
The method of alignment by locating centers of curvature is a strictly deterministic approach to alignment that is particularly helpful for complex, folded and off-axis optical systems. Further, the method does not impose tight (read costly) tolerances on edging or mounts. The same principles can be applied to the alignment of plane, fold mirrors. Finally, using aberrations is an easy way of aligning aspheric optics. It is not presently widely used because the instrument to determine the aberrations is usually an interferometer and they are generally too large to bring to the optics in question. The ideal device to view images is an autostigmatic microscope and, until recently, there have been no commercial sources for these. Because the commercial ASM’s include software as an integral part of the instrument it is not difficult to derive quantitative values for the pseudo aberrations most useful for alignment.
If planning for this deterministic alignment method is incorporated in the opto-mechanical design of optical systems immediately following the lens design itself there need be no further acknowledgements such as the one that appeared in a recent paper about the design, fabrication and assembly of the ARIES imaging spectrometer used on the 6.5 m Multiple Mirror Telescope6, namely, “Thanks, Koby Smith, for banging your head against the wall to align the thing.” If alignment is approached in a logical and systematic manner as part of the opto-mechanical design from the outset of a project there is no need for anyone to bang their head against a wall.
6. References
1R. E. Parks and W. P. Kuhn, “Optical alignment using the Point Source Microscope”, Proc. SPIE, 58770B, (2005).
2R. E. Parks, “Alignment of off-axis conic mirrors”, Optical Fabrication and Testing Workshop Technical Notebook, OSA, Flamouth, MA Sept. 1980, pp 139-45. A revised reprint is available at https://www.optiper.com/alignment%20of%20off-axis%20conic%20mirrors.pdf.
3C. Ai, L. Shao and R. E. Parks, “Absolute testing of flats(II); using odd and even functions”, Optical Fabrication and Testing Workshop Technical Notebook, OSA, Boston, MA 1992.
4C. Ai and J. C. Wyant, “Absolute testing of flats using even and odd functions,” Appl. Opt. 32, 4698- (1993)
5Work performed in collaboration with Breault Research Organization, Tucson, AZ.
6R. J. Sarlot and D. W. McCarthy, “A Cryogenic, 1-5 Micron Atmospheric Dispersion Corrector for Astronomical Adaptive Optics,” in Current Developments in Lens Design and Optical Engineering II, R. E. Fischer, R. B. Johnson, W. J. Smith, eds., Proc. SPIE 72, 4441 (2001).
Although the PSM is primarily an alignment instrument, it can also be used to determine the conjugates of parabolic and elliptical off-axis mirrors. By positioning the PSM at the sagittal and tangential foci of the mirrors, the conjugate distances of the mirror can be found using a laser range finder, for example. Knowing the sagittal and tangential radii of curvature (Rs and Rt), the vertex radius (Rv) is easily calculated. This information is used to verify that the mirror has been correctly manufactured and to aid in positioning the mirror in an optical system. Examples are shown of these steps.
1. INTRODUCTION
The alignment of off-axis aspheres is a subject that few people want to address because it is so different than aligning symmetric optics. An off-axis asphere has an optical axis, as opposed to a sphere that has no optical axis, just a center of curvature. Furthermore, the optical axis of the off-axis asphere usually does not pass through the surface of the mirror and certainly is not parallel to the normal to the surface at the center of the off-axis segment. On the other hand, off-axis aspheres are extraordinarily useful for many optical designs, and familiarity with them is essential for many optical systems.
This paper is an attempt to take some of the mystery out of off-axis parabolas and ellipses in terms of their geometry, and how to use their geometry to aid in their alignment. We will start by discussing some of the geometry that makes off-axis mirrors unique, and then describe how to find and measure the conjugates that are analogues to the center of curvature for a sphere. As opposed to a sphere with a center of curvature, an off axis asphere has two conjugates that define its axis, the two astigmatic foci at the centers of curvature of the tangential and sagittal radii of curvature. With the knowledge of how to find these conjugates, and a method of measuring the radii of curvature, it is possible to see that the mirror was manufactured correctly, and to see how the mirror should be aligned into the optical system for which it is intended.
2. GEOMETRY OF AN OFF-AXIS PARABOLA
Fig. 1 is a scale drawing of an off-axis parabola looking at a meridional section and along the optical axis (black vertical line). The off-axis section is the circle at the right edge of the pie section looking along the optical axis. It is aligned with the three vertical lines that defined the inner and out meridional extents of the off-axis section. The parent parabola is green and the blue circle has a radius equal to the vertex radius of the parabola while the purple circle segment, whose tangential radius is labeled Rt, is the best fit circle to the center of the off-axis segment. The light blue rays stopping at the optical axis define the sagittal radius of curvature, Rs.
The three radii are related by Rt = Rs^3/Rv^2 which makes it easy to find an unknown radius if the other two are known1. If a point source of light is placed on the axis of the parabola, a line image will form at the axis (light blue line perpendicular to the Rs ray). In general, the image will not be a line until the aperture of the off-axis section is masked, or stopped, down to a diameter where the coma in the off-axis asphere does not affect the astigmatism. How big a hole in the mask can be determined empirically, or an estimate of the coma may be made referring to Ref. 2.When the point source of light and the return line image are superimposed, the point source is on the normal to the surface at the center of the hole in the mask. The distance from the surface to the point source/line image is the sagittal radius, Rt. The astigmatic line image will lie in the meridional plane and is helpful in determining the azimuth of the vertex of the offaxis segment as well as determining the sagittal radius.
If the point source of light is moved back along the normal until the astigmatic line image is in focus it will be seen to be perpendicular to the meridional plane. The distance from the point source/line image here is the tangential radius, Rt. Since Rs = sqrt(Rv^2 + h^2) where h is the off-axis distance it is easy to find h.
3. GEOMETRY OF AN OFF-AXIS ELLIPSE
The geometry of an off-axis ellipse is a little more complex but the same basic geometry applies. Fig. 2 is a scale drawing of one of the parts we actually measured using the PSM and FARO arm. The green rays show the extent of the off-axis section relative to the foci to give a feel for the scale. The rays that bisect the rays going to the foci are those seen from the center of curvature of the off-axis segment. The right side of Fig. 2 shows the caustic region to give a better idea of the locations of the sagittal and tangential centers of curvature relative to the center of curvature of the vertex sphere.
As with the parabola, the sagittal foci lie on the axis of symmetry, or optical axis, while the tangential foci lie of the far side of the axis. From the way an ellipse focuses light from one focus to the other, we know the normal to the surface is the perpendicular bisector of the rays between the foci as shown. Just as with the parabola, we can find Rs and Rt, and using these values we can find Rv = (Rs^3/Rt)^1/2. For the ellipse we still need to find the conic constant, k, and the distance off-axis, h. To do this we make a mask as in the case of the parabola and measure Rs and Rt at 2 or 3 locations, h and ±delta h, where delta h is known. Two measurements will give an exact solution, while 3 or more will give a least squares solution using the relation that Rv^2 –k*h^2-Rs^2 = 01. The simplest method is to use 2 measurements at either edge of the off-axis ellipse and find the solution using the quadratic equation. One thing to remember is that delta h measured off the optic will be larger than it actually is, the distance from the axis of symmetry. Entering delta h as 1.4x less than the width of the optic is probably a good guess for a start.
Clearly with a concave ellipse this approach will get you close because the foci have to lie on the same line, the optical axis, as the sagittal foci. Also, for any given h, the line joining Rs and Rt lies on the normal to the surface. This will help locate the foci approximately. With this information it is then more precise to try to find the foci directly using the information derived from Rs and Rt. Using a point source such as the end of a single mode fiber at one focus and a microscope at the other focus it should be possible to locate the 2 foci to the precision necessary to meet system tolerances.
4. MEASURING THE SAGITTAL AND TANGENTIAL RADII
Using an autostigmatic microscope such as the PSM3, point the microscope at the mirror and locate the return image. Once the microscope is adjusted so the reflected point source is centered on the objective, focus the microscope to find either the sagittal or tangential focus. In general the reflected image will be too blurred to find a clean line image. Mask the mirror with an aperture small enough to produce a line return image. Adjust focus to get clean looking images such as that in Fig. 3.
When the microscope is well focused, bring a distance measuring device such as a laser distance measurer, or laser range finder4, up in front of the microscope and position it axially to get a focused Cat’s eye reflection off the rear of the distance measurer. Then take a distance reading to the mirror through the hole in the mask. Since most distance measurers calculate the distance from the rear surface of the instrument, the measurer reading is the sagittal or tangential radius, depending on which image is in focus. Fig. 4 shows how the measurement is made schematically.
Once these measurements have been made, the results may be compared with the prescriptions for the off-axis segments to see if the manufactured mirrors are to specification using the equations in the first part of the paper. It turned out in our case that one mirror was in spec and the other was not. Luckily it turned out that the specification was tighter than it needed to be and the mirror did not limit the performance of the system.
Once these measurements have been made, the results may be compared with the prescriptions for the off-axis segments to see if the manufactured mirrors are to specification using the equations in the first part of the paper. It turned out in our case that one mirror was in spec and the other was not. Luckily it turned out that the specification was tighter than it needed to be and the mirror did not limit the performance of the system.
5. USE OF THE SAGITTAL AND TANGENTIAL FOCI FOR ALIGNMENT
There are at least two ways the focus information can be used for the alignment of off-axis mirrors. First, the measurements can be used directly by adding alignment features to the optical bench that the mirrors will be installed in. Since the two foci produce line images in reflection, we can use polished cylindrical artifacts to simulate the line foci. An inexpensive source of suitable artifacts are “plug gauges”5, cylinders about 50 mm long in diameters ranging from <1 mm to 25 mm or more. These are used the same way polished balls are as physical realizations of points to focus a PSM on, but in this case the cylinders are realizations of lines. Kinematic mounts should be made so 2 plug gauges are positioned where the sagittal and tangential foci are supposed to be located in the finished mirror system.
To align an off-axis segment, a PSM is focused on the line image formed at the axis of the plug gauge, the gauge is removed and the mirror adjusted so its focus appears in the same location as the line formed by the plug gauge. Fig. 5 shows a typical image on reflection from a plug gauge. The mirror can be located in 3 degrees of freedom, axially, one degree of translation, and one degree of rotation about the normal to the mirror surface. Once one focus is adjusted, the PSM is moved to the second plug gauge, and focused on it. The gauge is removed and the mirror adjusted by rotating around the first focus until second focus is correctly positioned laterally. This process may take some iteration because it may be difficult to make the mirror rotate around the first focus although with sufficient forethought the mirror mount could be designed with this adjustment built in.
A second method of alignment, an indirect one, is what we did. We located plug gauges at the two foci and then measured the locations of the gauges relative to fiducials on the mirrors. Fig. 6 shows how a plug gauge was adjusted to be at the same location as the line image formed by the mirror sagittal focus, in this case. This meant that when the mirrors were installed in their optical bench using the fiducials around the edges of the mirrors, we were effectively positioning the foci to their correct positions in space.
6. RESULTS OF MEASUREMENTS ON AN OFF-AXIS MIRRORS
The mirrors we measured were about 250 mm square and CNC machined out of 6061-T6 aluminum and then smoothed and polished by hand to a specular surface. One of the mirrors is seen behind the mask in the left hand part of Fig. 6. The ultimate use did not require the polish as they are to go in a terahertz wavelength (857 μm) radio telescope. On the other hand, we wanted to be sure the mirrors were sufficiently good to meet the telescope spec, and had been correctly machined and not deformed by the polishing.
Following the procedure described above we got the results shown in Tables 1 and 2. The standard deviation in terms of setting at the best focus of the line focus was about ±4 mm for the parabola and ±10 mm for the ellipse. The distance measuring laser gauge gave consistent readings within ±1 mm. Thus both mirrors had larger errors in their radii than could be attributed to measurement error. On the other hand, the radius errors amount to sag errors over the full aperture of 30 and 50 μm in the case of the ellipse, and 160 and 190 μm in the case of the parabola, compared with λ = 857 μm.
After reviewing these errors in manufacture in the optical design code it was felt that with a minor spacing adjustment the mirrors would work just fine as they were. This finding coupled with the knowledge of where the fiducials were relative to the radii of curvature meant that the system would perform as expected and could be successfully aligned.
7. CONCLUSION
We have shown how to determine the vertex radius of curvature and off-axis distance of off-axis parabolas by measuring the sagittal and tangential radii of curvature with an autostigmatic microscope such as the PSM. We have gone on to show how the conic constant may be determined as well by making multiple measurements of the radii of curvature for more general conics. This information is useful as part of incoming inspection to see if the optics ordered are the optics delivered. Further, we have shown how the locations of the radii of curvature can be used as a tool in aligning the offaxis mirrors into their optical systems using two different approaches to alignment.
REFERENCES
Smith, W., Modern Optical Engineering, 2nd Ed., McGraw-Hill, New York, 445-6 (1990)
Parks, R. E., Evans, C. J. and Shao, L., “Test of a slow off-axis parabola at its center of curvature”, Appl. Optics, 34, 7174-8 (1995).
Laser trackers are an accurate and efficient tool for finding the locations of features in a threedimensional space but they rely on Spherically Mounted Retroreflectors (SMR) to return the laser beam to the tracker. If the feature cannot be contacted or it is not convenient to use an SMR another method must be used to follow the beam. We describe methods using a dual imaging and autostigmatic microscope for locating the features and two methods for tracking the microscope location depending on the type of tracker used. This converts a contact probe, large area CMM into a non-contact CMM by coupling a laser tracker with a dual purpose autostigmatic microscope. We begin with a brief description of the microscope followed by the alignment of the microscope to tracking and scanning laser metrology stations.
2. Point Source Microscope:
The imaging, autostigmatic microscope in question is called a Point Source Microscope (PSM)1 and has both a single mode fiber as a point source of light for the autostigmatic function and a LED behind a diffuser to provide Kohler illumination for imaging. The sources may be used independently or simultaneously. In the autostigmatic mode the PSM has lateral sensitivity of <1μm and similar axial sensitivity with an auxiliary lens for finding the centers of curvature of tooling balls or optics like mirrors and lenses. In the imaging mode the lateral sensitivity depends on the objective used but is in the neighborhood of a couple microns and the Cat’s eye reflection from a surface gives axial sensitivity to a similar resolution. It remains to show how to couple this non-contact ability to locate centers of curvature, the optically important feature of a lens or mirror for alignment purposes, to a high level of sensitivity to laser tracker systems that can determine locations in 3-dimensional space to similar sorts of accuracies.
3. Follower type laser tracking systems:
A follower type laser tracker is similar to a surveyor’s theodolite but is more sophisticated in that it is active. It sends out a laser beam along the telescope axis and the telescope will follow the beam if it is retroreflected back using a corner cube (generally a SMR that has the feature that the apex of the cube corner is accurately located at the center of the ball or spherical mount). The tracker will also measure distance using an interferometer mode if the SMR is moved from the tracker calibration SMR nest to a nest mounted on the measurand without breaking the laser beam. Fig. 1 shows how the follower tracker scheme works in general.
3.1 Alignment of the PSM to an SMR:
SMR’s are made in several convenient sizes, ½”, 7/8” and 1½” diameters, along with corresponding SMR “nests”, usually steel cones with a magnet at the apex to hold the SMR seated in the cone. A nest and corresponding SMR are mounted at a convenient location and the tracker is locked onto the SMR and its location in 3-D is noted. The SMR is removed from the nest and a grade 25 or better steel ball of the same diameter is placed in the nest so that its center is in the same location as the SMR. Then the PSM is adjusted so the focus of the objective is located at the ball center, something that can be done to <1μm in all three dimensions.
3.2 Alignment of the tracker to the PSM:
Attached to the PSM is a plate with a plane mirror in a mount that can be adjusted in tip, tilt and piston and a nest and an SMR. The plane mirror, shown schematically in Fig. 1, is nominally located half way between the objective focus and the SMR on the plate and perpendicular to a line between the focus and SMR. This arrangement is shown in Fig. 2. The mirror reflects the tracker laser beam back toward the SMR on the plate. The plane mirror is adjusted until the reflection from the SMR on the plate has the same apparent location as the SMR originally located at the PSM focus. The mirror is then adjusted such that the tracker sees the virtual image of the SMR at the objective focus. Now the assembly of PSM, plane mirror and SMR can be moved at a unit and the tracker will follow the PSM focus in all three dimensions as long as the PSM is not rotated so far that the tracker laser beam walks off the plane mirror.
4. Scanning type tracker system:
A scanning type tracker system uses several high speed rotating prism stations to sweep line images around a workspace. The prism scanners are accuracy synchronized with a clock. In the work space are detectors that resister when a beam sweeps by. Comparing the prism clocks and detector signals the detector locations can be accurately determined by time delay triangulation.
4.1 Alignment of the detectors to the PSM:
With the scanning system, three detectors are fastened to the side of the PSM facing two scanning prism stations. The PSM is focused on the center of a conveniently located steel ball. In this position the detectors are scanned by two scanning stations a known distance apart. Since three detectors on the PSM are scanned the plane of the detectors is determined relative to the scanning stations. The PSM with detectors attached is then moved to a different orientation while still being focused at the center of the ball and another set of data is taken to determine the plane of the detectors. This operation is repeated for a third orientation of the PSM while the PSM is centered on the ball. The three planes defined by the detectors will appear to rotate about the center of the ball, that is, a normal to each of the planes through the center of the ball are all equidistant as shown in Fig. 3.
This means the center of the ball, or focus of the objective, can be determined from the three measurements and once the distance from the center to the planes of the detectors is determined and recorded, any other position of the PSM can be related back to the center of the ball. This calibration is completely analogous to the initial use of a master ball and a touch probe on a Coordinate Measuring Machine (CMM) to establish the zero of the CMM coordinate system.
4.1.1 Using the calibrated PSM:
Once the center has been determined by this calibration, when the PSM is moved to any other location and the positions of the three detectors determined the location of the focus can be related to the center of the ball in all three coordinate directions. Any software that might be used with a CMM can also be used to analyze the data the scanner tracker gathers. This makes it possible to use the PSM precisely as a non-contacting probe with an apparent zero probe tip radius for any sort of coordinate measurements over large distances.
5.0 Conclusion:
We have shown how an autostigmatic microscope, and in particular, the Point Source Microscope (PSM) as a non-contact probe, can be used with laser tracker systems, either the follower type or the scanning type. In the first case an auxiliary mirror and tracker ball are used to make the tracker think it is looking at the focus of the PSM. In the second case, the PSM is calibrated in a way analogous to using the master ball on a CMM and then the PSM can be used as a zero radius probe tip for non-contact coordinate measurements over large distances. In both cases the PSM can be used either to find a center of curvature to 1 micron sensitivity in three dimensions or used in the imaging mode to locate a feature on a surface to 2 o3 microns in all three dimensions. The fact that the PSM images and can be set in all three coordinates to micron precision makes it a valuable part of an extension to contacting laser tracker systems.
6.0 References
1. Optical Perspectives Group, LLC, Tucson, AZ 85750, www.optiper.com. 2. J. Burge, et. al., Use of a commercial laser tracker for optical alignment, Proc. SPIE, 6676, 6676OE, (2007).
