MFT was mentioned in five of the papers given at the SPIE Conference on Telescopes in Edinburgh, Scotland at the end of June 2016 by authors from six different international research organizations.
PROC. SPIE 99055O, SEE MENTION OF MFT ON P. 19, FIG 18.
The surface roughness measurements of a silicon plate with a multilayer coating to reflect Xrays taken with the MFT are consistent with each other going from 2.5x to 10x magnification, consistent with the atomic force microscope for higher spatial frequency measurements and consistent with the model of the surface roughness. The figure shows a map of the surface taken with the MFT, upper left, and a graph showing the consistency of the various measurements and the model over many orders of magnitude of spatial scale.
PROC. SPIE 99120O, MFT NOTED ON P. 10, FIGS. 16 & 17
Shows the MFT sitting on the 4.2 m mirror and the lap top computer sitting along side it with a map of the mirror surface on the screen. Figure 17 shows 3 examples of the surface roughness taken at 3 different places on the mirror but all giving results in the 1 nm rms range over a sample area of 3 x 2.4 mm. Figure 18 shows that these surface roughness measurements converted into BRDF illustrate the mirror finish meeting the specification. It had previously been shown that the bare Zerodur mirror could not have been measured directly for BRDF because of the polycrystalline nature of the substrate but by measuring the surface roughness there was a path to measuring and meeting the specification (see Tayabaly, et. al., “Use of the surface PSD and incident angle adjustments to investigate near specular scatter from smooth surfaces”, Proc. SPIE 883805, 2013).
PROC. SPIE 960307, MFT MENTIONED ON P. 6 AND FIG. 2
Roughness tolerances for Cherenkov telescope mirrors on p. 5-6 and Fig 2, gives a description of the MFT in detail and shows the MFT sitting on a Cherenkov mirror substrate and an example of the surface roughness of the dielectrically coated mirror that was about 1 nm rms. The paper goes on to show that a variety of mirror substrates and coatings were measured for surface roughness and the resulting surface roughness maps are shown in Fig. 3 that range from 0.58 nm rms to about 12 nm rms depending on coating and exposure to the environment.
PROC. SPIE 99120Q, RESULTS OF MFT MEASUREMENT ON P. 6 AND FIG. 9
Polishing and testing of the 3.4 m diameter f/1.5 primary mirror of the INO telescope, p. 7, Fig 9 shows the results of 156 separate measurements made on various parts of the mirror with an average roughness of 0.6 nm rms. This was a mirror made of Zerodur so the surface roughness could not be measured using scattering, and surface roughness had to be used to see that the mirror met spec. Also, because of the speed of the mirror it would have been difficult and time consuming to have made replicas to measure the surface roughness.
PROC.SPIE 990578, MFT RESULTS ON PP. 4-5 AND FIGS. 5 & 6
Ion beam figuring of thin glass plates: achievements and perspectives, P 4-5 and Figs. 5-6, indicates the MFT was used to measure the surface roughness of ion beam polished glass plates only 0.4 mm thick, yet because of the low mass of the MFT it was possible to set the MFT directly on the thin plates to make the measurements. Figs. 5 and 6 show the surface roughness maps after various amounts of material was removed by ion beam polishing and the resulting change in roughness. The places on the substrates were carefully aligned so that it was possible to show the evolution of the change in roughness. Again the data were highly consistent. Special mention was made of the low mass being particularly useful in this study.
The main reason is that the other two major factors in performance, optical design and optical fabrication, have already been improved to the very limits of what can be accomplished. After spending good money on a near perfect design and fabrication of optical components does it make any sense not to assemble them in perfect alignment?
By perfect alignment we mean placing the elements where the design says they should in the theoretical optical and mechanical design, not just within some tolerance band, but precisely where the design says they should be. Only this way can you get performance at the same level as the perfection of the design and fabrication of the components.
In the last several decades with the help of incredible computing power optical design has reached the limits of perfection. Optical systems are being designed with vastly better performance than ever before by making use of aspheres and coatings that could only be used because of the computing power available these days. Unfortunately these advanced designs could not be made because optical fabrication methods had not kept up with the power of optical design.
Now with computer controlled polishing techniques like MRF, diamond turning and molding of both glass and plastic elements the aspheres that help with performance because of their design are now practical to make to high quality. Similarly coatings to enhance performance have been improved to the point that making them any better is no longer cost effective.
Now comes the hard part; how do you position these near perfect components, mechanical and optical, relative to each other so they perform as well as the theoretically perfect design? One way, the way usually followed is to tighten the tolerances on both the optical and mechanical parts until they have to go together perfectly but this is impossible to do because some slop has to be left or it is impossible to get the glass into the metal mount.
Another way is to leave loose tolerances for edging and bores of lens barrels so the element can be positioned where the design specifies it should be. This is where a tool like the PSM comes in. The PSM can be positioned so its focus is where the center of curvature of a surface should be according to the design and then the surface adjusted until it is centered to the PSM reference cross hairs.
Clearly this is not the way to assemble optics on a mass production basis. But when performance is at a premium such as in lenses for reconnaissance and cinematography, for example, it is far more efficient and cost effective to allow looser tolerances on glass and metal, and then individually align each element as it should be.
I remember many years ago seeing sophisticated lens systems assembled from well-made glass and metal components which were then tested for optical performance. They often failed the optical test and were sent back to the assembly department where they were taken completely apart and re-assembled with the hope that this time they might pass the performance test. In hindsight this was a ridiculous procedure. With the aid a a PSM and a little Fixturing the lens systems could have been assembled so they passed the optical test the first time, every time. This is the smart way to do alignment.
Measuring the radius of curvature of a concave surface – Main historical use
Modern version of an ASM uses internal infinite conjugate optics
Use of an ASM for alignment of optical systems
Other uses of an ASM
Conclusions
DESCRIPTION OF AN ASM
First description in English literature is Drysdale, Trans. Opt. Soc. London, 1900
Fig. 2 from the Drysdale paper of 1900
Further from the Drysdale paper
CAT’S EYE AND CONFOCAL FOCI
CAT’S EYE
Cat’s eye reflection
Objective focused on surface
Out going rays re-enter on opposite side of objective
If surface tilted, reflected rays parallel outgoing rays in collimated space
Cat’s eye used for setting crosshairs
Cat’s eye used for setting reference
CONFOCAL FOCI
Confocal reflection
Rays focused at center of curvature
Rays hit surface at near normal incidence and re-trace themselves
If surface tilted, rays do not re-trace and will not center on crosshairs
Confocal used for alignment
Confocal for bringing CofC to reference
EXAMPLES OF CAT’S EYE AND COFC SPOT IMAGES
OUT OF FOCUS CAT’S EYE SPOT IMAGE
IN FOCUS CAT’S EYE
Notice Shutter and Gain with focus
Locating an ephemeral point in space with 3 degrees of freedom to μm precision
OUT OF FOCUS & DECENTERED COFC SPOT
IN FOCUS BUT DECENTERED COFC SPOT
IN FOCUS AND CENTERED COFC SPOT
MEASUREMENT OF RADIUS OF CURVATURE
CONSISTS OF THREE STEPS:
Focus on the concave mirror surface to get a Cat’s eye reflection Set the reticle or electronic cross hairs on the reflected point image This established the optical axis of the ASM
Move the ASM back to near the center of curvature of the concave mirror Locate the reflected focused spot which may not be aligned to the objective Tilt the mirror until the reflected focused spot enters the objective Focus the ASM on the reflected spot and center it on the crosshairs Note the distance of the ASM on a linear scale
Move the ASM forward until it is focused on the mirror surface Moving from center of curvature means moving on a normal to the surface Get a sharp focus the Cat’s eye reflection Cat’s eye reflection will necessarily be centered on the cross hairs Read the distance of the ASM on the linear scale The difference of the Cat’s eye and confocal positions is the radius of curvature of the mirror
MEASUREMENT OF RADIUS OF CURVATURE
Focus on surface, used Cat’s eye reflection to set crosshairs
Move to confocal, adjust microscope so reflected spot in focus and centered on crosshairs, note linear scale reading
Move to focus on surface and get well focused Cat’s eye spot. Note scale reading Difference in readings is the radius of curvature
If this concept is well understood all other applications are easy
MEASUREMENT OF LONG RADIUS OF CURVATURE USE DEFOCUSED COLLIMATOR
Find s by putting a plane mirror in front of collimator
Put long radius surface in front of collimator and note ds
Since to first order efl = s, 1/s = 1/(s – ds) + 1/R, we find R = -s(1 + (s/ds)) (Be careful of signs, use common sense)
A CONTEMPORARY VERSION OF THE ASM IS THREE INSTRUMENTS IN ONE
Autostigmatic microscope
Internal SM fiber source
Electronic autocollimator
Simply remove objective
Video imaging microscope
Image plane parafocal with ASM focus
Internal LED Kohler source
SOME ADVANTAGES OF THE CONTEMPORARY DESIGN
Use of solid state light sources – compact, internal, low heat, monochromatic SM fiber coupled laser diode – bright for ease of alignment, near perfect spot Video camera – ergonomic, high position sensitivity, settable reference Software – permits high resolution centroiding on reflected spot
Large dynamic range on reflected light intensities
Recording and storage of Star images for optical quality determination
Centroid data easily coupled into other scales, a CMM, for example
OTHER USES OF THE ASM; DESIGNED FOR ALIGNMENT
Perfect for locating centers of curvature and foci of optical systems Use as a sensor on a centering station using a rotary table to define an axisUse was to align the elements of a f-theta laser scanner lens to a common axis Lens system had spherical and toroidal lenses and an “off-axis” mirror ASM mounted to the ram of a coordinate measuring machine Used a large x, y, z stage to pick up centers of curvature and align to axis
Don’t think like a lens designer and where rays go
Think about where centers of curvature should go and how to get them on a common axis
USE TWO ASM’S TO ALIGN AN “OFF-AXIS” LENS
Radius of convex side longer than working distance of objective, need extra lens
SET-UP USING 2 ASM’S TO ALIGN LENS
ALIGNMENT OF FOLD MIRRORS
Plane fold mirrors have 3 degrees of freedom, 2 tilt and one displacement< Optical and mechanical design will show where the center of curvature should be located when the fold mirror is proper aligned A ball in a fixture will mechanically locate this position, and ASM can verify
ANOTHER EXAMPLE OF A FIXTURE FOR ALIGNMENT
THE ROLE OF STEEL BALLS IN ALIGNMENT
Steel balls are a physical realization of a point in space Something you can physically touch as opposed to a theoretical object The ball center, the “point”, defines 3 translational degrees of freedom in space The ASM transfers an optical point, a CofC or focus, something you cannot touch, to the center of a ball, something that can be located physically Steel balls are inexpensive, extremely precise and come in many sizes Grade 5 chrome steel balls are round to 125 nm and cost about $3 each Can be thought of as convex optical grade mirrors Plug gauges are the cylindrical equivalent of balls and define axes in 3 DofF (Plug gauges are Go/no go pins for gauging the size of holes)
ALIGNMENT USING ABERRATIONS
An ASM is a “Star” test device showing the point spread of an aberrated wavefront It has sensitivity to about lambda/8 or lambda/10 Useful for quick check of quality of optical surfaces as they are assembled into systems Alignment of a parabola as an example
Initially the return spot will not be centered on the crosshairs of the ASM The parabola or autocollimating mirror are tilted until return spot on crosshairs
ALIGNMENT USING ABERRATIONS (CON’T)
When return spot lies on the crosshairs, the rays strike the flat at normal incidence However, the normal to the flat may not be parallel to axis of parabola As a consequence, the return spot will show coma
To finish the alignment, tilt the flat while keeping return spot on the crosshairs until the coma is reduced to a symmetrical spot. The entire alignment process takes only minutes to accomplish
OTHER USES OF AN ASM – FINDING LENS CONJUGATES
FINDING FIRST ORDER LENS CONJUGATES
Finding the radius of curvature of one side is direct measurement This assumes it is concave or there is sufficient working distance
Almost any lens can be reversed and measured through the side if not enough working distanceTo find the other conjugates it is necessary to model with a lens design program Or use first order equations and an iterative equation solving program See Parks, R. E., “Measuring the four paraxial…, Appl. Opts., 54, 9284 (2015)
ZERO INDEX MATERIAL – A USEFUL TRICK
When using an ASM or an interferometer most setups are double pass Light comes from the instrument, reflects at normal incidence off the last surface and retraces itself back into the instrument For a quick insight to the test it is a lot of work to trace a double pass system The trick; reverse the system and make rays leave the last surface at normal incidence To do this have rays from infinity travel through a medium of 0 index to the last surface Then n*sin(θ) = n’*sin(θ’) = 0, so θ’ = 0, or the rays leave the last surface normal to it! Now a marginal ray height solve after the last refraction shows the paraxial focus
Credit for the idea; I don’t know who deserves it I learned it from Jim Burge at UofA, Optical Sciences I suspect he may have learned it from Roland Shack If someone knows a better attribution I like to know.
AN EXAMPLE – FINDING COFC’S AND SURFACES
Assume a simple optical system such as an air spaced doublet Find the centers of curvature and surfaces vertices looking into the system
Reverse elements, object at infinity and n = 0, float by stop on last surface
MRH = 26.403 = 24.395 = 39.445 = -94.453 Object on first surface, image space f/# large, stop on last surface
MRH = -7.471 = -5.492 = -3.368 = 0
FIND THE INDEX OF REFRACTION OF A BALL
For small angles a = h/2r, and the normal = 2a, so the refracted ray angle is an/2 The ray angle relative to the x axis is 2a – an/2 = a(1-n/2) The mrh = h/(h/r(1-n/2)) = 2r/(2-n)
Or, n = 2(mrh – r)/mrh Works even if ball behind a window in a thermal chamber, but use ray trace
FIND THE INDEX OF A LIQUID AND RADIUS OF A SUBMERGED SURFACE
MEASUREMENT OF ANGLE
As shown earlier, by simply removing the objective the ASM is an autocollimator with sub-arc second sensitivity The bright mode of the laser source makes initial alignment easy in ambient light The small beam size makes it particularly useful for inspecting small prisms
ASM’S AND COMPUTER GENERATED HOLOGRAMS
A CGH pattern can simulate a ball, that is focus light a specific distance above the CGH
If balls are used to kinematically locate a CGH, a pattern to locate the balls can be included as part of the overall pattern. Then an ASM can precisely locate the balls. The balls, cemented in place, become an integral part of the CGH test artifact.
Because a CGH pattern can simulate a ball, a CGH can be made as an artifact for locating a group of points in space precisely located to < 1 μm in 3 dimensions.
An ASM mounted on a robot arm, for example, could be used to pick up the points one at a time to train and calibrate the robot.
EXAMPLE OF CGH HOLOGRAM
Printed on a 150 mm square photomask substrate Each circular pattern produces points several distances above the CGH Actual photograph is not available at the moment CGH courtesy of Arizona Optical Metrology, LLC, www.cghnulls.com
CONCLUSIONS
While autostigmatic microscopes (ASM) are over 100 years old, modern technology makes them truly practical for many diverse optical metrology needs.
Once the basic operation of measuring the radius of curvature with an ASM is understood, it becomes obvious that an ASM has many more useful applications.
Almost everything discussed here can also be done with an interferometer with greater precision. However, if the ultimate in precision is not needed the ASM is more convenient to use because of its small size, light weight and ease of mounting. Further, in some applications the greater coherence of an interferometer make some of the applications more difficult to perform because of multiple fringe patterns.
In many instances an ASM is a cost effective and easy to use alternative to an interferometer.
Could measure physically, but may not want to, or can’t
Measurements needed
Radius of curvature but may not have working distance – reverse lens so backside concave
Optical center thickness to rear vertex
Back focal length from one or both sides
Need at least 4 measurements to solve for 4 unknowns
Extra measurements increase confidence
Measurements that can be made
Center thickness
Rear Radius
Back focal length
No closed form solution for unknowns
Use spreadsheet
Find difference between measured & guessed values
Square differences and sum
Make sum zero by varying unknowns
Use a lens design program
Model the various measurement configurations
Use multi-configuration option
Use plane surfaces, guess thickness and a model for index
Use optimizer to find solution
Spreadsheet example
N, t and r2 were estimated and a, b and c calculated
Solver used to minimize lower right hand cell to give calculated n, t and r2 shown above.
Lens design example
Configuration 1 shown for calculation of bfl
Grayed out lines are ignored
Lens design example con’t 1
Configurations 1, 2 and 3 are looking thru short radius first Configurations 4,5 and 6 are looking thru long radius first Line 2 shows what the measurements should be knowing the index, thickness and two radii
Lens design example con’t 2
Lens design example con’t 3
Radii, thickness and index are set as variables
Optimized with small entrance pupil for paraxial solution
Conclusions
Use all practical conjugate measurements in model
Works with interferometer or autostigmatic microscope
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).
