Author: csadmin

Practical Considerations For Using Grating Produced Bessel Beams For Alignment Purposes

Written by csadmin on July 6, 2021. Posted in Centering, Published Papers. No Comments on Practical Considerations For Using Grating Produced Bessel Beams For Alignment Purposes

ABSTRACT

Bessel beams are useful for alignment because they create a small diameter, bright, straight line image in space perpendicular to the Axicon, or Axicon grating, producing the beam that is an exact analog of a single ray in a ray tracing program. Here we limit our discussion to Bessel beams produced by plane gratings whose pattern is evenly spaced concentric circles that are illuminated by a point source of light on the grating axis. The gratings produce a more nearly ideal Bessel beam than a lens type Axicon, and the plane grating serves as a plane mirror as well in an alignment setup so the combination define four degrees of freedom in space rather than the usual two.

Most discussions of Bessel beams assume illumination with collimated light. We have found it advantageous to use a point source for illumination because it is easy and less expensive to use a single mode fiber as a source than a precision collimating lens the diameter of the Axicon. Besides, collimated illumination produces a Bessel beam of finite length in transmission while in theory a beam of infinite length is created using a point source.

With these assumptions about how the beams are produced and details about the grating diameter and line spacing it is easy to calculate the useful length of the Bessel beam in reflection from the grating, the usual matter of concern when using the grating for alignment purposes in a double pass test setup. Other practical matters are also discussed such as lens centering with a test apparatus with no moving parts.

1. INTRODUCTION

Credit for the discovery of Bessel beams generally goes to back to Durnin¹ in 1987, but really the credit should go to McLeod² in 1954 where he describes the invention of the Axicon because the beam created by an Axicon is a Bessel beam. Unfortunately for McLeod he did not have a laser at his disposal and so the bright spot created by his Axicon did not show much (any) of the structure surrounding the bright spot and he did not realize he had stumbled on this new form of light beam. Besides, McLeod was a very practical person primarily interested in alignment of optical systems, not the physics of the beam produced by the Axicon³.

Even after McLeod wrote a second paper⁴ describing uses of the Axicon for alignment there was not much interest in Axicons until Durnin’s1 sparked an interest because of the so-called non-diffracting nature of Bessel beams. Also, Durnin and his coworkers were initially creating their Bessel beams not with Axicons, but rather with opaque screens with a narrow annulus that created the Bessel beam on the axis of the annulus. This led Vasara⁵ to realize Bessel beams could be created by plane gratings, in part, to make the beam more efficient in terms of light through put by using the full aperture instead of just an annulus.

In spite of several papers^6,7,8 including the widely distributed Optics & Photonic News⁹ mentioning uses of Bessel beams for alignment, virtually all the interest in Bessel beams has been in other areas of optics, astronomy and physics. There seems to be almost no interest in this simple yet powerful technique for the practical, everyday alignment uses such as cementing doublets and centering optics in a barrel, let alone aligning optics in 2 and 3 dimensional space where alignment becomes more of a challenge particularly if it has to be done precisely. The purpose of this paper is to attempt to illustrate some of the practical concerns of using Bessel beams so it is easier for others to take advantage of this powerful alignment technique.

2. WHAT IS A BESSEL BEAM AND HOW IS IT PRODUCED?

Before getting into the practical issues of using Bessel beams it makes sense to review what Bessel beams are and how to produce them. Referring to Fig. 1, a plane wavefront is incident on a narrow annular aperture centered on and at the back focus of a lens.

Fig. 1 Creating a Bessel beam using a plane wavefront and an annular slit at the back focus of a lens (after14)

This is how Durnin, et. al. ¹ created their Bessel beams. In the plane of the page, the lens collimates the light from the upper portion of the slit to produce a plane wavefront progressing downward from the lens that has a width of the slit diameter, while the lower portion produces a plane wavefront of the same width progressing upward. Since the picture is symmetric about the axis of the annulus and lens, these two wavefronts produce a set of nested cones of light in the region where the wavefront overlap.

The phase of the light at the apexes of the nested cones interferes constructively along the axis creating a line of light whose intensity is much greater than in the region surrounding the axis. This bright line is the core of the Bessel beam and is the useful portion for centering. The intensity of the light in the core along the axis varies in an oscillatory manner and gets less intense near the lens but never goes to zero as shown in Fig. 2a. Perpendicular to the axis the light also varies in rings of diminishing intensity away from the bright core as shown in Fig. 2b.

Fig. 2a Variation in intensity of the Bessel core in the direction of propagation for a plane wavefront (red) and converging wavefront (blue) (left ) from reference 11 and Fig. 2b variation in intensity perpendicular to the axis of the beam (right)

From a practical standpoint, the Durnin method of using an annulus is inefficient because most of the aperture of the lens is obscured. A physical, cone shaped glass Axicon as McLeod used also creates a Bessel that uses all the light incident on the clear aperture of the Axicon. Fig. 3 illustrates how the Axicon creates a nested set of cones of light although only one is shown because making a figure with many cones is difficult. For each different ray height of the spherical wavefront impinging on the Axicon a different diameter ring of virtual sources is created that cross the axis of the Axicon at a different distance from the tip.

Fig. 3 Illustration of how a conical Axicon creates the nested cones of light to form a Bessel beam

A third way of creating a Bessel beam is to use a pattern of equally spaced, concentric rings printed on a photomask substrate, in other words, a computer generated hologram (CGH)⁵. This can be pictured similarly to Durnin’s approach but no lens is needed. Looking at the pattern of circles edge on with the center of the pattern in the plane of the page, the pattern acts like a linear diffraction grating to an incident plane wave. A small amount of light goes straight through the grating as the 0 order while much of the rest of the light is diffracted into + and – first orders at an angle of λ/d where λ is the wavelength of the incident light and d is the pattern line spacing. Now the nested cones are made up of the + 1^st order light as the page is rotated 360 degrees around the axis of the pattern.

Roughly 40% of the incident light goes into the transmitted Bessel beam for a binary grating pattern and 40% into the reflected beam. While this is less efficient light wise than a physical Axicon, the CGH has 2 distinct advantages over the glass Axicon. First, the CGH is also a plane mirror and therefore simultaneously defines 5 degrees of freedom, 3 translations and 2 angles, a great advantage to anyone doing alignment. The second advantage over the cone shaped Axicon is that the grating pattern is almost perfect in the sense that CGHs can be written with an rms precision on the order of 1 part per million or better¹⁰ over a scale of spatial wavelengths of at least 10^4.

There are two questions that may be asked about the precision, what about wavelength of illumination and the flatness of the substrate. First, the Axicon gratings work at any wavelength. You can create a Bessel beam with white light. Regarding substrate flatness, it is hard to imagine a low order deformation that will affect the straightness of the Bessel beam. Power and astigmatism may affect the shape of the rings around the core but it would have to be an error like the “S” shape of coma before the straightness of the beam would be affected, and this high an order of deformation is difficult to induce mechanically.

A final comment of the relative advantages of a conical glass Axicon versus a grating. At the present time a physical Axicon 25 mm diameter is less expensive than a similar size grating in unit quantities by perhaps a factor of 2. In some cases they are essentially the same price. Because the grating Axicons can be produced by contact printing the price will become much less expensive with higher volumes. Since Axicon gratings are “perfect” and more flexible to use than true conical Axicons the balance of the discussion will be limited to grating Axicons.

3. DESIGN AND USE OF AXICON GRATINGS

When Axicons are discussed the immediate mental picture is that they are illuminated with a collimated light source. Most of the literature assumes this because it is a little easier to describe the theory. However, use with a collimated source limits the scope of use and the ease of implementation. First, a good lens the same diameter as the Axicon is needed to collimate the incident light. Second, the collimated input limits the theoretical length of the transmitted Bessel beam. Using a point source of light a known finite distance from the grating permits a Bessel beam in transmission of almost any length. Because any Axicon makes relatively inefficient use of the light incident on it, a laser source is almost a necessity in practice to produce a long Bessel beam.

An adjustable 1 to 10 mW laser diode source coupled into a single mode fiber makes an ideal source with which to illuminate the grating via a free space coupling. Such a fiber patch cord in the visible will have a near perfect Gaussian output with a NA of about 0.1. This source placed about 125 mm behind a 25 mm diameter grating gives about optimum coupling to the grating, at least for illumination purposes. This convenient set of initial parameters will be used now to examine the Bessel beams produced by these constraints. It will be obvious how to deviate from these values depending on the specific situation.

A next obvious question is the line spacing of the pattern. I made a reasoned guess at 10 μm lines and spaces to give a grating spacing of 20 μm. Using this spacing with 635 nm light gives λ/d = 0.03175 = 1.815° = α. It has turned out that this was a good choice. Gratings with this spacing are easy to make and the diffraction angle seems to be useful for all applications I have tried so far. This is not to say there will not be a case where another spacing is a better choice but I cannot see anything wrong with this choice, at least as a good place to start.

3.1 Properties of the Bessel beam in reflection

Because the grating line pair spacing of 20 μm has worked out well it will be used for further discussion. Also, it has been convenient to size the grating at a 25 mm diameter so we’ll use that as well in the example but a practical upper limit would be 140 mm for a 6 x 6” photomask substrate. If we put a point source of light a distance z = 125 mm in front of an Axicon grating with 20 μm/lp spacing and illuminate it with 635 nm light we have the situation in Fig. 4 where we assume the grating radius is 12.5 mm = R_max, and the diffraction angle was increased to 5° for clarity.

Fig. 4 Creation of a Bessel beam by a point source in reflection from an Axicon grating

Light rays (red) from a point source at the left of Fig. 4 reflect from the Axicon grating. The reflected rays appear to emanate from a virtual point source at the right of the figure. On either side of the reflected rays are plus and minus 1st order diffracted rays (blue) that appear to emanate from a virtual annulus in the plane of the virtual point source. The radius of the annulus is the distance z from point source to grating times the tangent of the diffraction angle α. Diffracted rays from equal and opposite sides of the axis of the grating interfere on the axis of the grating to form the core of the Bessel beam while rays from opposite sides of the axis but different heights at the grating interfere to create the rings around the core.

By looking at the rays impinging on the center of the grating it is clear that there will be ray crossings starting immediately to the left of the grating to form the beginning of a Bessel beam in reflection. As the ray heights increase on the grating the diffracted ray crossings proceed to the left until they reach a height of 4 mm, for our example, where the crossing extends to infinity. Beyond that the diffracted rays start to diverge and create virtual crossings to the right of the grating that mimic the real crossings to the left of the grating.

For the reflected Bessel beam the usual method of creating and observing it would be to use an autostigmatic microscope (ASM) with the point source in the microscope illuminates the Axicon grating and observes the reflected Bessel beam. In this case the reflected Bessel beam length never exceeds the distance from the focus of the ASM to the grating and this distance will be limited by the diameter of the grating. The maximum distance the ASM can be from the grating is limited by the zonal radius of the grating. Once z = R_max*tan(α) = 393.38 mm, for our example, the virtual annulus is at infinity with a radius of Rmax. As z increases from there the virtual annulus moves to the left of the grating and the diffracted rays diverge so they never enter the ASM objective. The other 1st order rays are always diverging. This means when using an ASM with an Axicon grating in reflection the maximum length of the Bessel beam will be R_max*tan(α). Since Bessel beams are self-healing¹² a point inside the limit just stated will create a Bessel beam to the left of the source provided the source does not obscure too much of the beam.

Another practical aspect of moving the ASM too far from the grating is the objective will have a reasonable NA, typically about 0.3 for a 10x objective. As you move farther from the grating the intensity of the illumination is decreasing as z^2 which is not bad in and of itself, but as the source illumination is increased scattered and ambient sources of light increase the background illumination around the core. The point here is to use the reflected Bessel beam to align the ASM to the grating and then align a point source on the other side of the grating to the ASM to create a longer length useful Bessel beam¹³. Because the point source creating the transmitted Bessel bean can be placed close to the grating the illumination is intense and the beam as mentioned earlier can go to infinity in theory.

3.2 Properties of Bessel beams created in transmission

Fig. 5 shows what happens when a point source illuminates the grating in transmission. Assume the source is still at 125 mm from the grating but the diffraction angle is 5° to spread the rays for clarity. The Figure shows a point source illuminating the grating with the 0 order rays (red) passing through the grating. On either side of each transmitted ray are plus and minus 1st order diffracted rays (blue) that appear to emanate from an annulus of radius z*tan(α) surrounding the point source. As with the reflected ray case, the diffracted rays on either side of the grating axis and the same height at the grating cross the axis to create the core of the Bessel beam. Rays from differing heights at the grating form the rings around the core.

Fig. 5 Bessel beam formation in transmission using a point source of illumination

As long as the point source is closer to the grating than R_max/tan(α) the Bessel beam propagates from the grating to infinity. This means the Bessel beam created in transmission can be used with greater flexibility than the reflected beam but there does not appear to be a good method of assuring the axis of the Bessel beam is strictly perpendicular to the grating other than aligning the transmitted beam to an ASM that has been previously aligned using the reflection mode. If not aligned in this manner the Bessel beam can be several degrees off perpendicular without affecting the quality of the beam¹⁴. In some applications the alignment with the grating makes no difference, for example, when using the beam to determine straightness. However, if the beam is used for alignment it is usually necessary for the beam to be perpendicular to the grating.

3.3 Other practical considerations concerning using Bessel beams

3.3.1 Axicon grating light efficiency
Axicon gratings are not very efficient light wise. At any particular observation point along the Bessel beam you are only seeing the light that make it through an annulus the width of the annulus. For example, the ring at 4 mm radius where the diffracted rays are normal to the grating has an area of 0.2516 mm² and rings inside this are progressively smaller. This is why the intensity shown in Fig. 2a is low close to the grating. For this reason a SM fiber coupled light source with a variable intensity of several mW is a practical size source. The source does not have to be monochromatic, or even close to monochromatic, to create a Bessel beam. White light will work if you can get enough into a fiber to get useful light in the diffracted beam.

3.3.2 Use of Bessel beams with quad-cells
Keeping with the ring size topic, using a Bessel beam with a quad-cell does not work. The energy spread around the central core is close to uniform because every ring has nearly the same energy as the rings on either side of any particular ring¹⁵. The reason it is easy to center on the central core with a digital camera is that the energy density is about 8x greater than in the first ring. When the camera shutter speed is set to give a threshold of about half the peak intensity of the core, the only pixels above the threshold are pixels in the core and centroiding is a simple as finding the center of gravity of the pixels above threshold.

3.3.3 Ease of initial alignment with Bessel beams
On a related topic, because there is energy spread out laterally way beyond the core it is easy to know which way to adjust a mirror or lens to bring the core into the field of view of the microscope objective used to view the Bessel beam. As the intensity of the light source or the shutter speed is decreased, the rings around the central are visible even though the central core is many mm outside the typical field of view of about 1 mm for a 10x objective and modest size format digital camera.

The best way to think about this advantage is to think about aligning an autocollimator to a plane mirror a couple meters away. It is a 2 person job in a darkened room using a flashlight shining in the eyepiece. Once reflected light is back in the objective the job is done, but getting the light in the aperture of the autocollimator is a real trick. With the Bessel beam the rings are a flag waving to tell you which way to tilt the mirror to get light in the aperture even though you are grossly misaligned to begin with.

3.3.4 Aligning point source to the grating axis
The point source illuminating the grating must be on the axis of the grating within limits that are, in practice, fairly loose otherwise the core of the Bessel beam brakes up into a checkerboard pattern of dots. The details of how far off axis are given in this paper by Bin and Zhu¹⁶. A method of perfectly aligning the point sources to the grating in either reflection or transmission was previously given¹³.

In addition, the central core also breaks up if the Bessel beam goes through or is reflected from an optic that introduces sufficient aberration. For example, if a lens is sufficiently tilted relative to the Bessel beam the astigmatism introduced will break the core into a pattern of dots. There is still information in the pattern but it is much harder to interpret than the central core. Again, this topic is beyond the scope but some insight may be gained from Bin and Zhu¹⁶. In practice it takes a wavelength or 2 of aberration before there is an effect on the core.

3.3.5 Commercial availability of Axicon gratings
Finally, for those who want to experiment with Axicon gratings they are available commercially for reasonable prices¹⁷. If the use of these gratings grows the price is bound to come down.

4. METHOD OF USING A BESSEL BEAM TO FIND TILT AND DECENTER SIMULTANEOUSLY

As a final topic on practical uses of Axicon gratings we describe a method for determining the centering and tilt of a lens without moving anything but the lens itself in 4 degrees of freedom. The principle behind the method is that if we know the location of two points in space we know the origin and slope of the line between the points. What is needed is a device that will sample a Bessel beam simultaneously at two points along the beam. One way of sampling the Bessel beam at two axially displaced locations is to use an optical trombone where one light path goes straight through (blue) while the other (dashed red) is diverted through the trombone to increase its optical path length as shown in Fig. 6. The light arriving in the focal plane of the observing instrument, usually a microscope, comes from two axial locations along the Bessel beam separated by twice the distance of the fold mirrors to the beamsplitters. Before inserting the trombone beam sampling device, the viewing microscope crosshairs are centered on the Bessel beam coming from the Axicon grating. Then the sampler is inserted in the beam. The sampler, depending on the type of beamsplitters used, will shift the beam more or less from the crosshairs if it is not well aligned in angle. Once the sampler is aligned the beam passes through the sampler undeviated as in Fig. 6.

Fig. 6 Axial beam sampler aligned with a Bessel beam and microscope

Adding a tilted and decentered lens element between the grating and the sampler will displace the beam at the microscope focal plane but by different amounts depending on whether the beam has travelled the long or short path as shown in Fig. 7.

Fig. 7 A tilted and decentered lens inserted between the Axicon grating and the axial beam sampler producing different displacements of the two beams at the focal plane observing microscope

In order to align the lens in both tilt and decentered to the viewing instrument, both central cores of the Bessel beams must lie on the microscope crosshairs. If the observing instrument has a resolution of <1 μm (typical of a Point Source Microscope¹⁸ with a 10x objective) and the distance between axial observing locations is 100 mm the lens can be centered to <1 μm and aligned parallel to the axis of the beam to <2 seconds of arc without having to move any part of the observing instrument. The advantages of aligning lenses without having any part of the alignment apparatus move other than the adjustments to the lens itself are obvious for improving productivity.

5. CONCLUSION

We have explained how Bessel beams are created using Axicon gratings and have shown how to calculate the useful range of the beam in reflection. There is no practical limit to the range in transmission. In addition, we have discussed several practical considerations for the use of Bessel beams for alignment in conjunction with observing instruments that use digital cameras. In particular, the ease of alignment if the setup is initially badly misaligned so no bright light is in the sensor field of view. It was pointed out that Axicon gratings are commercially available and that the quality of the Bessel beam produced is a higher quality than those produced by conical axicons although the gratings are only about half as efficient in light use.

Finally we showed how to precision align a lens element in tilt and decenter by using an optical trombone to sample the Bessel beam at two axially separated locations. The technique improves productivity because there are no moving parts in the alignment setup and adjustments to tilt and decenter can be dialed in with adjustment screws.

REFERENCES

[1] Durnin, J., “Exact solutions for nondiffracting beams. I. The scalar theory”, JOSA-A, 4, 651-4 (1987).

[2] McLeod, J. H., “The Axicon: A New Type of Optical Element”, JOSA, 44, 592-7 (1954).

[3] (Personal opinion from meeting McLeod in 1967 at Eastman Kodak Company.)

[4] McLeod, J. H., “Axicons and Their Uses”, JOSA, 50, 166-9, (1960).

[5] Turunen, J., Vasara, A. and Friberg, A., “Holographic generation of diffraction-free beams”, Appl. Opts., 27, 3959 (1988).

[6] Vasara, A., Turunen, J. and Friberg, A., “Realization of general nondiffracting beams with computer generated holograms”, JOSA A, 6, 1748 (1989).

[7] Fortin, M., Piche, M. and Borra, E., “Optics test with Bessel beam interferometry”, Opts. Express, 12 5887 (2004).

[8] Gale, D. “Generacion y aplicacion de haces Bessel en trabajos de alineacion”, Rev. Cub. Fisica, 27, 28 (2010).

[9] Jaroszewicz, Z., Burnall, A. and Friburg, A., “Axicon-the Most Important Optical Element”, Optics and Photonics News, April 2005, p. 34.

[10] J. Ye, M. Takac, C.N. Berglund, G. Owen, R.F. Pease, “An exact algorithm for self-calibration of two-dimensional metrology stages”, Prec. Eng., 20, 16, (1997).

[11] Dong, M and Pu, J., “On-axis irradiance distribution of axicons illuminated by a spherical wave”, Optics & Laser Tech., 39, 1258 (2007).

[12] Bouchal, Z., Wagner, J. and Chlup, M., “Self-reconstruction of a distorted nondiffracting beam”, Optics Communications, 151, 207 (1998).

[13] Parks, R., “Alignment using axicon plane gratings”, Proc. SPIE, 10747, 1074703, (2018).

[14] McGloin, D. and Dholakia, K., ‘Bessel Beams: Diffraction in a new light”, Contemporary Physics, 46, 15-28, (2005).

[15] Durnin, J., Miceli, J. and Eberly, J., “Comparison of Bessel and Gaussian beams”, Opt. Lett. 13, 79 (1998).

[16] Bin, J. and Zhu, L., “Diffraction property of an axicon in oblique illumination,” Appl. Opt. 37, 2563-2568 (1998).

[17] https://optiper.com/en/products/buy/axicon-grating

[18] https://optiper.com/en/products/point-source-microscope

Need Custom Optical Test Equipment?

Written by csadmin on June 15, 2021. Posted in News. No Comments on Need Custom Optical Test Equipment?

WHY START FROM SCRATCH WHEN YOU CAN ORDER A PSM FROM OUR WEBSITE?

It may surprise you but about 15% of Point Source Microscopes (PSMs) purchased are built into custom optical test hardware. Optical Perspectives supplies a CAD model of the PSM to help the customer integrate the PSM into their test hardware design. When the custom hardware is built the PSM is bolted in place, connected to its computer and the test hardware is ready to use as an autocollimator, alignment device or centering sensor.

COTS APPROACH

This COTS approach reduces the time and cost of custom optical test hardware by avoiding the development and procurement phase of obtaining a precision sensor and software for optical test equipment.

The PSM is compact and lightweight so it is easy to mount to almost any structure via the many tapped mounting holes in its body. Two USB connections to a computer with installed and proven PSM Align software is all that is needed to be up and running.

If a change is needed in the software to optimize the PSM for your application it is easily made on industry standard, LabVIEW™ based, PSM Align software. Optical Perspectives will even provide the source code if a customer wants to introduce their own modifications.

PSM FORM FACTOR

The PSM coupled with its custom, precision tip/tilt mount and right angle adapter is an autocollimator with better than 1 arc second resolution.

In this configuration, the output beam can be oriented 360 degrees relative to the PSM body and the total package has a form factor of 160 x 110 x 54 mm and a mass of about 1 kg.

For use as an alignment or centering sensor the PSM has a form factor of 200 x 110 x 32 mm and a mass of less than 1 kg.

PSM CONFIGURED FOR MOUNTING ON A CMM IN PLACE OF THE TOUCH PROBE

There are also adapters to mount the PSM in other centering devices or for mounting as the sensor on a CMM in place of a touch probe.

Use with a CMM is ideal for aligning complex, precision optical systems to assure that all components are positioned exactly to design to CMM accuracies.

Announcement of Re-Publication of “Optics and Optical Instruments—Preparation of Drawings for Optical Elements and Systems: A User’s Guide”

Written by csadmin on May 4, 2021. Posted in News. No Comments on Announcement of Re-Publication of “Optics and Optical Instruments—Preparation of Drawings for Optical Elements and Systems: A User’s Guide”

FROM THE OSA PUBLISHING BOOKSHELF

OSA Standards Committee
eds. Ronald K. Kimmel and Robert E. Parks

We hope you appreciate this republication of ISO 10110 Optics and Optical Instruments—Preparation of Drawings for Optical Elements and Systems: A User’s Guide, first published in 1995. This open-access republication is intended to give you a feel for the ISO 10110 standard and an overview of its general scope and methodology. It is not intended for use as a standard as it is hopelessly out of date. Copyright 1995

When you have convinced yourself of the usefulness of ISO 10110, go to www.ISO.org or www.ANSI.org and order the standard. Yes, we know it is pricey, but it is a cost of doing business in the optics industry. Ultimately, using the standard will save you money. The advantage of using ISO 10110 is that the optics world is global and, if your drawings are done according to this standard, they will be more likely to be understood worldwide.

If you find there are parts of ISO 10110 that put you to a disadvantage, or you have something to add to the standard, please contact Patrick Augino at the Optics and Electro-Optics Standards Council (OEOSC) Exec_Director@oeosc.org and join OEOSC. OEOSC is the US ANSI member of the ISO optical standards writing committee, TC172. As a member of OEOSC you will have the opportunity to work on updates to the standard and will receive proposed updates for review and approval.

Respectfully,
Robert E. Parks
04 May 2021

Using the PSM as an Autocollimator

Written by csadmin on April 2, 2021. Posted in News. No Comments on Using the PSM as an Autocollimator

The other day I got a call from a PSM user asking about calibration. What he was really asking about was the setting of the zero, or origin, on the video screen.

CROSSHAIRS IN THE CENTER OF THE FIELD

This is the same sort of “calibration” people talk about when using autocollimators, which are the crosshairs in the center of the field. Here you can use a corner reflector or rotate the collimator in its mount to see if the target appears to move. If the target moves as the autocollimator is rotated about its axis, the crosshairs are not centered. (For more on autocollimators, see below.)

EQUIVALENT CALIBRATION

The equivalent calibration for the PSM is to focus on a specular surface to get a well-focused return spot, a Cat’s eye reflection, and click the Set Ref Pnt button to center the crosshairs on the return spot electronically. This operation is the equivalent of bore sighting a rifle scope. When the crosshair is centered on the Cat’s eye reflection the focus of the PSM objective is centered in the crosshair.

Thus, when a return reflection is also centered in the crosshair, the return reflection is coincident with the outgoing light focus. In this way you can be sure you are at the center of curvature of a concave mirror to better than 1 μm when the PSM is used with a 10x objective, the standard sold with the PSM. Obviously, a higher resolution is achieved with a higher power objective.

THE CALIBRATION FACTOR

If by calibration you mean when the PSM says the return spot is 54.2 μm from the crosshair, is it really 54.2 μm or is it 54.4 μm?

For most users, simply setting the Calibration Factor to 1.00 when using the standard 10x objective is good enough. For those who want to know the distance to the last μm the answer is to use a calibrated line width standard and measure it to see if the value you get with the PSM is the same as the standard. If it is not, the Calibration Factor can be tweaked to give a precise reading.

When using an objective other than the 10x Nikon objective supplied with the PSM you may want to change the Calibration Factor to get the correct reading in μms. For those not having a suitable line width standard, we have standards traceable to NIST for sale in our webstore.

THE PSM ALSO WORKS AS AN AUTOCOLLIMATOR

Recently we have sold several PSMs to a customer that wanted the PSM strictly as an autocollimator.

They wanted to build the PSM autocollimators into their hardware as permanent measurement devices and did not have space or stiffness to support a standard autocollimator that tends to be 500 mm or so long and weighs several kilograms.

As you may (or may not) know, the PSM works as an autocollimator by simply removing the objective and it has a resolution of better than 1 arc second.

For this particular customer, the PSM was a perfect solution since the PSM is about the size of your hand and weighs about half a kilogram. Another advantage for this customer was that their target was rather small, less than 10 mm in diameter. This fit nicely with the PSM collimated beam output diameter of 6 mm, much better than a standard autocollimator with a beam diameter of over 25 mm where most of the light falls off the target or is reflected as scattered light.

MACHINE VISION AUTOMATION SCHEME FOR LIMITED SPACE

I am publishing this article, because I got the call from someone who wanted a PSM as an autocollimator for just this reason, to incorporate in a machine vision, automation scheme with limited space.

This got me thinking that we have always stressed using the PSM for alignment and centering and have treated its use as an autocollimator as a very secondary use.

The call from the customer who wanted to use the PSM for an autocollimator, made me realize that there is a customer base who really needs a compact, electronic autocollimator. The PSM may be just what they are looking for.

Adding Mechanical Datums to CGHs and Fresnel Mirrors

Written by csadmin on March 8, 2021. Posted in News. No Comments on Adding Mechanical Datums to CGHs and Fresnel Mirrors

In general, computer generated holograms (CGHs) and plane Fresnel mirrors (and lenses), made by the same techniques as CGHs, have optical “datums” or foci that are “rigidly attached” to the CGH or Fresnel plane substrate and move in six degrees of freedom with the substrate.

THIS CONCEPT IS MORE EASILY SEEN BY CONSIDERING A GRATING PATTERN FOR A FRESNEL SPHERICAL MIRROR AS SHOWN IN FIG. 1.

Fig. 1 Chrome on fused silica Fresnel zone pattern for a spherical mirror. The extraneous artifacts that look like contamination is contamination from incomplete cleaning of the pattern

This two-dimensional Fresnel zone pattern will reimage a point source placed at its center of curvature exactly the same as if it were a three dimensional solid spherical mirror and will re-image the point source in transmission as though it were a solid lens. It is obvious that if this pattern moves in three degrees of translation and two degrees of tilt the center of curvature will move with the substrate. For a Fresnel mirror of an off-axis ellipse or hyperbola with two foci not on a line perpendicular to the substrate, the foci will move in all six degrees of freedom with the substrate.

Thus the center of curvature or foci move with the substrate as though they were rigidly attached even though you cannot see or physically touch the foci. The foci are only visible by putting a point source of light at one focus and viewing the reflected point image at the other. The CGHs behave the same way. The aspheric wavefront they produce moves with the substrate. If you know where the substrate is in space (and the design of the pattern) you know by analysis where the foci are and vice versa.

THE PROBLEM IS HOW DO YOU RELATE THE FOCI TO THE SUBSTRATE SO THE FOCI OR ASPHERIC CGH PATTERN ARE PRECISELY LOCATED WHERE YOUR OPTICAL DESIGN SPECIFIES.

One solution is to print spherical Fresnel zone patterns at known locations relative to the main pattern during the same process as the main pattern is written. Then you know the centers of curvature of the Fresnel patterns relative to the main pattern with a precision on the order of tens of nanometers. Now the challenge is to turn these virtual centers of curvature into something physical that can be probed with a coordinate measuring machine, a laser tracker or to serve as seats for a kinematic mount.

We follow an idea first described by Laura Coyle¹ where steel balls were centered on the spherical Fresnel mirror patterns but modify the concept to make it what we think is more practical to implement. What we will describe is not the only method. A commercial vendor of CGHs is using another method that is an offshoot of the Coyle method².

Instead of mounting balls directly to the CGH substrate, a method we found awkward and tedious³, we attach spherically mounted retroreflector (SMR) nests to the substrate over the Fresnel patterns to give a more solid mounting method and to reduce the final height of the attachment except for when metrology is needed.

Fig. 2. A ½” Grade 5 steel ball seated in a ½” SMR nest manufactured so the center of the ball is ½” above the bottom of the nest

Because this variety of SMR nest is made so that it holds the center of the ball ½” above the bottom of the nest within 10 μm, we specify that the Fresnel pattern over which the ball/nest pair are mounted have a ½” radius of curvature. We also specify where the centers of the Fresnel patterns are located in the plane of the CGH to the main pattern. This means we know where the Fresnel pattern centers of curvature are relative to the main pattern to tens of nm in the plane of the substrate and ± 5 μm perpendicular to the substrate.

FIG. 3 SHOWS AN EXAMPLE OF THE FRESNEL OFF-AXIS CONIC TO WHICH WE WILL ATTACH THE BALL/NEST PAIRS.

Fig. 3. Off-axis plane Fresnel conic mirror

The square patterns in the corners of the CGH in Fig. 3 are the patterns the vendor would use to position balls. The circular patterns just inside the square patterns are the spherical mirror patterns we will use.

In order to attach the nest/ball pairs the CGH is held firmly on a vacuum chuck beneath a PSM focused on the pattern. The CGH is tapped gently to center the Fresnel pattern (Fig. 1) under the PSM. Then the PSM is raised ½” to pick up the center of curvature of the Fresnel pattern. By first centering the PSM on the pattern itself it is easy to pick up the center of curvature because it is guaranteed to be in the PSM field of view.

WITH THE CENTER OF CURVATURE IN THE FIELD OF VIEW, THE SET REF POS BUTTON IN THE PSM SOFTWARE IS CLICKED TO CENTER THE ELECTRONIC CROSSHAIR ON THE RETURN SPOT AS IN FIG. 4.

Fig. 4 Screenshot of the electronic crosshair centered on the return spot to 0.1 and 0.4 μm in x and y respectively

WITH THE CGH STILL FIRMLY HELD, SEE FIG. 5, A BALL/NEST PAIR ARE SLID ONTO THE CGH AND ROUGHLY CENTERED OVER THE FRESNEL PATTERN, FIG. 6.

Fig. 5 CGH held on a vacuum chuck under the PSM centered on the Fresnel pattern.

Fig. 6 Ball/nest pair sitting on the CGH over the Fresnel pattern.

BY GENTLY TAPPING THE BALL/NEST PAIR THE REFLECTED SPOT FROM THE BALL CENTER CAN BE CENTERED ON THE CROSSHAIR TO LESS THAN 1 ΜM. IT TAKES A MINUTE AT MOST TO POSITION THE BALL/NEST PAIR TO THIS PRECISION. THE SCREENSHOT IN FIG. 7 SHOWS THE RESULT OF THIS ALIGNMENT TO 0.4 AND 0.4 ΜM IN X AND Y RESPECTIVELY.

Fig. 7 Reflected spot from the ball center centered on the electronic hair.

With the ball/nest pair centered on the crosshair now carefully add drops of cement at the nest/CGH interface while checking the PSM software that you have not disturbed the alignment of the pair. Five minute epoxy is a good choice for cement because it gives you a small time window in case the pair moves. Also, the epoxy will not “set” in 5 minutes. More like 10 to 15 minutes before it is safe to move the CGH to the next Fresnel pattern. After an overnight cure you may want to add a little addition epoxy to fully secure the nests. Fig. 8 gives an idea of what the drops of cement might look like.

Also, the cement tends to pull out into a thin hair when you pull your applicator away from the drop of cement. Make sure the hair does not fall on the main CGH pattern. It may be well to protect the pattern before cementing.

Fig. 8 Drops of cement at the base of the nest to secure the nest to the CGH.

In all it will take about an hour to secure all four ball/nest pairs to a CGH. It would be wise to wait a day before removing the balls from the nests as the balls are held in with a magnet and it requires some force to remove the balls.

When finished you will have four balls attached to the substrate within < 1 μm each of their ideal location in the plane of the CGH and within ± 5 μm perpendicular to the substrate. If more precision is required perpendicular to the substrate the nests can be lapped on fine silicon carbide lapping paper until the required ball/nest height match is met. The PSM can be used to determine this height by looking in at the side of the ball where there is the higher lateral sensitivity.

¹ L. E. Coyle, M. Dubin, and J. H. Burge, “Locating computer generated holograms in 3D using precision aligned SMRs,” in Classical Optics 2014, OSA Technical Digest (online) (Optical Society of America, 2014), paper OTh1B.2.
https://www.osapublishing.org/abstract.cfm?URI=OFT-2014-OTh1B.2

² Arizona Optical Metrology LLC, http://www.cghnulls.com

³ Parks, R. E., “Optical alignment using a CGH and an autostigmatic microscope “, Proc. SPIE, 10377, 103770B (2017)

⁴ Hubbs Machine & Mfg. Inc., https://hubbsmachine.com/

How Repeatably Can the Point Source Microscope Find Best Focus at a Center of Curvature?

Written by csadmin on February 20, 2021. Posted in News. No Comments on How Repeatably Can the Point Source Microscope Find Best Focus at a Center of Curvature?

Recently, a client asked how well can you focus if you really had to do better? I did not know but it was easy to do an experiment with our centering station that has a motorized stage and the ability to log data as the stage moves.

It is easily demonstrated that the PSM lateral sensitivity to centroiding on a return reflection from a center of curvature is better than 1 μm with a 10x objective. In the usual case the sensitivity is better than 0.2 μm. However, the sensitivity axially, or in the direction of focus is less sensitive, typically ± 2-3 μm judging by the size and shape of the image on the video screen.

WAS I SURPRISED BY THE RESULTS!

Using our centering station I got repeatability of better than 0.1 μm using the center of a 1/8” steel ball as my mirror and a 10x objective with a NA of 0.25 on the PSM. Classically, the depth of focus is λ/2*NA or about 0.635/.5 = 1.27 μm in this case.

To do the experiment to find focus you have to adjust the shutter speed on the PSM so there are about 10-15 pixels above threshold at what appears from the video screen to be best focus. The area designation on the PSM control panel is a count of the number of pixels above threshold so the illumination is easy to set to get the right number of pixels. Then you scan through where you expect best focus while logging the number of pixels above threshold as you scan. These data are saved to a file that is then copied to Excel. When the data of number of pixels versus scan position are plotted as in the graph below you can fit a second order polynomial as shown in the equation on the chart.

Remembering that we can find the maximum of the curve by taking the derivative and setting it to zero, we get -2*81691*x -707493 = 0, or x = 4.3303 mm. When this scan was repeated another 4 times I got 4.3303, 4.3302, 4.3303 and 4.3301 mm as the scan position at maximum pixels above threshold. This represents repeatability of less than 0.1 μm even though the data are rather noisy due to the small number of pixels used in the data.

This experiment points out the advantage of using a digital camera on the PSM. Without the ability to digitize the intensity at each pixel it would be impossible for this process to work.

The exact set of parameters used in this experiment may not be optimized, but this data shows the remarkable sort of focus repeatability that can be achieved with the PSM. It may be possible to do even better.