However, observing a few simple precautions will improve the results of the calibration.
These precautions are detailed in the “Instructions for Using CaliBall” in approximately the order they should be followed.
Topics discussed include the evolution of the classical autostigmatic microscope (ASM) into an all-purpose optical alignment tool whose use has been described in over 60 optical engineering papers that illustrate real-world systems applications.
The evolution that led to the current instrument, the Point Source Microscope or PSM, is due to a convergence in technologies of solid state light sources, digital cameras, modest cost computers and software to operate these devices to create a small, lightweight and ergonomic optical test instrument with many functions.
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.
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.
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).
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.
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.
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.
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 reflection
Confocal reflection
Notice Shutter and Gain with focus
Locating an ephemeral point in space with 3 degrees of freedom to μm precision
CONSISTS OF THREE STEPS:
If this concept is well understood all other applications are easy
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
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
Radius of convex side longer than working distance of objective, need extra lens
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
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)
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
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
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)
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.
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
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
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
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.
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
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.
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.
Configuration 1 shown for calculation of bfl
Grayed out lines are ignored
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
Radii, thickness and index are set as variables
Optimized with small entrance pupil for paraxial solution