Interferometers and Conventional Testing of Mirrors
We are often asked if testing with interferometers is better than a conventional Null test. The answer is a resounding "No".
For high accuracy in astronomical optics, interferometers cannot compete with the time honoured method of a knife edge and the human eye in a Double Pass Null Test. If they could, we would be using an Interferometer instead of conventional methods.
"Conventional Methods" - The Double Pass Null Test
What follows is a description of the Double Pass Null Test as carried out at Oldham Optical. This is the basic test we use on all large parabolic mirrors. The description is very simplified and is aimed at peak to valley (PV) measurement, but all the Double Pass strengths are brought out to illustrate why it is such a good test of a mirror. This test is also known as "auto-collimation" and most professional mirror makers agree with us that it is the definitive bench test of a parabolic mirror.
The strengths of the Double Pass Null test are as follows:-
Double pass shows double the error.
Test results obtained from one simple micrometer movement.
Measures error directly - No derived figures.
Can always measure to better than 1/30λ.
Only a good Optical Flat needed, rest of equipment can be "cheap and cheerful"
Easy way to check the Optical Flat by repeating test with Optical Flat moved or turned on axis.
Only accurate alignment of mirror and Optical Flat needed.
Therefore apart from a simple multiplication, the Double Pass Null Test directly measures the error on the surface (or on the Wavefront of course!) Figures as low as 0.11mm might at first seem small and difficult to measure, but that is exactly why the knife edge is equipped with a micrometer movement that can measure horizontal distance to an accuracy of better than 0.01mm.
So What Could Go Wrong With The Double Pass Null Test?
About the only thing that can is a problem with the optical flat. Ours are better than PV 1/20λ and are all tested by external Optical Engineers. If any problems are suspected with an optical flat then the problem may be in the optical flat support. - the optical flat can be rotated on its axis (say 45 degrees), and the test done again. Any difference between the test results would suggest a problem with the optical flat support.
The Double Pass Null test therefore has an easy method of checking for problems with the only part that matters, - the optical flat. Setting up a Double Pass Null Test involves only one accurate alignment. This is to line up the Optical flat at exactly 90 degrees to the mirror axis. This does entail both horizontal and vertical angle and generally takes about 15 minutes to set-up a new mirror the first time it comes off the polishing machine.
Subsequently it only takes about 1 minute once the settings are known. Finding the exact focus of the converging beam with the knife edge is easy and intuitive. The micrometer movement controlling the knife edge enables it to be found and set to better than 0.01mm in typically less than a minute. After this quick set-up, the remaining error on the mirror surface can be read off.
One of the strengths of the Double Pass Null test is in the name itself. Light reflects off the mirror twice, so that errors are doubled compared to testing on the sky.
The only disadvantage of the Double Pass Null is that the area directly in the centre of the system cannot be measured. This is because there has to be a central hole in the optical flat to allow the testing to take place! However in a Newtonian, the centre is obscured/covered by the elliptical flat and in a Cassegrain, the secondary mirror obscures/covers the central area. We always ensure when testing that the hole in the optical flat we use is smaller than the elliptical flat or secondary mirror to be used.
The diagram adjacent shows the basic arrangement of a parabolic mirror set up under test conditions facing an optical flat that has a central hole.
A point light source is set up near the focal point of the mirror and shines through the central hole onto the surface of the parabolic mirror. The light reflects back (parallel to the axis of the system) to the optical flat which reflects it back along the same path to the parabolic mirror again.
It reflects off the parabolic mirror a second time and returns to a focus near the original light source. In practice the light source has to be set up just slightly off axis so the focus of the reflected light can be accessed, or use a beam splitter to maintain axial symmetry. A knife edge is set up at the exact point of focus.
The knife has micrometer adjustments to allow it to be adjusted slowly and accurately into the returning light cone. The detector used in the Double Pass Null test is of course the "MK1 Eyeball". In our case the person wielding the eyeball has developed the skill from carrying out the test a great number of times. Whilst an amateur setting up this test for the first time would certainly benefit from being led through the test by a more experienced person, once they has been led through the test once, they would probably be able to repeat it on their own.
The next diagram is an enlargement of the light rays passing the knife edge. If the mirror is the perfect parabolic shape then all the rays of light will come together at the focal point. If the knife edge is moved on its micrometers it will be possible to find a single position at which all the light rays are cut off by the smallest vertical movement. The observer would see an instantaneous Null (total blocking of all light), as the knife edge is moved into the beam (vertical movement as shown on the diagram.)
In practice, it is not possible to make an absolutely perfect mirror, although some of us can get fairly close! When the parabolic surface is not absolutely perfect the light rays coming back will not pass through one fixed point. They will range around the nominal focal point.
In this next diagram the range is shown by the solid and dotted lines. Say in this next example that light rays from the centre of the mirror are represented by the solid lines and rays from the edge of the mirror are represented by the dotted lines. Everywhere else focuses somewhere in between. If the knife edge is adjusted to the same point as in the first diagram, then only part of the mirror (the centre), will be Nulled.
There will be a dark centre on the mirror where it is Nulled and the image on the outer areas of the surface will be dark and the other side will be light. Once at this position, horizontal movement of the knife edge will make the dark centre expand out to a ring and continue to expand out across the surface of the mirror.
The ring will reach the edge of the mirror when the knife edge is in the dotted position shown corresponding to the rays from the edge of the mirror. The horizontal movement of the knife edge needed to move from the Null at the centre to the Null at the edge is a direct measure of the surface error on the mirror. So once the test is set up and adjusted, only one movement of the micrometer, noting two positions, is needed to take the test results, this is complemented with a high power eyepiece.
There are plenty of texts giving the mathematical relationship between the horizontal movement and surface error and we are not going to explain them in detail here.
Using a 20" F/4 mirror as an example, the horizontal movement equating to PV 1/10λ error on the wavefront is 0.11mm or 0.0044". For a PV 1/4λ wavefront error, the figures are about 0.28mm or 0.011".
Therefore apart from a simple multiplication, the Double Pass Null Test directly measures the error on the surface (or on the wavefront of course!)
Figures as low as 0.11mm might at first seem small and difficult to measure, but that is exactly why the knife edge is equipped with a micrometer movement that can measure horizontal distance to an accuracy of better than 0.01mm.
Mechanically the set-up can theoretically measure PV Wavefront on our 20" mirror to an accuracy better than 1/100λ.
However it is not quite as good as that because the exact position at which the Null reaches the edge of the mirror is partly subjective.
Some figure better than 1/30λ is readily achievable. An advantage is that the testing method involves only one movement of the micrometer.
Testing Using An Interferometer
An Interferometer can be built from scratch, but they may be proprietary devices bought from a specialist company. "Zygo" is a very well known and respected brand name but there are others. Interferometers use two main techniques to measure errors on mirrors. The technique most often used for Astronomical mirrors is called "Fringe Analysis". In this method an Interferometer is set up to generate fringes between the object under test and a reference object.
The fringes are then compared with an ideal set of fringes generated by a computer. Any difference between the two sets should indicate an error in the mirror under test but at times the error is in the Interferometer setup!
The method will be covered in detail later, but first a brief description of the other technique, with a caveat that it is not often used.
This second technique is called "Phase Shifting Interferometry" It requires a more expensive Interferometer capable of automatically shifting components in the optical path a known amount during a succession of individual tests.
Each individual test is similar, but a bit different to the "Fringe Analysis" method so when the results of all the tests are then summed together in the controlling computer, it can remove some of the errors in the Interferometer set-up and give a more accurate set of results. Unfortunately this equipment is generally too expensive to use on Astronomical mirrors and we rarely see it used in practice.
So the method most often used for Astronomical mirrors is "Fringe Analysis" and this technique operates as follows. The simplest example of how an interferometer generates fringes can be seen from the description of elliptical flat testing elsewhere on our website and partially repeated here.
For elliptical flats - the flat is compared against a known good reference flat. This is done by taking a known good optical flat and just simply laying the elliptical flat to be tested on top of it. The air trapped between the two glass surfaces is sufficient to cause a slight angle and generates fringes. With this set-up, the fringes are 1/2λ apart. From the resulting fringes, the quality of the flat can be judged. In the case of a flat we are looking for straight fringes.
An Interferometer has to be more complicated because the reference flat and the piece under test are physically separated.
There are several ways to construct an Interferometer and we have chosen one method to describe in detail. We chose this method primarily because we feel it is more straightforward. Once the principle behind one type of Interferometer is understood, it should be easy to understand the other types.
In this method - a point light source is first converted to parallel light using a lens system and fed to a beam splitter. Part of the split beam is reflected off the reference flat and part off the piece under test. The two returning light beams are recombined and fed to the observer or a detector like a CCD Camera.
Usually there is a deliberate small angle on the reference flat to generate fringes. Instead of the "Mk1 Eyeball", the detector in an Interferometer is usually a CCD camera. This takes a picture of the result and feeds the information into a computer. The computer looks at the various blacks, whites and shades of grey in the picture fed from the camera.
We understand it tries to locate the centre of the black fringes. It then decides if the fringes are straight lines and each straight line is a constant distance from its neighbours. If it sees deviations from straight lines, or differences in distances between the lines, it works out what the deviations mean in terms of error on the mirror surface.
It is admitted the final results are presented in a far better form than any Double Pass Null Test! You can have coloured 3D pictograms and tables of figures attractively printed out. This all sounds simple, but there are hidden issues in the system that are virtually never explained.
The CCD Camera is reporting levels of black, white and shades of grey to the computer. The sample picture above is very typical of such a picture. Although it is a good picture, look closely - Note that it is not even and has differences in the shadings of grey across the lighter areas. This is not too bad if the fringes are straight and towards the centre of the picture.
The computer must estimate where the centre of the fringes are and if the fringes are straight and well away from an edge the computer processing may deal with the shadings fairly well. However - we suggest the technique has problems at the edge of the mirror. Here it may have only part of a black fringe with no "white" area outside it to use as a reference when fixing the fringe centre. It cannot be as accurate in these areas.
If it makes an error in estimating where the centre of the fringe is, then the results will suggest the mirror has errors at these points around the edge. To give evenly lit pictures the Interferometer must have a light source and collimation system that gives a very even brightness across the full field of view of the beam splitter. In practice the single lens system shown in the diagram above would certainly not be sufficient.
It is not often considered that the CCD Camera used as the detector must have a very equal response from all its pixels. Problems with uneven lighting or pixel areas in the detector with different responses have the potential to affect the results.
Even if the lighting and CCD Camera are perfect, it is possible that air movement at the time the test picture is taken may affect the results. This could in theory be countered by taking a number of pictures and comparing them to see if air movement was an issue. However our opinion is that it is not as good as the human eye and brain used in the Double Pass Null test, which views the results over a few seconds and discards air movement.
The description above is of a flat surface, there are additional complications to test a spherical or parabolic surface. The usual technique is to convert the flat collimated light beam from the beam splitter to a spherical wavefront with an additional lens. To give the greatest accuracy, the lens must have a F/ ratio slightly faster than the mirror under test. A very accurate lens is needed to convert the collimated light beam to a spherical wavefront within say an accuracy of least 1/20λ and the reference flat within the Interferometer needs to be better than that accuracy.
Then assuming that a double pass system is being used, the optical system is as below.
Spherical & Parabolic Shapes
A parabolic mirror can be tested at the centre of curvature instead of at the focal point, but in doing so the accuracy drops by at least half. The large optical flat is not required, but if nothing else was done to the optical arrangement, there would be a large amount of spherical aberration.
To counter this, an extra lens known as a "Ross Correction Lens" can be inserted into the system to correct for spherical aberration.
This means there is yet another very accurate optical part needed and that also needs centring and lining up accurately with the other optics. But this is a common method used by interferometer testers to avoid the expense of an optical flat.
There are now three elements instead of one that need to be extremely accurately made. There may also be problems aligning the optics. Counting the Interferometer optics as one unit, there are four sets of optics to line up and space correctly.
It is necessary to:-
Line up Interferometer, Parabolic Mirror & Lens accurately on the same axis
Check Parabolic Mirror, Optical Flat and Lens are each set at 90 Degrees to the axis
Check distance between Mirror and Lens exactly correct
You need to be extremely accurate with these settings because you are looking for errors less than 1/10λ. If any of these settings are wrong the Interferometer will give an incorrect result. Anything off axis will suggest Astigmatism in the mirror. Anything not at 90 degrees will suggest Coma.
Examples of how small an error in positioning an optical element and the error it causes are given later.
There are controls on the Interferometer that use internal software to attempt to correct for set-up errors. There are options to remove "Coma", "Astigmatism" & "Piston" errors due to set-up.
However, we suggest that there are too many variables in the equations for it to completely null the image. So while these controls can take some of the set-up error out, what is left is reported as errors on the mirror’s surface under test. If you want an accuracy better than 1/10λ, these errors are often significant.
We are not aware of an easy method to “set-up” the full Interferometer system. One method we know of starts by examining the output to minimise "S" shaped fringes.
Seeing "S" bends in the fringes suggests coma in the system due to one or more of the optical components not being at 90 degrees to the axis. The tester adjusts settings to minimise the "S" before continuing the testing. If you can see "S" bends in the Interferometer report, its extremely likely it was not set up accurately.
It seems setting-up an interferometer is really trial and error. The various optical parts are shifted around until the errors seem to be at a minimum that gives the straightest fringes. The problem in doing this is that the error on the mirror is extremely small to start with.
It can easily be covered up by the set-up errors.
Those errors may interact with each other and the real error to produce a false minimum, which the tester cannot detect.
Setting up an Interferometer is more difficult compared to a double pass Null test. We are not saying it can't be done, but it is highly skilled and, if it is not done properly, the results from the Interferometer will suggest the Mirror is a lot worse than it really is.
Oldham Optical has attempted at various times to talk with some of the interferometer testers. We have found it extremely difficult to get meaningful information on either the optical arrangements, the method of setting up the test, or how the interferometer software attempts to eliminate set-up errors. I am afraid our experience has been that the testers are unwilling or unable to answer detailed questions.
We arbitrarily placed the Ross lens 300mm in front of the interferometer on the optical axis (Z axis) and then optimised the Ross lens radii until it achieved a value better than 1/20λ PV. The result is the picture at bottom right in Fig 1.
Once the system was set up and optimised, we deliberately moved the Ross lens 3 mm along the axis.
A small shift of the interferometer position was then needed to allow the out going and return beams to coincide in the interferometer. The result is Fig 2 adjacent.
This suggested a error a little worse than 1/3λ. Just to make this clear - This means if an Interferometer was used to test a perfect mirror with the Ross lens 3mm out of position along the axis, it would appear that the mirror had a PV of 1/3λ when it was in fact a perfect mirror!
1mm movement would suggest the mirror was about PV 1/10λ out.
We then moved the Ross lens back to its correct position at 300mm along the axis and then shifted it off the optical axis (Y axis) by 3mm.
The result is Fig 3 adjacent
This position gives 1 1/2 fringes of astigmatism,
So a mirror tested at these settings would appear to be PV 1.5λ out which is a massive amount in an astronomical mirror!
Scaling that back to get an accuracy of 1/10λ requires the Ross lens to be positioned within 0.2mm of the optical axis of the system.
We would find it very informative if an interferometer tester can explain how he positions the Ross lens on the optical axis to the accuracy needed - And then how he determines where along the optical axis to position it. But if he cannot position the lens accurately, he cannot obtain accurate results from the interferometer testing.
This example is just about positioning the single Ross lens in relation to the mirror. We have not considered the alignment to the body of the interferometer or the placement of the extra lens used to convert from a flat to a spherical wavefront. If one lens and mirror cannot be positioned properly, then how can the other optical items be correctly aligned?
We know of yet another method being used: the Ross correction lens can be left out and the fringes created from the spherical aberration can be used instead of tilting the reference flat.
Although we are aware that this method has been used on some mirrors, a 20" F/4 would show about 54 fringes from spherical, and straightaway it is difficult to see how accuracies within a typical RMS of 1/35λ could ever be achieved.
You are be asking the interferometer plus all the lenses in the set-up to have a total accuracy to better than 1/10 of a percent! The computer has the job of subtracting the fringes seen in this set-up from what a perfect mirror would give and use any remainder to calculate the error on the mirror surface or Wavefront.
This will only leave extremely subtle shades of grey to calculate error from. Spherical aberration produces circular fringes and they are not regularly spaced: there will be a big gap in the centre of the mirror and the fringes would crowd together towards the edge of the mirror.
This will give poor accuracy in the centre within the first fringe. There will also be accuracy issues at the edge due to the fringes being extremely close together.
The picture adjacent is of the idealised fringes from a 6" F/8 generated by computer. If you look carefully at the inner black fringe in this picture, you will note a well defined outer edge with a sharp transition between black and white, but the inner edge of the fringe is less distinct with more and longer shades of grey.
This would indicate that the real optical centre of the fringe may be nearer its outer edge than in the physical centre of the black band, where you may be tempted to place it. So where is the exact optical centre of this fringe?
There are no fringes in the centre of this picture, so the computer may try to work solely with the level of grey. If the light source does not produce even illumination across the width of the picture or the CCD response is not perfect, the Interferometer results will suggest there is a bump in the centre of the mirror.
To counter this, the mirror, or the internal reference in the Interferometer, can be tipped slightly off axis again. The picture adjacent is the idealised computer generated fringes from the 6" F/8 tipped 2.5 waves, (5 fringes), and set at “best fit”.
This does give some fringes across the centre of the mirror but they are now curved and of variable width instead of straight. Now that they are curved and with different densities of grey each side, It is again difficult to work out where the centre of the fringes are.
The tester is expecting the interferometer software to note the errors in the set-up and subtract them from the final result. For this test we show the final result adjacent to the fringes. If you consider the surface underneath the black line superimposed, the shape of the mirror under the line is again an "S" curve.
This is coma caused by some misalignment in the set-up. It is unlikely the interferometer software can correctly isolate and subtract the error due to the coma especially if or where there is another small error like astigmatism or the set-up is not quite on the focal length. The result will appear as an apparent error on the mirror.
How are we sure its errors in the set-up and not in the mirror - That's dead easy - we can't make mirrors with shapes like this!
The process of grinding, polishing and figuring a mirror is basically rotary and is symmetrical. Astigmatism is removed by the mirror maker in the early part of the process. Therefore any errors in the mirror will nearly always be symmetrical. Either not quite the correct curve on the mirror or perhaps some circular zones.
ERR - No zones on our mirrors, - thank you very much!
So seeing an "S" curve on the fringes and then on the mirror profile is a "Dead-Give-away" that the interferometer set-up was incorrect and the software was unable to process the results correctly. We have just mentioned coma so far. There is probably also some astigmatism in the set-up plus some spherical aberration caused by an incorrect distance between the various optical elements. Then there is the real error on the mirror. We suggest there are too many terms for it to properly separate out the real error. This test reported the PV error on the mirror was 0.5λ.
But its certainly a pair of very nice pictures for the test report. There can be no argument it looks extremely professional - This might help convince you the test is accurate.
The error from poor set-up is still the dominant error in this test. Even with just the small bends at top and bottom of the fringes to suggest coma, it's still impossible to derive a meaningful figure for the real error on the mirror surface. This test reported the PV error on the mirror was 0.14λ.
Certainly we can speak for ourselves and probably a lot of other professional mirror makers, that any error remaining in our mirrors is predominantly symmetrical. Probably due to not quite having the correct curve. But still within specification! Any signs of asymmetry in Interferometer test results point to difficulties in the Interferometer set-up.
Next is a mirror test result that has the mirror looking more like a bent bottle top!
Unless someone can give us a better explanation we believe its an example of where a dark fringe lies along the edge of the mirror and the interferometer software can't interpret it accurately. In this case its happening on opposite edges at east and west.
This is mentioned as a problem earlier on this page On the edge of the mirror the interferometer may have only part of a dark fringe with no "white" (actually green in those pictures), area outside it to use as a reference when fixing the fringe centre.
We believe the interferometer software cannot reliably find the centre of the fringe at these positions so introduces an error. This particular test reported the PV error on the mirror was PV 0.2λ.
Interferometers are very good at producing impressive reports. Unfortunately that can inspire over-confidence in their results.
We suggest that Interferometers are completely fine where the accuracy required is above a wavelength. However Astronomical mirrors are large in comparison to interferometer optics and the accuracy required is a small fraction of a wavelength. In this area test results from Interferometers become highly dependant on the equipment quality and the skill of the operator. In practice there is no easy way to set-up an Interferometer test so no way of avoiding errors creeping into the set-up. Undetected errors in the set-up appear as apparent errors in the mirror under test.
Even if the set-up is perfect and the tester is absolutely superb, there is a limit on accuracy imposed by the extra optics in the Interferometer. Results will be less accurate than those obtained with a Double Pass Null.
Along with most other professional manufacturers of astronomical mirrors, we believe the most accurate method of testing a mirror remains the conventional Double Pass Null Test.
Since this is virtually all due to the peaks at the east and west edges, and they are probably errors in locating the fringes, the mirror was really extremely good and certainly better than 0.1λ.
We will repeat yet again that any errors remaining in a professionally made mirror ought to be symmetrical. Any sign of asymmetry in interferometer reports ought to be a "Dead-give-away" that there were problems in the Interferometer set-up or the software interpreting the fringes.
It is possible to simulate the setup of the various optical elements and then move one of them to see the error it introduces. Using the ray tracing programme Zemax, we have set up an example of a parabolic mirror with a Ross lens being tested at the centre of curvature.
In this example shown (Fig 1), the mirror is a 200mm diameter F/5 parabolic mirror with a Ross lens tested at the centre of curvature. The basic optical layout of the mirror with Ross lens and focus position is shown at bottom left with the “Prescription” for the optical system above it.
Another thing that intrigues us about Interferometer testing is we often see test results suggesting a mirror has astigmatism, but it does not appear that the very simple test for astigmatism using an eyepiece is carried out to confirm the astigmatism exists. Astigmatism is very rare in a professionally made mirror. If this simple test confirmed that no astigmatism exists, then any results from an interferometer suggesting otherwise are wrong and probably due to an incorrect setup.
We believe this simple test for astigmatism is crucial. We believe a mirror should always be proved free of astigmatism before any other bench testing is carried out. This test is always carried out on our mirrors before they go for the Double Pass Null.
Then we have confidence there is no astigmatism in the mirror. We believe this simple test should also be applied before testing with an interferometer.
The strengths of Interferometer Testing are:-
Able to sample tens or hundreds of points on the mirror and calculate RMS & Strehl ratio quickly.
Results can be highly customised. It can produce highly impressive reports containing pictures, graphs, 3D pictograms and tables of figures.
The attractive reports inspire confidence in the testing and imply it has an impressive accuracy.
(We don’t agree about the impressive accuracy of course!)
If you are considering an independent Interferometer test, you may wish to clarify the following details first:-
The Model of Interferometer to be used
Confirm the method [Fringe Analysis?] [Double Pass Optics?]
A full diagram of the optical path used for the tests
Details of any additional optics used; Including Lens details; F/ ratios; focal lengths; Distances & Spacing
Method of setting up and use of the equipment
Any ancillary equipment or programmes used to process and produce the results.
If you have problems obtaining these basic details, then you might choose to look elsewhere to get your mirror tested? You might also ask for the test on your mirror to be done twice - repeated with the mirror rotated through 90 degrees.
"Dead-Give-Aways" For Interferometer Set-up Problems
If you do get an interferometer test done, there are some things you can look for in the interferometer report that indicate it was not performed adequately. All below are examples seen in Interferometer test reports.
The first thing is do the results look central? If it does not look central something in the optical set-up is off-centre and that is going to introduce errors like coma and astigmatism. (Most reports we see do show some astigmatism, which if it was really there would be easy to test for on the sky!)
An obvious example of something off centre is adjacent.
Much more serious is obvious coma in the interferometer results. The test report you receive will usually have a picture of the wave-front as seen by the interferometer. An example of this is shown below in the left hand picture.
If you see "S" bending in the fringes, like in this example below, the report probably wont explain this is coma due to errors in the interferometer set-up. One or more of the optical elements involved was not quite on axis or was at a small angle to the axis.