There is an incredible amount of interest in testing mirrors using Interferometers and we are always being asked if testing with Interferometers is better than a conventional Null test?
H*6W q The answer is a resounding "No"
{G-k NU Interferometers cannot compete with the "Time Honoured" method of a knife edge and the human eye in a Double Pass Null test for accuracy. If they could, we would be using an Interferometer instead of conventional methods.
!~Z"9(v'C But it is amazing the faith placed in an Interferometer result! We are occasionally getting challenged about the specification of our mirrors on the basis of a poor Interferometer test. There seems to be a semi religious belief that the Interferometer result is correct and our method is wrong, - when in reality it is the opposite way round!
SWLo|)@[/ Even firms in the optics industry who should know better are being taken in by Interferometer results. We are making some information available on the level of accuracy that can be expected from our tests compared with Interferometer tests.
Zd& S @Z "Conventional Methods" - The Double Pass Null Test
2zpr~cB= 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 test of a parabolic mirror.
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JS77M-A c h];I{crh The diagram adjacent shows the basic arrangement of a parabolic mirror set up under test 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.
X?Au / 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.
kVL .PY\K 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.
p[cX O= 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.
I:.s_8mH} 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. While 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 he has been led through the test once, - he would probably be able to repeat it on his own.
Ss`LLq0LO The point being made here about the Double Pass Null Test is that if you have access to an optical flat, - through an Astronomy group for instance? - all the other equipment is easily made or readily available and the test is easy to do.
PW4q~rc=: 
SA z 9FX-1,Jx 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.)
D,6:EV"sa E.f%H( b In practice, it's 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.
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s @C}P [
3Hf Q 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.
`x|?&Ytmf9 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 rest of the mirror will still be light.
N ;gfbh] 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.
16 $B> So once the test is set up and adjusted, only one movement of the micrometer is needed to take the test results.
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W4N{S.#! XilS!, There is a relationship between the Focal Ratio of the mirror and the horizontal movement of the knife edge to work out the error on the mirror.
*8Z32c+C An easy way to show it is a graph like the one adjacent.
>V~E]P%@ From one simple measurement and the use of a graph, the Double Pass Null Test directly measures the error on the surface, (or on the Wavefront of course!)
z:;CX@)* The knife edge movement is not great. A typical value may be around 0.1mm. This might at first seem small and difficult to measure, but that's 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 its 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.
HV.t6@\}; An advantage is that the testing method involves only one movement of the micrometer.
^s=8!=A( So What Could Go Wrong With The Double Pass Null Test?
v1[29t<I! 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 were suspected with an optical flat, - then a Null test can be repeated using a different part of the optical flat. Then the optical flat can be rotated on its axis (say 90 degrees), and the test done a third time. Any difference between the three test results would suggest a problem with the optical flat. The Double Pass Null test therefore has an easy method of checking for problems with the only part that matters, - the optical flat.
*or(1DXP8 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 as the settings are known.
kl`W\t F 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 at the centre of curvature. A 1/10λ mirror on a double pass shows the same error as a 1/5λ mirror tested at the centre of curvature.
/ +\ 9S The strengths of the Double Pass Null test are as follows:-
uc=B,3 - 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.
Testing Using An Interferometer
99S ^f:t 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.
eIlva? 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 is supposed to indicate an error in the object being tested,- but all too often, we are finding that the error is really in the Interferometer setup!
{FG j] * 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. The 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.
s >en So the method most often used for Astronomical mirrors is "Fringe Analysis" and this technique operates as follows.
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OPi 0~s S:Hl/:iV 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.
?CZd Ol 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, - and that is often, - but not always, the case with an Interferometer.
-12U4 h<e 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's more straightforward to understand. Once the principle behind one type of Interferometer is understood, it should be easy to understand the other types.
VQs5"K" 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.
J05e#-)<K C+]I@Go'Tk 
5\ v3;;A[ 92c HwWZ! 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 apart 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.
?5p>BER? It is admitted the final results are output 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.
LscG Ts, 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's a good picture, - Look closely, - Note that it's not even and has differences in the shadings of grey across the lighter areas.
W/ \g~=vo 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.
9^x> 3Bo 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.
vIvIfE In our experience it is common to see Interferometer results suggesting that there are several "peaks" spaced around the edge of a mirror. These results imply the mirror is asymmetric.
=%7-ZH9 If asymmetry really existed it would of course clearly show up in a Double Pass Null test, or an even simpler test with an eyepiece. Real astigmatism is rare in professionally made mirrors due to the methods used to figure the mirrors. We suggest errors in locating the centre of a fringe correctly are responsible for a lot of perceived asymmetry rather than genuine faults on the mirror surface.
t7pFW^& 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.
0"R|..l/ Even if the lighting and CCD camera are perfect, it is possible 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, that views the results over a few seconds and discards air movement.
]iW R o' Spherical & Parabolic Shapes
*i,%,O96Nz The description above is of a flat surface, there has to be 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 an F/ ratio slightly faster than the mirror under test.
*Ly6`HZ9 If you are going to use a Interferometer to test a Parabolic mirror, then the best arrangement you can possibly use is the double pass optics straight from the Null test! You need the same optical flat from the Double pass Null test.
[7-?7mp!B A very accurate lens is needed to convert the collimated light beam to a spherical Wavefront within say an accuracy of least 1/20λ. Of course the reference flat within the Interferometer wants to be at least this accuracy as well. You now have at least three elements instead of one that need to be extremely accurately made.
3^ClAE"8 
l}h!B_P' And you have just got yourself a lot of problems aligning the optics up. Counting the Interferometer optics as one unit, you now have four sets of optics to line up and space correctly. You will need to:-
2eogY# _g8yDfcLG - Line up Interferometer, Parabolic Mirror & Lens up accurately on the same axis
- Check Parabolic Mirror, Optical Flat and Lens 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 and if the distance between the mirror and the lens is not absolutely correct, the mirror will not appear parabolic.
N+ |d3X! Putting the lens spacing issue another way - If this dimension is slightly wrong, - the mirror will often appear to have a large bump in the centre. We do see lots of Interferometer pictures showing this effect.
xo )P?- There are controls on the Interferometer that use internal software to attempt to correct for set-up errors. You will see 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 them out. So while these controls can take a lot of the set-up error out, what is left is reported as errors on the mirror surface. If you want an accuracy better than 1/10λ, these errors are often significant.
]|@^1we We are not aware of an easy method to set up the full Interferometer system other than by simple trial and error, using the mirror results as the trials.
)+^+s d So 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 poorer than it really is.
VUc%4U{Cti Finally, - You may wonder why you would ever bother with an Interferometer test if you already had the optical flat for a Double Pass? - We think that's a very Good Question!
} \f0 A- There are ways of testing without the Double Pass, but they are not as accurate because they lose the prime advantage of the doubled error.
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sA~]$A;DM! b>W %t The other methods test the mirror at the centre of curvature instead of the focal point. 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.
sKWfX Cd 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 it also needs centring and lining up with the other optics.
i%/+5gq We have heard of another method being used. The Ross correction lens can be left out and the fringes deliberately created from the spherical aberration can be used instead of tilting the reference flat. Although we are aware 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 fraction of a wavelength could ever be achieved with it.
B~mj 8l4 This will not stop the computer in the Interferometer offering a result, - but could you trust it to be accurate to a fraction of a wavelength? - We certainly don't think you can!
wzA$'+Mb 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.
aX VFc5C\ 
zA 3_Lx! 1 zZlC# V But it's worse that that! - 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?
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So where the exact optical centre of this fringe?
#E[0ys1O 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.
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F
[M,]? !i50QA|(G 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), off axis. This does give some fringes across the centre of the mirror but they are now curved and of variable width instead of straight. Now they are curved and with different densities of grey each side, - It's again difficult to work out where the centre of the fringes are.
mw!F{pw Can you say where the centres of the fringes are in this adjacent picture? - You will need to consistently get within say 1/20λ, to achieve the sort of accuracy required.
`uFdwO'DD And remember! - these are ideal pictures generated by computer and not the real output seen by the Interferometer CCD camera, which may be affected by uneven lighting, uneven CCD response and any air movement happening at the time!
<%d>v-=B We would have liked to offer you a picture of the fringes for a 20" F/4, but the fringes are far too crowded to show on a picture that would fit on this page.
HQ g^
h The strengths of Interferometer Testing are:-
^~dWU> - 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.
That last part of the statement is certainly true - It does make people believe it has an impressive accuracy!
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xH7? tsf We don't often get chance to have a set of our mirrors sent all over Europe for testing. Most buyers of our mirrors are waiting to put their mirrors into a telescope! However a series of incidents from late 2004 where our mirror figures were questioned by a competitor using an Interferometer led to a recent series of tests using two different Interferometer testers and another pair of testers who use the Double Pass Null. We can offer real comparisons between three mirrors. The figures are all PV on the Wavefront.
Q8NX)R rH-23S #
1 Jonathan Owen did report some very unusual low level Asymmetry on top of this figure, which we could see on our testing, but it did not invalidate the specification of 0.1λ.
\85i+q:LuA #
2 A preliminary test gave 1.4λ and the follow up report gave 0.7λ
"[J^YKoF #
3 Very unfortunately this mirror was damaged in transit to Germany.
WE?5ehEme For both the JR & BH mirror, - the results from Wolfgang Grzybowski suggested the mirrors had high points at the edge and were slightly asymmetric. This pushed the recorded PV figures up. We tested both mirrors and found no evidence of significant asymmetry, - although see below for more detail on the BH mirror.
tA;}h7/Lc~ Jonathan Owen & Es Reid are very well known in the optical industry in the UK. They both tested the BH mirror with a Double Pass Null Test. Although we sold the mirror simply "as better than 1/10λ", our own detailed measurements did closely agree with the figure they recorded of 0.06λ.
WJ#[LF!e 0.06λ is exactly how Jonathan Owen recorded it in his written report. As a fractional value it is 1/16.7λ.
Tbq;h ?D The very low level astigmatism commented on for this mirror reported consisted of 8 radial spokes. We could see it in our test as well, - but it was notable it was not seen or reported by either Interferometer test. We believe the error was too small to be seen by the Interferometers.
Upe%rC( Although only one mirror was formally tested by Jonathan and Es in this series, - there is constant interchange between Oldham Optical and these gentlemen. Informal discussion, testing and comparisons are continually being done and we are completely confident that all parties deliver consistent results.
KPF1cJ2N The NA mirror was tested in the UK and then sent off to Germany. Unfortunately it became only the second of our mirrors to be damaged in transit in three years.
!zo{tI19 
T[gv0|+ (HVGlw'` Adjacent is an example of problems reported by an Interferometer at the edge of a mirror. The PV error in this case is of the order of 0.1λ, - but if not for the high point, it would record less than 0.05λ. The particular mirror that gave this result on the Interferometer was tested by ourselves and also by Es Reid and was not asymmetric as the Interferometer results suggest. It was almost certainly problems in locating the centre of a fringe at the edge, but air movement, or uneven lighting could have contributed.
";F'~}bDA It is pointed out that the mirror has to be fairly good before this asymmetry becomes visible, - say better than PV 1/4λ, but a simple search on the Internet will find large numbers of Interferometer pictures showing asymmetry just as described. The level of the asymmetry suggested in a lot of these results could easily be seen in a double Pass Null test, or an even simpler test with an eyepiece, If it really existed.
zfU{Kd We have been talking so far about good interferometer Testers. You can see from another column in the table that there are other people testing mirrors using interferometers and recording far worse results. To be quite fair to the firm in the table, - there are others out there just as bad. Please be extremely careful if you are considering an independent Interferometer test and you may want to ask for the following details first:-
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Ss, K-4PI+qQ\ - 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.
t_^4`dW` Conclusions
Y7|EIAU5Y Oldham Optical's Testing agreed very closely with another user of Double Pass Nulls. We expect all testers using Double pass Nulls to record close and consistent results. The accuracy of such tests should be better than say 1/30λ.
+%'( !A?*` Interferometer tests carried out by different testers are not consistent. We suggest that Interferometers are completely fine where the accuracy required is above a wavelength. For astronomical mirrors where the accuracy required is a small fraction of a wavelength, they become highly dependant on the equipment quality and the skill of the operator.
]G\}k There is a limit on accuracy imposed by the extra optics in the Interferometer and their results should always be worse than with a Double Pass Null.
\hXDO_U Interferometers results suggesting large smooth bumps in the centre of mirrors are much more likely to be errors in the Interferometer set-up or use.
d 0D] Q Where the mirror is better than say PV 1/4λ, Interferometer results suggesting problems at the edge of a mirror and asymmetry, are more likely to be related to the problems highlighted above.
rp$'L7lrX We believe the Double Pass Null test is more accurate and gives consistent results across different testers.
@dK Tx#gZ We believe our views are shared by most professional mirror makers.
)GpK@R]{ Oldham Optical will be continuing to use a Double Pass Null as the definitive test of a mirror.
vaLSH
xi Independent Testers
7dWS If you are considering an independent Interferometer test, then one of the best independent testers we have experience of is Wolfgang Gryzbowski. He can be contacted through our links page. Be extremely wary of some other Interferometer testers.
]Um/FA W If you are considering an independent Double Pass Null test then we will happily put you in touch with Jonathan Owen or Es Reid on application for their contact details.
OXA7w. ^ And Finally
~$'awY We may decide to re-test mirrors that are challenged by other testers, - but will of course charge for all the work involved when the mirror is found to be within specification.
h` q1 .A|udZ, 这个文章写的很好，希望对大家有帮助
