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?
-Pa R&0Tt The answer is a resounding "No"
GQYB2{e> 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.
+&.39q ! 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!
NCVhWD21| 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.
++BQ==@ "Conventional Methods" - The Double Pass Null Test
$49;\pBZl 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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Gkb[H&RZ SP4(yJ y& 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.
Q zY5S0 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.
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8}n 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.
nq\~`vH|Gd 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.
`We?j 7O 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.
9O\yIL 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.
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\*Z:w3;r G@U}4' V9 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.)
# 'I<q 2^)_XVX1 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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cXNR<` 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.
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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.
NW` Mc& 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.
OpmPw4?} 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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q& esI / }(\P@Z 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.
of>H&G)@ An easy way to show it is a graph like the one adjacent.
~n%]u! 6 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!)
eIbz`|%3 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.
V=E5pB`Pr An advantage is that the testing method involves only one movement of the micrometer.
@eP(j@(^ So What Could Go Wrong With The Double Pass Null Test?
!!6g<S7) 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.
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;Q|h$ n 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.
A bB+<0 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.
_+<AxE 9\ The strengths of the Double Pass Null test are as follows:-
EV_u8?va - 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
X\5EF7 :S 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.
o ot kf = 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!
1n# {c5T 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.
>[g.8'hI So the method most often used for Astronomical mirrors is "Fringe Analysis" and this technique operates as follows.
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cUwR6I9 T!|-dYYI 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.
ygxaT"3"= 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.
Q7_#k66gb7 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.
70Ei< 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.
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72dd% Nk?L<' 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.
wpOM~!9R 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.
C <H$}f The CCD camera is reporting levels of black, white and shades of grey to the computer. The sample picture above is very typical of such a picture. Although it's a good picture, - Look closely, - Note that it's not even and has differences in the shadings of grey across the lighter areas.
/brHB @$ 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.
3*e )D/l m 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.
6G:7r [ 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.
ZSn6JV'g 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.
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