On the subject of optical testing and rating: (How Astro-Physics Inc. rates their optics)

Much controversy now exists between claims from various manufacturers about the wavefront rating of optics, especially apo lenses. Markus [Ludes] has asked me to clarify my position on this subject, so that further confusion between wavefront ratings can be seen in light of reason, and further attacks against manufacturer's credibility can be avoided..

Manufacturers use interferometers to compare the wavefront errors of a finished optic against some reference standard. In the case of the interferometer, it is a reference sphere of known high quality which is used to form interference fringes with the optic under test. When testing a mirror, it would not matter what wavelength was used, since mirrors are totally achromatic. In the case of lenses, it matters greatly what wavelength is used, since there is typically only one point in the wavelength range where the lens was nulled or figured by the optician. Testing at another wavelength almost always results in a lower wavelength rating.

There are numerous methods for measuring and interpreting the results, so that testing the same optic on several different interferometer systems can result in different wavefront numbers. Typically, an optician will adjust the interferometer to display 6 to 8 lines across the aperture. Computer software then measures the deviation of these lines from parallelism, and assigns wavefront errors to the interferogram. These are sometimes further broken down to elements such as spherical error, astigmatism, coma, etc. This is repeated a number of times with the fringes tilted to various angles, and the reference optics, mirrors and beamsplitters may be rotated to eliminate any possibility of local errors being added to the test optic. The results are averaged in order to get a more accurate and realistic picture of the aberrations. These averaged results usually have the same RMS rating, but may result in better P-V ratings due to the cancellation of systemic errors.

There are some systems that use hundreds and even thousands of very tightly spaced fringes (Zeiss interferometer system in particular), so that there will be absolutely no gaps across the aperture that is not measured. The RMS ratings will again be similar, but the P-V will be overly pessimistic. I now quote from the "Bible" of optical shop testing. Malacara states: "The P-V error must be regarded with some skepticism, particularly when it is derived from a large number of measured data points, as is the case with phase shifting interferometry. Even relatively large wavefront errors often have little effect on the optical performance if the error involves only a very small part of the aperture. Because the P-V error is calculated from just two data points out of possibly thousands, it might make the system under test appear worse than it actually is. The RMS error is a statistic that is calculated from all of the measured data, and it gives a better indication of the overall system performance".

I cannot speak for the method used by other manufacturers to rate their optics, but the following is the method I use. The optic is normally nulled or figured to the best possible inside/outside diffraction pattern on a double pass autocollimator using a green light pinhole laser source and a seperate white light source. The pattern is checked for roundness (absence of astigmatism and coma) and smoothness (absence of roughness and zones). The reference element is then inserted into the optical path, and the corresponding fringes are captured on the computer using a small CCD camera. I use QuickFringe software developed in Canada and recommended by Peter Ceravolo, who also made my reference elements. These elements were certified by equipment at the Canadian Bureau of Standards. Many passes are taken to nullify the effects of dust particles and slight air disturbances in the optical path and the results are averaged. If the optic passes the 1/10 wave P-V criteria, it is ready for coating and assembly. If not, it continues to be figured and tested until it does pass. The test data in the form of the Zernicky Polynomials is stored on the computer, along with the serial number and other pertinent data, so that if a question arises in the future about some lens, it can be looked up in the database.

In day to day testing, the optician can pretty quickly tell whether a set of fringes will meet the performance goals or not. The fringe patterns that are recorded on the computer screen will not be absolutely clean, even if the optic under test is perfect. There always exists dust particles on the reference elements and autocollimating mirrors, as well as on the beam splitter cubes and laser collimating optics. Since interferometers are analog devices, this is akin to the clicks and pops that appear on vinyl phonograph records. This "noise" can cause the software to add spurious data points to the fringes where none should be, and this will normally lower the P-V rating, but again, the RMS is unaffected. In order to get a fair rating for the optics, I average multiple passes, something that Peter Ceravolo has recommended to do. Just as we would not downgrade the performance of the Chicago Symphony for every little recording noise, so I do not downgrade the performance of our optics because of interferometer noise. In fact, Quick Fringe software allows for the averaging of the various interference fringe runs, and then synthesizes a clean pattern that can be displayed in the final report. Some may call this a "fake" interferogram, but it is based on real data and is more representative of the actual performance than any one fringe pattern. Anyone who has watched in frustration the dancing Airy disc interference pattern in his telescope on an unsteady night can appreciate that the actual performance of the optic is not represented by a single snapshot of that pattern. Rather, if an average of many patterns is combined, the true picture will emerge.

May I summarize then, that the P-V wavefront ratings given by various manufacturers can differ considerably for the same optic. It depends on the test method used, and whether or not a single set of fringes is measured, or an average of many is used, and whether the software creates 100 test points or tens of thousands. They can vary also for RMS, if the optic is tested at different wavelengths, and has refractive elements in it. This is the case with short focus refractors, SCTs, less so with Maksutov systems. Variation can crop up if the optic is not supported properly, whether it was allowed to stabilize after being placed on the interferometer (the warmth of your hands will significantly distort the figure of the lens for some time) and whether the air is stable in the test setup.

It seems then that these numbers are useless to the final user. They are, however powerful tools to the experienced optician, even if they are less than enlightening to the final user. Rather, he should be concerned with whether the manufacturer has manufactured the optics well, than whether they meet or exceed a certain number. The test certificate is just a piece of paper, after all, and cannot gather light and resolve fine planetary detail. Secondarily, customers can and will misinterpret test data. Unless you have been on the front lines and actually used an interferometer to test and figure an optic, it would be difficult to know what all the numbers and squiggles on that piece of paper really mean. For these reasons, Astro Physics does not supply a test report, even though each lens' test data is recorded and stored at our facility.

Roland Christen
ASTRO-PHYSICS