Understanding Your Interferometric Test Results by James Mulherin

At Optical Mechanics our mission is to provide professional quality optics to the research and amateur astronomy community. To that end, we produce our OMI Newtonian mirrors adhering to a rigorous quality control process. The result is consistently high optical quality. Each OMI mirror is delivered with an interferometric certification that conforms to industry standards for research-grade astronomical optics. With this technical article we hope you will gain a better understanding of the critical interferometric certification process, what your interferometric test results mean and why interferometry is so important to ensuring that your optic will perform to your expectations. Each OMI mirror must meet or exceed specific wavefront quality specifications before it leaves our facility. These specifications are presented in the form of Peak-to-Valley (P-V), Root-Mean-Square (RMS) wavefront error, and Strehl ratio. The following paragraphs describe how these quantities are measured and what they mean. Below we describe the high-points of the iterative figuring and testing process whereby your mirror surface is polished from a sphere to a paraboloid. During this figuring process we use common phase modulation tests such as the Ronchi and Foucault tests. Then we explain why the final interferometric certification is so important to assuring that the mirror actually meets our pass criterion for wavefront quality. As a point of interest, we describe the string test; a basic technique that is used to make a qualitative assessment of your interferogram, and we present some sample interferograms that demonstrate the appearance of the third order Seidel aberrations; spherical aberration, astigmatism and coma. Finally, we visually inspect our OMI mirrors for scratches and pits during each step of the fabrication process to ensure that the mirror's surface meets well defined cosmetic quality standards. We describe this surface quality standard and what it means. Interferometric Wavefront Quality Specifications In an interferometric test, the shape of the wavefront produced by the optic under test is determined by combining its wavefront with a highly accurate reference wavefront. Constructive and destructive interference between the combined wavefronts produces interference fringes. These interference fringes are analogous to contour lines on an elevation map and they represent deviations of the wavefront under test from the optimal shape. The interference fringes are captured using a CCD camera and image capture board and displayed on a computer monitor. Fringe analysis software then picks hundreds of points along the fringes over the entire wavefront to accurately quantify the deviations. The output of the fringe analysis software describes the quality of the optic under test by reporting its P-V, RMS wavefront error, and Strehl ratio. The Peak-to-Valley wavefront error is a measure of the distance from the highest to the lowest point on the test wavefront relative to the reference wavefront. According to Optical Shop Testing by Daniel Malacara; "The P-V error must be regarded with some skepticism because it is calculated from the worst two interferometric data points out of possible thousands. It might make the system under test appear worse than it really is." Note that a mirror with a true P-V wavefront error of .25 wave, as verified by interferometry, will in any case meet or exceed the RMS wavefront and Strehl ratio criterion described below. Because P-V uses two points without regard to location on the mirrors surface, two mirrors may have the same P-V error but will be very different in overall quality. The difference in quality will be evident in the RMS and Strehl values. As an example, two mirrors may have the same P-V value due to a zone on the mirrors surface. Both of the mirrors have a high zone. The first mirror has its high zone near the center while the second has its high zone near the edge. The first mirror will have better RMS and Strehl values because the surface area covered by the high zone will be smaller in the center than at the edge. To obtain the RMS wavefront error, a large number of interferometric data points are measured over the entire area of the test wavefront. As explained in Optical Shop Testing; "The RMS error is a statistic that is calculated from all of the measured data and gives a better indication of the overall system performance." Due to its statistical nature, professional optical shops consider the RMS wavefront error to be the most useful measure of optical quality. By common convention an optic with RMS wavefront error of 0.0712 wave or less is considered diffraction limited. The Strehl ratio is another statistical measure of optical performance calculated from the interferometric test data. The Strehl ratio is the ratio of intensity of an aberrated wavefront to an unaberrated wavefront. In other words, the use of the Strehl ratio is a fundamental description of the amount of intensity reduction due to wavefront errors. A common convention is to consider an optic with a Strehl ratio of 0.8 or higher to be diffraction limited. The Strehl ratio and RMS wavefront error are mathematically related. It can be shown that a Strehl ratio of 0.8 corresponds to an RMS wavefront error of 0.0714 wave or approximately 1/14 wave. Why Interferometry is Important During the figuring process, the surface of your mirror is polished from a sphere to a paraboloid using an iterative process of testing and polishing to achieve the desired results. During this process we interpret the appearance of fringes in the Ronchi test and shadows in the Foucault test. Once the optician feels that the optic will pass the scrutiny of the interferometer, this test is performed. Due to the qualitative nature of the Ronchi and Foucault tests, and to the subjectivity in their interpretation, it is not infrequent that the interferometer will reject a mirror, sending it back for touch-up polishing. The interferometer is the final impartial go/no-go point in the quality control chain. It is a completely objective and accurate assessment of the quality of the optic under test. Although it is possible to produce diffraction limited mirrors using methods such as the Ronchi and Foucault test, it is impossible to accurately verify and the quality of the entire wavefront to a fraction of a wave without interferometry. The Ronchi and Foucault tests are excellent evaluation tools during mirror fabrication as they show the general shape of the wavefront as well as localized and high frequency errors extremely well. These tests can show localized errors as small as 1/100 wave. This makes them indispensable tools during mirror figuring. However, unlike interferometry, they do not provide a means of accurately quantifying the whole wavefront because they only measure a few points. Interferometry on the other hand, is an extremely strict statistical analysis that assures the customer of a truly diffraction limited optic over its entire wavefront.