Lianzhen Shao

Pixel-based absolute topography test for three flats.

We demonstrate a method of performing the absolute three-flat test by using reflection symmetries of the surfaces and an algorithm for generating the rotation of arrays of pixel data. Most of the operations involve left/right and top/bottom flips of data arrays, operations that are very fast on most frame grabbers and are available on most commercial phase-measuring interferometers. We demonstrate the method with simulated data as well as with actual data from 150-mm-diameter surfaces that are flat to less than 25 nm peak to valley.

Measurements of the LIGO Pathfinder optics

A number of 150 mm apertures in 250 mm diameter plano- concave with departures from the nominal figure of a few nm were carefully tested using phase measuring interferometry and the data reduced using pixel based absolute testing techniques. We discuss some of the data reduction techniques used as well as the precautions taken to verify the accuracy of the result. After accounting for systematic errors introduced by interferometer imaging, we show that the surfaces can be characterized to a few nm peak-to-valley over spatial scales form the measurement aperture to a few mm.

Haidinger interferometer for silicon wafer TTV measurement

We describe a novel, IR phase shifting Haidinger fringe interferometer for measuring the thickness, total thickness variation (TTV) and bow of silicon wafers. We show that by taking 3 interferograms of the wafer in different positions in the cavity it is possible to separate thickness, TTV and bow. We also show that bow has an effect on the measurement of TTV.

Interferometric testing of photomask substrate flatness

Conventional interferometric testing of the flatness of photomask substrates is rendered difficult by the long coherence length of the HeNe laser sources typically used in commercially available phase measuring interferometers appropriate for flatness testing. The Ritchey-Common configuration allows testing of flats in a spherical wavefront; this paper shows that, under appropriate conditions, high resolution surface flatness maps of photomask substrates may be obtained using instrumentation currently available in many optical shops.

Test of a slow off-axis parabola at its center of curvature

We describe the interferometric testing of a slow (ƒ/16 at the center of curvature) off-axis parabola, intended for use in an x-ray spectrometer, that uses a spherical wave front matched to the mean radius of the asphere. We find the figure error in the off-axis mirror by removing the theoretical difference between the off-axis segment and the spherical reference from the measured wave-front error. This center of curvature test is easy to perform because the spherical reference wave front has no axis and thus alignment is trivial. We confirm that the test results are the same as the double-pass null test for a parabola that uses a plane autocollimating mirror. We also determine that the off-axis section apparently warped as the result of being cut from the symmetric parent part.

Three-dimensional contouring on a numerically controlled grinder

The Large Optical Generator (LOG) recently completed the generating of six off-axis aspheres. It was decided to use the non-traditional technique of three-axis contouring to solve many of the fabrication and mounting problems. The process and the solutions it provides are discussed, as well as the resultant figure errors and how these compare to the traditional two-axis generating that LOG has done in the past.

Intensity Distribution In Out-Of-Focus Images Of A Rotationally Symmetric Optical System

A theory describing the intensity distribution in out-of-focus images of a telescope mirror is derived based on geometrical ray optics for a rotationally symmetric optical system. Surfaces at which the intensity distribution diverges are shown to be the same as the classic caustic surfaces. The contrast variations at out-of-focus positions are proportional to the square of the F-number of the system. For a large F-number system such as a telescope, the out-of-focus intensity distributions provide a sensitive method for determining zonal error distributions of the optical system.