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### Proceedings Paper

Calibration of symmetric and non-symmetric errors for interferometry of ultra-precise imaging systems
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Paper Abstract

The azimuthal Zernike coefficients for shells of Zernike functions with shell numbers n<N may be determined by making measurements at N equally spaced rotational positions. However, these measurements do not determine the coefficients of any of the purely radial Zernike functions. Label the circle that the azimuthal Zernikes are measured in as circle A. Suppose that the azimuthal Zernike coefficients for n<N are also measured in a smaller circle B which is inside circle A but offset so that it is tangent to circle A and so that it has the center of circle A just inside its circular boundary. The diameter of circle B is thus only slightly larger than half the diameter of circle A. From these two sets of measurements, all the Zernike coefficients may be determined for n<N. However, there are usually unknown small rigid body motions of the optic between measurements. Then all the Zernike coefficients for n<N except for piston, tilts, and focus may be determined. We describe the exact mathematical algorithm that does this and describe an interferometer which measures the complete wavefront from pinholes in pinhole aligners. These pinhole aligners are self-contained units which include a fiber optic, focusing optics, and a "pinhole mirror". These pinhole aligners can then be used in another interferometer so that its errors would then be known. Physically, the measurements in circles A and B are accomplished by rotating each pinhole aligner about an aligned axis, then about an oblique axis. Absolute measurement accuracies better than 0.2 nm were achieved.

Paper Details

Date Published: 18 August 2005
PDF: 12 pages
Proc. SPIE 5869, Optical Manufacturing and Testing VI, 58690R (18 August 2005); doi: 10.1117/12.623187
Show Author Affiliations
Donald W. Phillion, Lawrence Livermore National Lab. (United States)
Gary E. Sommargren, Lawrence Livermore National Lab. (United States)
Michael A. Johnson, Lawrence Livermore National Lab. (United States)
Todd A. Decker, Lawrence Livermore National Lab. (United States)
John S. Taylor, Lawrence Livermore National Lab. (United States)
Yoshio Gomei, Canon Inc. (Japan)
Osamu Kakuchi, Canon Inc. (Japan)
Seiji Takeuchi, Canon Inc. (Japan)

Published in SPIE Proceedings Vol. 5869:
Optical Manufacturing and Testing VI
H. Philip Stahl, Editor(s)