Error Analysis of Absolute Interferometric Testing Based on Reconstruction of Rotational Shear

Abstract:

Recently most of modern absolute measurement rotation the flats or spheres in the interferometer. We review traditional absolute testing of flats methods and emphasize the method of reconstruction of rotational shear. The rotation of the lens can lead to some errors such as angle rotation error, center excursion error and other coordinate system motion error. 36 Zernike polynomials are used to generate 3 flats and Matlab are used to simulate the arithmetic. There have some phase problems on FFT arithmetic in Matlab which can cause some errors. Results are shown about how these errors influence the accuracy. The analysis results can also be used in other interferometer systems which have the motion of the coordinate system.

• Periodical: Advanced Materials Research (Volume 346)
• Pages: 620-626
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.346.620
• Online since: September 2011
• Authors: Xin Jia, Ting Wen Xing
• Keywords: Absolute Testing, Metrology, Optical Testing, Rotational Shear

References

[1] Klaus R. Freischlad, Absolute interferometeric testing based on reconstruction of rotational shear, Appl. Opt. 40(2001).

DOI: 10.1364/ao.40.001637

[2] Chris J. Evans and Robert N. Kestner, Test optics error removal, Appl. Opt. 35(1996).

[3] G. Schulz and J. Schwider, Precise measurement of planeness, ', Appl. Opt. 6, 1077-1084(1967).

DOI: 10.1364/ao.6.001077

[4] G. Schulz and J. Grzanna, Absolute flatness testing by the rotation method with optimal measuring-error compensation, Appl. Opt. 31, 3767-3780(1992).

DOI: 10.1364/ao.31.003767

[5] K. -E. Elssner,A. Vogel.J. Grzanna, and G. Schulz, Establishing a flatness standard, Appl. Opt. 33, 2437-2446 (1994).

DOI: 10.1364/ao.33.002437

[6] B.S. Fritz, Absolute calibration of an optical flat, Opt. Eng. 23, 379-383(1984).

[7] C. Ai and J.C. Wyant, Absolute testing of flats decomposed to even and odd functions, in Interferometry: Surface Characterization and Testing, K. Creath and J.E. Greivenkamp, eds, Proc. Soc. Photo-Opt. Instrum. Eng. 1776, 73-83 (1992).

DOI: 10.1117/12.139247

[8] C. Ai and J.C. Wyant, Absolute testing of flats using even and odd functions, Appl. Opt. 32, 4698-4705(1993).

DOI: 10.1364/ao.32.004698

[9] C. Ai, L. -Z. Shao, and R.E. Parks, Absolute testing of flats using even and odd functions, in Optical fabrication and Testing, Vol. 24 of 1992 OSA Technical Digest Series(Optical Society of America, Washington, D.C., 1992).

DOI: 10.1364/oft.1992.pdp1

[10] F.M. Kuchel, Verfahren und Vorrichtung zur interferometrischen Absolutprufung von Planflachen, European patent EP 0 441 153 B1(14 August 1991).

[11] Chen Xu, Lei Chen and Jiayi Yin, Method for absolute flatness measurement of optical surface, Appl. Opt. 48 (2009).

[12] Peng Su, Absolute measurement of large mirror, Phd of University of Arizona. (2008).

[13] Xin Jia, Tingwen Xing, Error Analysis of Absolute Testing based on Even-Odd Functions Method, SPIE Vol. 7638-124(2010).

[14] Jia Xin, Xing Tingwen, Analysis of Absolute Testing based on Even-Odd Functions by Zernike polynomials, SPIE (2010) in press.

[15] Claus Freischlad, Method and apparatus for absolutely measuring flat and spherical surfaces with high spatal resolution, US Patent 6184994 (2001).