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Applied Optics

Applied Optics


  • Vol. 35, Iss. 7 — Mar. 1, 1996
  • pp: 1015–1021

Test optics error removal

Chris J. Evans and Robert N. Kestner  »View Author Affiliations

Applied Optics, Vol. 35, Issue 7, pp. 1015-1021 (1996)

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Wave-front or surface errors may be divided into rotationally symmetric and nonrotationally symmetric terms. It is shown that if either the test part or the reference surface in an interferometrie test is rotated to N equally spaced positions about the optical axis and the resulting wave fronts are averaged, then errors in the rotated member with angular orders that are not integer multiples of the number of positions will be removed. Thus if the test piece is rotated to N equally spaced positions and the data rotated back to a common orientation in software, all nonrotationally symmetric errors of the interferometer except those of angular order kNθ are completely removed. It is also shown how this method may be applied in an absolute test, giving both rotationally symmetric and nonsymmetric components of the surface. A general proof is given that assumes only that the surface or wave-front information can be described by some arbitrary set of orthognal polynomials in a radial coordinate r and terms in sin θ and cos θ. A simulation, using Zernike polynomials, is also presented.

© 1996 Optical Society of America

Original Manuscript: June 14, 1995
Revised Manuscript: September 19, 1995
Published: March 1, 1996

Chris J. Evans and Robert N. Kestner, "Test optics error removal," Appl. Opt. 35, 1015-1021 (1996)

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  20. Kuchel, in reviewing a draft of this manuscript, derived an alternative proof based on a Fourier series expansion of any arbitrary azimuthal profile that is concentric with the axis about which the part is rotated.
  21. The notation used here is that proposed by the NAPM IT 11 Standards Committee on Interferometric Testing, in which the subscript refers to the maximum radial order whereas the superscript gives the azimuthal order, with a negative sign indicating the sine rather than cosine) term.

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