15 December 1992 Absolute testing of flats decomposed to even and odd functions
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This paper describes a method for measuring the absolute flatness of flats. A function in a Cartesian coordinate system can be expressed as the sum of even-odd, odd-even, even-even, and odd-odd functions. Three flats are measured at eight orientations; one flat is rotated 180 degree(s), 90 degree(s), and 45 degree(s) with respect to another flat. From the measured results the even-odd and the odd-even functions of each flat are obtained first, then the even-even function is calculated. All three functions are exact. The odd-odd function is difficult to obtain. For the points on a circle centered at the origin, the odd-odd function has a period of 180 degree(s) and can be expressed as a Fourier sine series. The sum of one half of the Fourier sine series is obtained from the 90 degree(s) rotation group. The other half is further divided into two halves, and one of them is obtained from the 45 degree(s) rotation group. Thus, after each rotation, one half of the unknown components of the Fourier sine series of the odd-odd function is obtained. The flat is approximated by the sum of the first three functions and the known components of the odd-odd function. In the simulation, three flats (each is an OPD map obtained from a Fizeau interferometer) are reconstructed. The theoretical derivation and the simulating results are presented.
© (1992) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Chiayu Ai, Chiayu Ai, James C. Wyant, James C. Wyant, "Absolute testing of flats decomposed to even and odd functions", Proc. SPIE 1776, Interferometry: Surface Characterization and Testing, (15 December 1992); doi: 10.1117/12.139247; https://doi.org/10.1117/12.139247


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