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Proceedings Paper

Specification of optical surface accuracy using the structure function
Author(s): Ross Zhelem
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Paper Abstract

Irregularity of an optical surface is commonly characterized by peak-to-valley or root mean square error after subtraction of low order aberrations. It is sufficient if the surface is fabricated with the help of conventional techniques. Modern manufacturing methods employ undersized polishing tools generating irregularities on sub-aperture scales or mid-spatial frequencies. This is particularly important for the fabrication of aspheric or free-form surfaces. The smoothness of local polishing depends on how uniformly the influence of a tool is distributed and how well the dwell time is controlled over a part. Diamond turning is known for the variety of shapes, however, a single point tool tends to form surface features on the scale determined by the uniformity of feed rate. A deterministic way to quantify and specify mid-spatial irregularity is important for all areas of optical production. Interferometric map of an optical surface is usually obtained from original data by subtraction of the fit of 9 Zernike fringe polynomials corresponding to piston, tilt, focus and third order astigmatism, coma and spherical aberrations. This paper describes how to characterize the spectral content of residual surface height error, which depends on multiple factors during the fabrication. To quantify small scale irregularities, the residual error is regarded as a statistical process. The method of structure function is applied to the surface errors at different spatial scales yielding RMS height difference vs. physically measurable separation on an optical surface.

Paper Details

Date Published: 23 May 2011
PDF: 10 pages
Proc. SPIE 8083, Modeling Aspects in Optical Metrology III, 808310 (23 May 2011); doi: 10.1117/12.889143
Show Author Affiliations
Ross Zhelem, The Ohio State Univ. (United States)

Published in SPIE Proceedings Vol. 8083:
Modeling Aspects in Optical Metrology III
Bernd Bodermann, Editor(s)

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