This software allows one to down-sample a measured surface map for model validation, not only without introducing any re-sampling errors, but also eliminating the existing measurement noise and measurement errors.

At present, the surface map of an optic is measured using an interferometric instrument such as a Zygo interferometer. In such a case, the measured surface map has a high resolution and needs to be down-sampled before using it in model validation software. The software tool of the current two new techniques can be used in all optical model validation processes involving large space optical surfaces.

Down-sampling of a surface map is accomplished by using the analytical expressions of Zernike-polynomials of the given surface map for a low-spatial frequency component and the spectrum or the power spectral density (PSD) data of the given surface map for mid-spatial frequency component. The challenge is to decrease the matrix size of a measured optical surface height map to match it with a model validation software tool.

During the down-sampling of a surface map, this software tool preserves the lowspatial frequency characteristic of a given surface map through the use of Zernike polynomial fit coefficients, and maintains mid-spatial frequency characteristics of the given surface map by the use of the spectrum or the PSD data of the given surface map calculated from the mid- and the high-spatial frequency components of the original surface map.

These new methods do not introduce any aliasing and interpolation errors as is done by the conventional interpolation and FFT-based spatial-filtering method. Also, they automatically eliminate the measurement noise and other measurement errors such as artificial discontinuity.

This work was done by Erkin Sidick of Caltech for NASA’s Jet Propulsion Laboratory.

This software is available for commercial licensing. Please contact Daniel Broderick of the California Institute of Technology at This email address is being protected from spambots. You need JavaScript enabled to view it.. NPO-47711

This Brief includes a Technical Support Package (TSP).
Techniques for Down-Sampling a Measured Surface Height Map for Model Validation

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This article first appeared in the February, 2012 issue of NASA Tech Briefs Magazine.

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