This software allows one to up-sample or 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. Because the re-sampling of a surface map is accomplished based on the analytical expressions of Zernike-polynomials and a power spectral density model, such re-sampling does not introduce any aliasing and interpolation errors as is done by the conventional interpolation and FFT-based (fast-Fourier-transformbased) spatial-filtering method. Also, this new method automatically eliminates the measurement noise and other measurement errors such as artificial discontinuity.
The developmental cycle of an optical system, such as a space telescope, includes, but is not limited to, the following two steps: (1) deriving requirements or specs on the optical quality of individual optics before they are fabricated through optical modeling and simulations, and (2) validating the optical model using the measured surface height maps after all optics are fabricated. There are a number of computational issues related to model validation, one of which is the “pre-conditioning” or pre-processing of the measured surface maps before using them in a model validation software tool.
This software addresses the following issues: (1) up- or down-sampling a measured surface map to match it with the gridded data format of a model validation tool, and (2) eliminating the surface measurement noise or measurement errors such that the resulted surface height map is continuous or smoothly-varying. So far, the preferred method used for resampling a surface map is two-dimensional interpolation. The main problem of this method is that the same pixel can take different values when the method of interpolation is changed among the different methods such as the “nearest,” “linear,” “cubic,” and “spline” fitting in Matlab. The conventional, FFTbased spatial filtering method used to eliminate the surface measurement noise or measurement errors can also suffer from aliasing effects.
During re-sampling of a surface map, this software preserves the low spatial-frequency characteristic of a given surface map through the use of Zernike-polynomial fit coefficients, and maintains mid- and high-spatial-frequency characteristics of the given surface map by the use of a PSD model derived from the two-dimensional PSD data of the mid- and high-spatial-frequency components of the original surface map. Because this new method creates the new surface map in the desired sampling format from analytical expressions only, it does not encounter any aliasing effects and does not cause any discontinuity in the resultant surface map.
This work was done by Erkin Sidick of Caltech for NASA’s Jet Propulsion Laboratory.
The software used in this innovation is available for commercial licensing. Please contact Daniel Broderick of the California Institute of Technology at
This Brief includes a Technical Support Package (TSP).
Method for Pre-Conditioning a Measured Surface Height Map for Model Validation
(reference NPO-47593) is currently available for download from the TSP library.
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Overview
The document titled "Method for Pre-Conditioning a Measured Surface Height Map for Model Validation" by Erkin Sidick from NASA's Jet Propulsion Laboratory outlines a novel approach to enhance the validation of optical models used in systems like space telescopes. The developmental cycle of such optical systems involves deriving specifications for optical quality and validating these models using measured surface height maps after fabrication.
A key challenge in model validation is the "pre-conditioning" of these surface maps, which involves two main tasks: up- or down-sampling the measured surface maps to align with the data format required by model validation tools, and eliminating measurement noise or errors to ensure the resulting surface height map is continuous and smoothly varying. The document critiques traditional methods, particularly 2-dimensional interpolation, which can yield inconsistent pixel values depending on the interpolation method used (e.g., nearest, linear, cubic, spline). Additionally, conventional FFT-based spatial filtering methods for noise reduction may suffer from aliasing effects.
The proposed method addresses these issues by utilizing a more robust approach to surface map processing. It includes generating new surface map components with a 99x99 pixel grid size derived from Zernike-fit coefficients and a power spectral density (PSD) model. The document presents figures illustrating the measured surface height map, Zernike fits, and the differences between various components, emphasizing the importance of accurately capturing surface features.
To ensure that the new surface map components maintain the same root mean square (RMS) value as the original measured surface map, the method incorporates Monte Carlo simulations and multiple PSD realizations, which involve varying the random phase of the PSD function. This comprehensive approach has been implemented in MATLAB as a stand-alone software tool, which has been delivered to relevant project management teams, including those involved in advanced mirror development and wavefront control testing.
In conclusion, this document provides a significant contribution to the field of optical system validation, offering a refined methodology for processing surface height maps that enhances the accuracy and reliability of optical models, ultimately benefiting aerospace applications and beyond.
