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
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Techniques for Down-Sampling a Measured Surface Height Map for Model Validation
(reference NPO-47711) is currently available for download from the TSP library.
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Overview
The document titled "Techniques for Down-Sampling a Measured Surface Height Map for Model Validation" discusses innovative methods developed at NASA's Jet Propulsion Laboratory (JPL) for processing surface height maps of optical systems, particularly in the context of space telescopes. The primary focus is on two key challenges in the developmental cycle of optical systems: deriving optical quality specifications before fabrication and validating optical models using measured surface maps post-fabrication.
The document highlights the need for effective pre-conditioning or pre-processing of measured surface maps to ensure compatibility with model validation software tools. Traditional methods for up- or down-sampling, such as 2-dimensional interpolation, often lead to inconsistencies, as the same pixel can yield different values depending on the interpolation method used (e.g., nearest, linear, cubic, or spline). Additionally, conventional FFT-based spatial filtering methods can suffer from aliasing effects, which complicates the elimination of measurement noise and errors.
To address these issues, the document introduces two new down-sampling techniques that preserve the low and mid spatial-frequency characteristics of the surface map. The first method involves separating the original surface map into a low spatial-frequency component, represented by Zernike-polynomial fit coefficients, and a residual component that captures mid and high spatial-frequency characteristics. This separation allows for a more accurate representation of the surface map while effectively reducing measurement noise, such as "hot" and "dead pixels."
The document provides an example of down-sampling a surface map from 869x869 pixels to 100x100 pixels, detailing the steps involved in the process. The methods are designed to maintain the integrity of the surface map while ensuring that the resulting data is smooth and continuous, which is crucial for accurate model validation.
In conclusion, the techniques described in this document represent a significant advancement in the processing of surface height maps for optical systems. They offer a robust solution to the challenges of down-sampling and noise elimination, thereby enhancing the reliability of optical model validation. The methods have been implemented in MATLAB as a stand-alone software tool and delivered to the Advanced Wavefront Control Testbed project management team, showcasing their practical application in aerospace-related developments.
