Discrete fourier transform (DFT) analysis for applications using iterative transform methods
AssigneeThe United States of America as represented by the Administrator of the National Aeronautics and Space Administration
InventorBruce H. Dean
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Abstract
According to various embodiments, a method is provided for determining aberration data for an optical system. The method comprises collecting a data signal, and generating a pre-transformation algorithm. The data is pre-transformed by multiplying the data with the pre-transformation algorithm. A discrete Fourier transform of the pre-transformed data is performed in an iterative loop. The method further comprises back-transforming the data to generate aberration data.
Claims18
A method for determining aberration data for an optical system, the method comprising:
- providing an optical system comprising a signal processor;
- collecting intensity data generated by the optical system;
- calculating a similarity transform and an inverse of the similarity transform, based on the collected intensity data;
- calculating a discrete Fourier transform matrix in a diagonal basis, based on the collected intensity data;
- pre-transforming the collected intensity data using the processor, by multiplying the collected intensity data by one of the similarity transform and the inverse of the similarity transform, to generate pre-transformed data;
- performing an iterative transform operation on the pre-transformed data using the processor, by multiplying the pre-transformed data by the discrete Fourier transform matrix, a predetermined amount of times, to generate iteratively transformed data;
- back-transforming the iteratively transformed data using the processor, by multiplying the iteratively transformed data by one of the similarity transform and the inverse of the similarity transform, to form aberration data, wherein the iteratively transformed data is multiplied by the similarity transform when the intensity data is multiplied by the inverse of the similarity transform in the pre-transforming step, and the iteratively transformed data is multiplied by the inverse of the similarity transform when the intensity data is multiplied by the similarity transform in the pre-transforming step;
- and
- outputting the aberration data to a user.
An optical system comprising a signal processor and a control unit, the control unit being operably linked to the signal processor, wherein the signal processor is configured to perform a method comprising:
- collecting intensity data generated by the optical system;
- calculating a similarity transform and an inverse of the similarity transform, based on the collected intensity data;
- calculating a discrete Fourier transform matrix in a diagonal basis, based on the collected intensity data;
- pre-transforming the collected intensity data using the processor, by multiplying the collected intensity data by one of the similarity transform and the inverse of the similarity transform, to generate pre-transformed data;
- performing an iterative transform operation on the pre-transformed data using the processor, by multiplying the pre-transformed data by the discrete Fourier transform matrix, a predetermined amount of times, to generate iteratively transformed data;
- back-transforming the iteratively transformed data using the processor, by multiplying the iteratively transformed data by one of the similarity transform and the inverse of the similarity transform, to form aberration data, wherein the iteratively transformed data is multiplied by the similarity transform when the intensity data is multiplied by the inverse of the similarity transform in the pre-transforming step, and the iteratively transformed data is multiplied by the inverse of the similarity transform when the intensity data is multiplied by the similarity transform in the pre-transforming step;
- and
- outputting the aberration data to a user.
Dependencies are inferred from the claim text.