Restoring Low Spatial Frequency in Fizeau Fourier Transform Spectrometers
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Solution Overview
Problem
Fizeau Fourier transform spectrometers lack low spatial frequency information in their spectral data due to the cross-correlation of separate apertures, limiting the spectral bandwidth and accuracy of spectral data obtained.
Innovation Solution
The method involves generating object estimates with uniform spatial frequency information, applying the system spectral optical transfer function to adjust these estimates, and then applying a DC bias to restore low spatial frequency information, ultimately creating a panchromatic object estimate that matches the measured image by iteratively modifying the spatial frequency and optical transfer functions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If a Fizeau interferometer is used to collect spectral information, then the spectral bandwidth is improved, but low spatial frequency information is lost due to the cross-correlation of separate apertures
Solution Approach 1:
The patent introduces an intermediary computational process (iterative optimization algorithm) that mediates between the incomplete spectral data from the Fizeau interferometer and the desired complete spectral information. The algorithm acts as a mathematical intermediary to recover lost low spatial frequency components by optimizing the spectral estimate to match measured interferogram data.
Solution Approach 2:
The patent changes the parameter space by working in the frequency domain rather than directly in the spatial domain. By applying Fourier transforms and operating in the spectral frequency domain, the system can manipulate and recover spatial frequency information that is not directly accessible in the original measurement space.
2Measurement precision
If separate portions of the collected wavefront are interfered in a Fizeau Fourier transform spectrometer, then the spectral information is improved, but all low spatial frequency (DC) information is missing from the Fourier transform
Solution Approach 1:
The patent performs preliminary action by measuring the total intensity (DC component) separately through a zero-path-difference interferogram measurement before the main spectral analysis. This preliminary measurement of the DC component is then incorporated into the final spectral reconstruction to restore the missing low spatial frequency information.
Solution Approach 2:
The patent segments the spectral information recovery process into distinct components: the AC components from the spectral interferogram and the DC component from the zero-path-difference measurement. By treating these segments separately and then combining them, the system recovers the complete spectral information including the previously missing DC and low spatial frequency components.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach effectively restores low spatial frequency spectral information, improving the accuracy and completeness of spectral data obtained from Fizeau Fourier transform spectrometers, ensuring a better match with the measured panchromatic object image.
Implementation Method 1
Another approach to Fourier transform spectroscopy involves using a Fizeau interferometer, in which separate portions of a collected wavefront are interfered with each other to form interference patterns on an image plane.
Implementation Method 2
As the optical path length of one of the separate portions of the collected wavefront is changed, a phase delay is introduced between the portions, causing interference patterns to translate across the image plane.
Implementation Method 3
These interference patterns are Fourier transformed to extract spectral fringe visibility data for all field points.
Data Source
AI summary
A method of restoring low spatial frequency spectral information to an image using a Fizeau Fourier transform spectrometer (“FFTS”) system is provided. Portions of a wavefront collected by the FFTS are interfered. The interference patterns are Fourier transformed to generate spectral images. A region of the image is identified, for which spectral information is predetermined. Object estimates are generated, each of which corresponds to a spectral image. Each object estimate is iteratively adjusted applying a system spectral optical transfer function (“SOTF”) to it and modifying it until a match is made with the corresponding spectral image. Each adjusted object estimate is then iteratively restored by applying a system optical transfer function (“OTF”) to it and then applying a DC bias to it until a match is made between the identified region in the sum of the object estimates and the identified region of a measured panchromatic object image.