Reconstruction Matrix for Non-Uniform Interferogram Spectral Data
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Solution Overview
Problem
Hyperspectral imaging systems based on liquid-crystal polarization interferometers generate non-uniformly sampled interferograms, which pose challenges for accurate reconstruction of hyperspectral data-cubes using standard Fourier transforms, leading to artifacts and reduced signal strength, especially at shorter wavelengths.
Innovation Solution
A reconstruction matrix is formed with rows of periodic functions corresponding to selected wavelengths and columns representing reference retardances, allowing for matrix-vector products to transform interferograms into hyperspectral data-cubes, effectively handling non-uniform sampling and enhancing spectral data accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If standard Fourier transforms are used to reconstruct hyperspectral data-cubes from non-uniformly sampled interferograms, then the reconstruction process is simple and fast, but artifacts appear and signal strength is reduced especially at shorter wavelengths
Solution Approach 1:
The patent transforms the reconstruction approach by changing the mathematical parameters from standard Fourier transform to a customized transform that accounts for non-uniform sampling. This involves modifying the transform kernel to incorporate the actual sampling intervals, thereby resolving spectral artifacts and restoring signal strength at all wavelengths while maintaining computational efficiency through optimized algorithms.
Solution Approach 2:
The patent replaces the standard Fourier transform mechanical process with a customized reconstruction algorithm that substitutes the uniform sampling assumption with non-uniform sampling correction. This substitution involves replacing the standard transform kernel with a modified version that compensates for irregular sampling intervals, eliminating artifacts without sacrificing reconstruction speed.
2Adaptability or versatility
If non-uniform sampling is used in interferogram acquisition, then the measurement flexibility is increased, but reconstruction accuracy deteriorates due to artifacts
Solution Approach 1:
The patent introduces an intermediary reconstruction step that mediates between the non-uniform sampling data and the final spectral cube. This intermediary process involves calculating correction factors based on the actual sampling intervals and applying them during the transform process, thereby preserving the flexibility of non-uniform acquisition while eliminating the resulting artifacts in the spectral data.
Solution Approach 2:
The patent modifies the reconstruction parameters to match the non-uniform sampling parameters. By changing the transform kernel to incorporate the actual sampling intervals and positions, the system maintains measurement flexibility while restoring spectral accuracy, allowing adaptive sampling strategies without compromising data quality.
3Measurement precision
If matrix-vector products with periodic functions are used for reconstruction, then spectral data accuracy is improved and artifacts are reduced, but the computational complexity increases
Solution Approach 1:
The patent segments the reconstruction process into manageable matrix-vector product operations with periodic functions. By dividing the large-scale transform into smaller, structured matrix operations that can be parallelized, the system achieves high spectral accuracy while controlling computational complexity through efficient linear algebra implementations and potential hardware acceleration.
Solution Approach 2:
The patent creates a universal reconstruction framework using matrix-vector products that can handle both uniform and non-uniform sampling cases. This multi-functional approach uses the same mathematical structure for different sampling scenarios, reducing overall computational complexity by avoiding the need for separate specialized algorithms while maintaining high spectral accuracy across all cases.
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 method improves the accuracy and reduces artifacts in hyperspectral data reconstruction, maintaining dynamic range across the detectable optical spectrum and enhancing sensitivity at shorter wavelengths.
Implementation Method 1
a polarization interferometer that introduces a variable optical path delay between components of light that are polarized in orthogonal directions
Implementation Method 2
Hyperspectral imaging systems based on liquid-crystal polarization interferometers
Data Source
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AI summary
A reconstruction matrix used for calculating a hyperspectral data-cube includes rows of periodic functions. Each row of the reconstruction matrix corresponds to a selected wavelength and each column corresponds to a selected retardance of an interferometer. The periodic functions have as a parameter the selected wavelength of the corresponding row and are sampled at the selected retardances of each of the corresponding columns. An interferogram data-cube is obtained and includes an array of one or more simultaneously measured interferograms. Each row of the interferogram data-cube corresponds to one of the selected retardances and each column corresponds to a different interferogram from the simultaneously measured interferograms. A set of matrix-vector products for each of the interferograms is formed by multiplying the reconstruction matrix with a column of the interferogram data-cube to form the hyperspectral data-cube.