Optical Fourier Transform Phase Recovery via Component Segmentation
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Solution Overview
Problem
Conventional methods for performing optical Fourier transforms can only detect the amplitude of complex functions, losing phase information, which limits the ability to determine the full complex Fourier transform, and existing phase retrieval algorithms are iterative, inefficient, and not scalable.
Innovation Solution
A deterministic method that decomposes the input function into real and imaginary parts, further into even and odd components, performs optical Fourier transforms of these parts, perturbs them, and compares the results to determine the phase, allowing for the calculation of the full complex optical Fourier transform using intensity measurements only.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of information
If conventional optical Fourier transform methods are used, then the transform can be performed optically, but phase information is lost because only amplitude detection is available
Solution Approach 1:
The input complex function is decomposed into multiple component functions (real part, imaginary part, even parts, odd parts). Each component is processed separately through optical Fourier transforms, and the results are combined to reconstruct the full complex transform including phase information. This segmentation allows phase recovery by measuring amplitude components of decomposed functions.
Solution Approach 2:
A perturbation function is introduced as an intermediary to enable phase determination. By adding a known perturbation to the input function and measuring the change in amplitude of the optical Fourier transform, the phase information can be inferred indirectly through the relationship between the perturbation and the measured amplitude changes.
2Loss of information
If iterative phase retrieval algorithms are used, then phase information can be recovered, but the process becomes computationally intensive and slow
Solution Approach 1:
The input function is pre-decomposed into specific component functions (real/imaginary parts, even/odd parts) before optical processing. This preliminary decomposition structure enables direct determination of phase from amplitude measurements without requiring iterative refinement, as the component structure provides direct relationships between measured amplitudes and phase values.
Solution Approach 2:
The iterative computational algorithm is replaced with a direct optical measurement approach. Instead of using computational iterations to retrieve phase, the patent uses optical Fourier transforms of decomposed components combined with perturbation measurements to directly determine phase information, substituting mechanical/optical processes for computational iterations.
3Loss of information
If phase detectors are used to measure phase information, then full complex Fourier transform can be obtained, but the system becomes mechanically and optically complex
Solution Approach 1:
Phase information is extracted indirectly through amplitude measurements of decomposed component functions rather than directly measuring phase. By taking out the phase measurement problem and replacing it with amplitude measurements of specially prepared input components, the need for complex phase detectors is eliminated.
Solution Approach 2:
The perturbation function serves as an intermediary that enables phase determination through simple amplitude measurements. Instead of directly measuring phase with complex detectors, the perturbation mediates the relationship between the input function and the measured amplitude, allowing phase inference through simple intensity measurements.
4Quantity of substance
If larger FFT sizes are processed, then more comprehensive transform results are obtained, but processing time increases significantly
Solution Approach 1:
The computational FFT algorithm is replaced with an optical processing system. Optical Fourier transforms can be performed in parallel for all spatial frequencies simultaneously, meaning processing time does not increase with transform size. The optical system processes the entire function at once rather than iterating through computational steps, eliminating the time penalty for larger transforms.
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
Enables the recovery of phase information from intensity measurements, enabling full complex-to-complex Fourier transforms to be performed optically with high speed and precision, independent of function size, using few physical measurements and achieving higher precision than hardware accuracy.
Implementation Method 1
The Fourier transform lens 103 is positioned at a distance f along the common optical axis from the SLM 101 and is arranged to receive spatially modulated light 104 from the SLM. The camera sensor 105 is positioned at a distance f along the common optical axis from the Fourier transform lens 103 and is arranged to receive converging light 106 from the Fourier transform lens 103.
Implementation Method 2
The photodetector array 105 is positioned at the rear focal plane of the Fourier transform lens to capture the intensity distribution of the converging light 106.
Data Source
AI summary
A method of performing a complex Fourier transform of an input function including amplitude and phase information, including decomposing the input function into a plurality of sub-functions, wherein the Fourier transform of each sub-function includes an amplitude function and a phase function in which the phase is constrained to a plurality of possible phase values. The phase function of the Fourier transform of each sub-function is determined with an optical system that measures the amplitude function of an optical Fourier transform of the sub-function and changes in the amplitude function of the optical Fourier transform caused by applying a perturbation function to the sub-function. The determined phase functions and the measured amplitude functions are combined for each of the sub-functions to form the complex Fourier transform of the input function.