Wavefront Deformation Estimation via Linearized Optical Transfer Function
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Solution Overview
Problem
Current methods for estimating wavefront deformations in optical systems require significant computation time, especially for real-time applications, due to iterative processes that increase with the number of aberrations to be corrected, making them unsuitable for on-board systems with limited processing power.
Innovation Solution
A non-iterative analytical method that linearizes the optical transfer function in each diversity plane, allowing for the estimation of wavefront deformations and the observed object using a model based on decomposition of the pupillary transmission into sub-pupils, autocorrelation, and linearization of terms, enabling direct estimation without iterative minimization.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If iterative phase diversity method is used to estimate wavefront deformations, then measurement precision is improved, but productivity deteriorates due to significant computation time
Solution Approach 1:
The patent transforms the nonlinear iterative phase estimation problem into a linear non-iterative problem by changing the parameter representation. Specifically, it uses the relationship between phase deformations and the optical transfer function, where the phase spectrum can be directly obtained from the argument of the transfer function without requiring iterative minimization. This parameter transformation enables real-time processing while maintaining accuracy.
Solution Approach 2:
The patent replaces the iterative mechanical minimization process with a direct analytical solution based on optical transfer function properties. Instead of repeatedly adjusting parameters to minimize a cost function, the method directly computes the phase spectrum from the measured intensity data using the relationship φ(ν) = arg[H(ν)], where H(ν) is the optical transfer function. This substitution eliminates the iterative loop entirely.
2Productivity
If iterative minimization algorithms are used to reduce the number of iterations, then productivity is improved, but device complexity increases due to requirements for powerful processors
Solution Approach 1:
The patent extracts the essential information needed for phase estimation directly from the optical transfer function without requiring complex iterative algorithms. By taking out the phase spectrum φ(ν) = arg[H(ν)] as a direct observable from the intensity measurements, the method eliminates the need for powerful processors to run iterative minimization, enabling implementation on simpler hardware platforms.
3Measurement precision
If phase diversity method with multiple images is used, then measurement precision is improved, but loss of time increases due to acquisition and processing of multiple images
Solution Approach 1:
The patent performs preliminary action by establishing the analytical relationship between the optical transfer function and phase spectrum before actual measurement. The method pre-defines the transformation H(ν) → φ(ν) = arg[H(ν)], so that when intensity data is acquired, the phase can be immediately computed without requiring multiple images or iterative processing. This preliminary formulation enables single-image real-time processing.
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 significantly reduces calculation time, making it suitable for real-time applications and on-board systems by simplifying the system of equations to solve for the object or disturbances without iterations, while maintaining accuracy in deformation estimation.
Implementation Method 1
a determination of the optical transfer function of the system by autocorrelation of the pupillary transmission of its pupil
Implementation Method 2
the linearization, in said optical transfer function, of each of the terms of the autocorrelation as a function of the coefficients of the deformation sought
Data Source
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AI summary
The invention relates to a method of estimating at least one deformation of the wave front of an observation system or of an object observed by said observation system, characterized in that: at least one diversity image is acquired, in the vicinity of the focal plane of the observation system, in at least one diversity plane, the diversity image comprising a known diversity deformation; and in that in each diversity plane, an image model is determined based on at least one decomposition of the physical pupil of the system into a plurality of subpupils; a decomposition over each subpupil of the sought-after deformation in the form of at least one known deformation weighted by coefficients to be determined; a determination of the transfer function of the system by autocorrelation of its pupil; the linearization of each of the terms of the autocorrelation as a function of the coefficients of the sought-after deformation, the linearization being performed in the vicinity of the known diversity deformation; the object observed and noise; and in that on the basis of the image model(s) determined and of the image(s) acquired, the sought-after deformation(s) or the observed object is (are) estimated.