Wavefront Error Detection Using Extended Nijboer-Zernike Theory
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Solution Overview
Problem
Conventional wavefront error detection methods for large-aperture optical lenses face challenges such as low resolution, high calculation complexity, and difficulty in accurately determining the defocus position, particularly in the sub-aperture stitching method used in iterative phase retrieval.
Innovation Solution
A device and method utilizing an extended Nijboer-Zernike (ENZ) theory for modal-based optimization phase retrieval, which includes a point light source, half mirror, lens to be tested, plane mirror, and image sensor, performing phase retrieval on a defocus intensity image to obtain wavefront error, using an iterative optimization algorithm to correct for cross terms and determine the true defocus position.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Area of stationary object
If sub-aperture stitching method is used in conventional iterative phase retrieval, then measurement coverage for large-aperture optical lens is improved, but detection accuracy deteriorates due to position errors and operational complexity
Solution Approach 1:
The patent divides the large-aperture optical lens measurement into multiple sub-apertures that are sequentially measured and stitched together. The measurement aperture is segmented into smaller regions, each measured independently, then combined to form the complete wavefront map of the large-aperture lens.
Solution Approach 2:
The patent introduces an intermediary optimization function that uses modal decomposition (Zernike polynomials) to bridge the sub-aperture measurements. This intermediary mathematical model corrects position errors and ensures smooth transitions between adjacent sub-apertures, improving overall measurement accuracy.
2Measurement precision
If high sampling number is used in phase retrieval, then measurement precision is improved, but calculation complexity increases
Solution Approach 1:
The patent transforms the high-dimensional phase retrieval problem by changing parameters through modal decomposition. Instead of directly solving for all pixel phases, the solution is expressed in terms of Zernike polynomial coefficients, reducing the parameter space and simplifying calculations while maintaining measurement precision.
Solution Approach 2:
The patent applies local quality optimization by using modal decomposition that focuses on dominant wavefront error modes. Rather than uniformly processing all spatial frequencies, the method prioritizes correction of significant Zernike modes, reducing computational load while preserving essential measurement information.
3Ease of operation
If conventional iterative phase retrieval is used, then in-situ detection capability is improved, but difficulty in determining defocus position increases
Solution Approach 1:
The patent implements feedback through an optimization loop that iteratively adjusts the defocus position. The algorithm uses the measured intensity distribution and compares it with the theoretical point spread function, providing feedback to refine the defocus position estimate until convergence is achieved.
Solution Approach 2:
The patent performs preliminary action by using modal decomposition to estimate the defocus position before completing the full phase retrieval. This preliminary estimation provides a good initial guess that accelerates convergence and reduces the difficulty of determining the accurate defocus position.
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 precise, one-time full-aperture measurement of wavefront error without requiring accurate initial defocus position measurement, allowing for accurate wavefront error determination even with partially overexposed images.
Implementation Method 1
the phase retrieval method inversely infers the phase distribution by using the diffraction spot acquired at the focal plane or defocus position
Implementation Method 2
extended Nijboer-Zernike (ENZ) theory
Data Source
AI summary
The disclosure provides a device for detecting a wavefront error by modal-based optimization phase retrieval using an extended Nijboer-Zernike (ENZ) theory. The detection device includes a point light source (1), a half mirror (2), a lens (3) to be tested, a plane mirror (4) and an image sensor (5). The wavefront error of the component under test is characterized by using a Zernike polynomial, and a Zernike polynomial coefficient is solved based on an ENZ diffraction theory. The present disclosure realizes the one-time full-aperture measurement on the wavefront error of a large-aperture optical component, and can use a partially overexposed image to achieve accurate wavefront error retrieval. Meanwhile, the present disclosure overcomes the contradiction between underexposure and high signal-to-noise ratio (SNR) caused by a limited dynamic range when the image sensor (5) acquires an image. The detection device is simple and does not have high requirements for the experimental environment.