Stitch Measurement System for Astronomical Mirrors
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Solution Overview
Problem
The stitch technique for combining partial measurements in optical testing of astronomical mirrors faces challenges in precision due to system errors, especially when using non-circular data from circular partial measurement regions, leading to dropped precision and varying coefficients in Zernike polynomial definitions.
Innovation Solution
A method involving lattice formulation to divide partial measurement regions into first and second regions, defining orthogonal function sequences, and calculating system errors through linear combinations and consistency functions to optimize correction variables, allowing for precise surface shape measurement.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If Zernike polynomials are used to define system errors on circular partial measurement regions, then the measurement can be performed using standard orthogonal functions, but precision drops when correcting system errors on non-circular data existence regions
Solution Approach 1:
The patent applies local quality by formulating orthogonal function sequences that are specifically adapted to each partial measurement region's actual data existence region shape, rather than using a uniform circular basis. This allows the mathematical basis to match the local geometry of where measurement data actually exists, improving correction precision for each region while maintaining ease of definition through systematic orthogonalization procedures.
2Adaptability or versatility
If Zernike polynomials are used for system error definition, then a consistent mathematical framework is provided, but coefficients of bases become different depending on the bases used, reducing consistency
Solution Approach 1:
The patent changes the fundamental parameter of the mathematical basis from fixed Zernike polynomials defined on circles to dynamically formulated orthogonal function sequences that adapt to each partial measurement region's specific geometry. This parameter change ensures that the basis functions inherently match the data existence regions, making coefficients consistent across different regions while maintaining mathematical rigor through orthogonalization.
3Device complexity
If partial measurement regions are combined without overlapping, then the measurement process is simpler, but high-resolution information is lost
Solution Approach 1:
The patent applies segmentation by dividing the overall measurement region into multiple partial measurement regions that do overlap, then systematically formulating orthogonal function sequences for each region. The segmentation approach, combined with the mathematical correction method, allows overlapping regions to capture high-resolution information while the orthogonal function formulation provides a systematic way to process and combine these segmented measurements, resolving the contradiction between simplicity and information retention.
Data Source
AI summary
The present invention provides a stitch measurement method for making a plurality of partial measurements, and obtaining an overall shape by combining partial measurement results, including a step of dividing, on lattices, each peripheral partial measurement region including an external portion of an overall measurement region into a first region inside the overall measurement region and a second region outside the overall measurement region, and dividing each central partial measurement region which does not include any external portion of the overall measurement region into a first region and a second region according to division patterns of the peripheral partial measurement region, a step of formulating first orthogonal function sequences on the first regions, and a step of defining linear combinations of respective functions of the first orthogonal function sequences on the first regions as first system errors for the respective partial measurement regions on the overall measurement region.