Reflecting Mirror Surface Shape Optimization via Heating Sheets
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Solution Overview
Problem
Conventional cooling schemes fail to meet the high accuracy surface-shape requirements of reflecting mirrors in fourth-generation synchrotron radiation light sources and high pulse repetition frequency free-electron laser devices, as they are time-consuming and limited by optimization algorithms, often resulting in suboptimal surface shape compensation.
Innovation Solution
A method that determines heat flux vectors based on a response matrix, thermal deformation vector, and perturbation terms to minimize residual surface shape errors, applying these vectors to heating sheets to optimize the mirror surface shape efficiently.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If conventional multi-parameter optimization method is used in finite element analysis software, then surface shape compensation can be achieved, but the optimization process is very time-consuming and limited by optimization algorithms
Solution Approach 1:
The patent segments the optimization problem by dividing the mirror surface into multiple measurement points and representing the surface shape through a Zernike polynomial coefficient vector. This segmentation transforms the complex multi-parameter optimization into a more manageable form that can be efficiently solved using the proposed iterative algorithm, significantly reducing computation time while maintaining high precision surface shape compensation.
Solution Approach 2:
The patent changes the optimization parameters from direct surface height values to Zernike polynomial coefficients, which provide a more efficient parameter space for optimization. By working in this transformed parameter space and using the response matrix to relate heat flux vectors to coefficient changes, the optimization converges much faster than conventional methods while achieving the same precision goals.
2Manufacturing precision
If more than ten electric heaters are used to compensate surface shape, then surface shape control capability is improved, but the complexity of voltage/current optimization increases and may not yield satisfactory results
Solution Approach 1:
The patent implements a feedback mechanism where the actual surface shape measurements (represented by Zernike coefficients) are continuously compared with the target shape, and the heat flux vectors are iteratively adjusted based on the residual errors. This feedback loop enables effective control of multiple heaters by systematically coordinating their outputs to achieve the desired surface shape, reducing the complexity of controlling ten or more heaters simultaneously.
Solution Approach 2:
The patent replaces the conventional trial-and-error mechanical optimization approach with a mathematical model-based system. By establishing the response matrix that relates heat flux vectors to Zernike coefficient changes, and using iterative mathematical optimization instead of physical trial-and-error adjustments, the system efficiently coordinates multiple heaters with reduced complexity.
3Temperature
If conventional cooling schemes are applied, then thermal management is achieved, but the high accuracy surface-shape requirements (RMS height error several nm, slope error less than 100 nrad) cannot be met
Solution Approach 1:
The patent directly exploits thermal expansion by applying controlled heat flux vectors through heating sheets to induce precise surface shape changes that compensate for thermal deformation. Instead of merely cooling the mirror, the system uses localized heating to actively shape the surface, achieving nanometer-level precision by leveraging the thermal expansion properties of the mirror material in a controlled manner.
Solution Approach 2:
The patent changes from passive cooling to active thermal shaping by controlling the temperature distribution through optimized heat flux vectors. By precisely adjusting the thermal parameters (heat flux magnitude and distribution) across different regions of the mirror, the system achieves surface shape control with RMS height errors of several nanometers and slope errors below 100 nrad, far exceeding conventional cooling capabilities.
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 quickly determines an effective surface shape optimization scheme, reducing RMS height error from 40 nm to 0.009 nm and slope error from 192.7 nrad to 0.4 nrad, significantly improving the precision and efficiency of surface shape compensation.
Implementation Method 1
When the reflecting mirror absorbs the X-ray from the upstream, it will lead to the thermal deformation of the mirror surface
Implementation Method 2
a REAL (Resistive Element Adjustable Length) cooling scheme using an electric heater (i.e. electric heating sheet) for temperature compensation
Data Source
AI summary
The present disclosure provides a method and an apparatus for optimizing surface shape of a reflecting mirror. The method for optimizing surface shape of the reflecting mirror includes: determining each heat flux vector based on a response matrix, a thermal deformation vector and each perturbation term; determining each residual surface shape error based on the response matrix, the thermal deformation vector and each heat flux vector satisfying constraint conditions; and applying a heat flux vector corresponding to a minimum value of each residual surface shape error to a heating sheet of the reflecting mirror to optimize the surface shape of the reflecting mirror. The present disclosure may quickly determine an effective surface shape optimization scheme and meet the requirement of high-precision surface shape.