Optical Surface Modification via Eigenvalue-Based Particle Irradiation
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Conventional methods for changing the surface shape of optical elements via particle irradiation often fail to achieve the desired accuracy due to the complexity of boundary conditions and constraints in the processing process.
Innovation Solution
A method and device that model the surface shape change using a merit function optimized by determining eigenvalues of an integral operator, allowing for a locally resolved effect distribution of particle irradiation to produce precise surface changes, incorporating Tikhonov regularization and external constraints to address ill-defined inverse problems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If conventional simulation methods are used to determine energy dose distribution for surface shape change, then the processing process can be simplified, but the manufacturing precision of the surface shape change deteriorates
Solution Approach 1:
The patent transforms the control problem from direct energy dose specification to eigenvalue-based parameter optimization. By changing the mathematical representation from conventional simulation parameters to eigenvalues and eigenfunctions of an integral operator, the system achieves both computational efficiency and high precision in surface shape modification.
Solution Approach 2:
The patent replaces conventional iterative simulation methods with an analytical solution based on integral operator theory. This substitution of mathematical approach transforms a computationally intensive process into an efficient eigenvalue problem, simultaneously improving ease of manufacture and maintaining manufacturing precision.
2Manufacturing precision
If the control variable is optimized using eigenvalues of an integral operator, then the manufacturing precision of surface shape change is improved, but the device complexity increases
Solution Approach 1:
The patent uses eigenfunctions as mathematical templates or 'copies' that represent optimal irradiation patterns. Instead of performing complex real-time simulations, the system pre-calculates eigenfunctions and uses them as reference patterns for control, reducing device complexity while maintaining high manufacturing precision.
Solution Approach 2:
The patent performs preliminary calculation of eigenvalues and eigenfunctions before the actual surface modification process. This pre-computation stores the optimal control parameters in advance, eliminating the need for complex real-time calculations during processing and reducing the operational complexity of the control system.
3Manufacturing precision
If a locally resolved effect distribution is applied through particle irradiation, then the manufacturing precision is improved, but the productivity decreases due to extended processing time
Solution Approach 1:
The patent segments the irradiation process into distinct eigenmode components, each corresponding to a specific spatial frequency or pattern of surface modification. This segmentation allows the control system to address different regions and features independently, achieving high local precision without requiring exhaustive scanning of the entire surface.
Solution Approach 2:
The patent utilizes the periodic or repeating nature of eigenfunctions to optimize irradiation patterns. By recognizing that eigenfunctions represent fundamental modes of surface modification, the system can apply irradiation in systematic, repeating patterns that efficiently achieve the desired surface shape change, improving productivity while maintaining precision.
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 high-accuracy surface shape modifications by optimizing the control variables for particle irradiation, ensuring precise production of desired surface changes with improved efficiency and accuracy.
Implementation Method 1
radiating particles onto the surface of the optical element with a locally resolved effect distribution corresponding to the determined predefinition for the control variable, for the purpose of producing local surface changes at the surface of the optical element
Data Source
AI summary
A method for changing a shape of a surface of an optical element by particle irradiation includes: modelling the problem of determining a resulting change of the surface shape of the optical element from a control variable; determining a predefinition for the control variable of the particle irradiation from a predefined desired change of a surface shape of the optical element by ascertaining an extremum of a merit function; and radiating particles onto the surface of the optical element with a locally resolved effect distribution corresponding to the determined predefinition for the control variable, for the purpose of producing local surface changes at the surface of the optical element. Ascertaining the extremum corresponds to the solution of an Euler equation. The Euler equation defines an integral operator. The eigenvalues of the integral operator are determined, and the predefinition is a linear combination of a finite number of eigenfunctions of the integral operator.