Wavefront Reconstruction in Grating Shearing Interferometry
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Solution Overview
Problem
Existing wavefront reconstruction algorithms in grating-based lateral shearing interferometers require a constant shear amount, which is not feasible in large NA optical systems with varying shear distribution, leading to increased computational complexity and reduced accuracy.
Innovation Solution
A method that simultaneously compensates pupil coordinate distortion and shear amount change by establishing a coordinate correspondence relation using an inverse solving algorithm, building a polynomial fitting matrix, and reconstructing the wavefront using least-square methods, allowing for accurate wavefront reconstruction even with changing shear distributions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional wavefront reconstruction algorithms are used in large NA optical systems, then the algorithms can process wavefront data, but the shear amount varies with position causing coordinate distortion and reduced measurement precision
Solution Approach 1:
The patent pre-calculates the coordinate transformation relationship between the detector plane and pupil plane before wavefront reconstruction. By establishing the mapping relation in advance through inverse solving algorithms, the method eliminates the need for complex real-time coordinate transformations during reconstruction, thereby maintaining measurement precision while reducing computational complexity.
Solution Approach 2:
The patent transforms the coordinate system parameters by establishing a polynomial mapping relationship between detector coordinates (xd, yd) and pupil plane coordinates (x, y). This parameter transformation compensates for the shear amount variation and coordinate distortion caused by large NA, enabling accurate wavefront reconstruction without increasing device complexity.
2Adaptability or versatility
If linear interpolation is used to estimate shear phase in large NA systems, then the problem of varying shear distribution can be addressed, but computational complexity increases and accuracy is limited
Solution Approach 1:
The patent replaces the mechanical interpolation process with a mathematical polynomial fitting approach. Instead of using linear interpolation to estimate shear phase at different positions, the method uses pre-established coordinate transformation relations and polynomial fitting to directly calculate wavefront coefficients, thereby maintaining adaptability to varying shear distribution while significantly reducing computational complexity.
3Measurement precision
If polynomial fitting is used to model wavefront with varying shear, then accurate reconstruction can be achieved, but the calculation complexity increases compared to constant shear assumptions
Solution Approach 1:
The patent performs the computationally intensive coordinate transformation calculations in advance, before actual wavefront reconstruction. By pre-calculating the mapping relationship between detector coordinates and pupil plane coordinates, the method stores these transformation parameters for rapid reuse during reconstruction, thereby achieving accurate polynomial fitting without increasing reconstruction time.
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 method enables minimal calculation complexity and faster wavefront reconstruction by calculating the coordinate transformation relation once, effectively compensating shear amount changes and coordinate distortions, while maintaining accuracy.
Implementation Method 1
a wavefront to be measured is diffracted by a grating and then propagates along different diffraction directions to form diffracted wavefronts of different orders
Implementation Method 2
when any two diffracted wavefronts are subjected to shear interference, shear amounts corresponding to shear interference phases at different positions are also different
Data Source
AI summary
Method for simultaneously compensating pupil coordinate distortion and shear amount change in a process of wavefront reconstruction in grating transverse shear interference. Where a wavefront is diffracted by a grating, the shapes and light paths of the diffracted wavefronts of all the orders are different, so that on one hand, a coordinate system detected by a detector plane is distorted relative to a pupil coordinate system, and on the other hand, a shear amount changes along with a coordinate position.