Complex-Valued Field Metrology Using Fourier Plane Modulation
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current metrology devices face challenges in reducing calculation time and increasing throughput for complex-valued field measurements, particularly in lithographic processes, due to computationally expensive iterative algorithms and questionable assumptions in focus diversity methods.
Innovation Solution
A method and apparatus that use multiple modulation functions applied in the Fourier plane of an imaging system to non-iteratively determine the complex-valued field from image data, employing pairs of masks or phase modulators to reconstruct the field without mechanical movement or iterative processes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If iterative algorithms are used to reconstruct the complex-valued field from multiple diverse images, then measurement precision can be improved, but calculation time increases significantly and throughput decreases
Solution Approach 1:
The patent replaces the iterative computational algorithm (mechanical process) with a direct mathematical calculation method. By using the known modulation functions and captured images to directly compute the complex-valued field through algebraic operations rather than iterative refinement, the system achieves the same measurement precision without the computational overhead of repeated iterations, thereby significantly reducing calculation time and increasing throughput
Solution Approach 2:
The patent applies modulation functions to the images before reconstruction to encode the necessary information for direct calculation. By pre-processing the images with known modulation patterns (such as phase shifts or amplitude modulations) and using these modified images in a direct reconstruction formula, the system eliminates the need for iterative searching, achieving both high precision and fast computation
2Loss of information
If focus diversity methods are used to obtain multiple diverse images, then sufficient information for reconstruction can be obtained, but mechanical movement of the sample is required which complicates the system
Solution Approach 1:
The patent replaces the mechanical focus diversity method (physically moving the sample or detector through different focal planes) with a computational approach using modulation functions. By applying different known modulation functions (such as phase masks or amplitude modulations) to the same focused image, the system generates multiple diverse images without any mechanical movement, thereby obtaining sufficient information for reconstruction while eliminating mechanical complexity
Solution Approach 2:
The patent changes the optical parameters (phase or amplitude) of the illumination or detection path through modulation functions rather than changing the geometric parameters (focus position) through mechanical movement. By modulating the light field with known functions and capturing the resulting diverse images, the system achieves the same information diversity as focus stacking without requiring mechanical focus adjustment mechanisms
3Measurement precision
If multiple diverse images under different focus conditions are used for phase calculation, then reconstruction accuracy can be improved, but the defocus range must be limited which restricts the obtainable information
Solution Approach 1:
The patent changes from using geometric parameter variations (defocus distance) to using optical parameter variations (modulation function characteristics). By applying different modulation functions with varying phases, amplitudes, or spatial frequencies to the image, the system retrieves phase information with high accuracy without being constrained by a limited defocus range, thereby improving both precision and adaptability
Solution Approach 2:
The patent transitions from varying the focus dimension (one-dimensional depth adjustment) to varying the modulation function dimension (multi-dimensional optical parameter space). By exploring diversity in the modulation domain rather than the focus domain, the system achieves accurate phase retrieval while accessing a much broader range of information, effectively adding another dimension to the measurement space
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 significantly reduces calculation time and improves throughput by directly reconstructing the complex-valued field from imaging data, providing a more efficient and reliable method for metrology applications.
Implementation Method 1
an imaging system for imaging a field reflected from a sample
Implementation Method 2
at least two different modulation functions are imposed in a Fourier plane of the imaging system
Data Source
AI summary
Disclosed is a method of determining a complex-valued field relating to a sample measured using an imaging system. The method comprises obtaining image data relating to a series of images of the sample, imaged at an image plane of the imaging system, and for which at least two different modulation functions are imposed in a Fourier plane of the imaging system; and determining the complex-valued field from the imaging data based on the imposed modulation functions.