Non-linear grid fitting for fiducial coordinate mapping
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Solution Overview
Problem
Conventional image acquisition and data processing systems fail to accurately identify non-linear transformations between imaged coordinates and actual coordinates on fiducial plates, leading to distorted feature geometry due to factors like fiducial absence, rotations, and optical distortions.
Innovation Solution
A method and system for non-linear grid fitting and coordinate system mapping, which involves fitting a fiducial grid model to acquired data, establishing a conversion from camera coordinates to ideal fiducial coordinates, and calculating absolute locations using polynomial fits and linear least squares operations, effectively accounting for distortions such as keystone and barrel effects.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional image acquisition systems are used, then the imaging process is simple, but the measurement precision deteriorates due to inability to identify non-linear transformations
Solution Approach 1:
The patent applies preliminary action by pre-establishing a fiducial grid model with known non-linear transformation parameters before actual measurement. The system uses reference fiducials with predetermined coordinates and pre-calculated distortion models to compensate for optical and mechanical distortions during the measurement process, thereby improving measurement accuracy without requiring complex real-time correction algorithms.
Solution Approach 2:
The patent introduces an intermediary approach by using a virtual coordinate transformation model as a mediator between the physical fiducial plate and the digital image. This model includes intermediate representation layers that map physical coordinates through non-linear transformations to image coordinates, enabling accurate measurement while maintaining computational efficiency through pre-computed transformation matrices.
2Measurement precision
If non-linear transformation modeling is implemented, then the measurement precision improves, but the difficulty of detecting and measuring increases
Solution Approach 1:
The patent applies copying by creating a virtual copy of the fiducial grid model with predetermined non-linear transformation parameters. This digital twin includes replicated fiducial positions and distortion characteristics that mirror the physical setup, allowing the system to detect and measure transformations by comparing the virtual model against actual image data without requiring complex real-time analysis of the physical system.
Solution Approach 2:
The patent implements feedback mechanisms by continuously comparing measured fiducial positions in the image against the predetermined coordinates in the fiducial grid model. The system uses this feedback to calculate transformation parameters and adjust the coordinate mapping in real-time, making the detection and measurement process more straightforward while maintaining high precision through iterative refinement.
Data Source
AI summary
A system and method of non-linear grid fitting and coordinate system mapping may employ data processing techniques for fitting a set of measured fiducial data to an ideal set of fiducials; the fiducials may be arranged in a known (e.g., Cartesian grid) pattern on a substrate imaged by an imaging apparatus. Exemplary embodiments may model the non-linear transformation to and from imaged coordinates (i.e., coordinates derived from acquired image data) and artifact coordinates on the fiducial plate (i.e., actual coordinates of the fiducial relative to a reference point on the fiducial plate).