Ultra-Precision Freeform Surface Alignment via Iterative Coordinate Transfer
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Solution Overview
Problem
Current methods are inadequate for characterizing ultra-precision freeform surfaces with sub-micrometer form error accuracy, particularly due to geometrical complexities and limitations in coordinate alignment and projection techniques.
Innovation Solution
A method involving feature point selection, zone pairing, and iterative coordinate adjustments using a transfer matrix to minimize separation between surfaces, employing algorithms like Bezier and B-Spline for precise alignment and error calculation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional coordinate alignment methods are used for freeform surfaces, then the measurement process is simplified, but the alignment precision cannot achieve sub-micrometer level
Solution Approach 1:
The coordinate alignment process is divided into three distinct stages: first-degree separation (translation alignment using centroid), second-degree separation (rotation alignment using principal moments of inertia), and third-degree separation (fine adjustment). This segmentation allows each stage to focus on specific alignment tasks, achieving sub-micrometer precision while maintaining systematic control over the complexity
Solution Approach 2:
The method performs preliminary alignment actions in a predetermined sequence before final measurement. First, translation alignment is performed using centroid coordinates, then rotation alignment using principal moments of inertia, and finally fine adjustment. This preliminary action framework ensures that major misalignments are corrected before detailed measurement, achieving high precision without overwhelming complexity
2Productivity
If feature points are selected for alignment, then the alignment process becomes more efficient, but the accuracy may be insufficient for ultra-precision surfaces
Solution Approach 1:
The alignment method segments the efficiency-accuracy tradeoff by applying different strategies at different stages: feature points (centroid, principal moments of inertia) are used for coarse alignment to ensure efficiency, while subsequent fine adjustment stages use all measured points to achieve ultra-precision accuracy. This segmented approach allows both efficiency and high precision to be achieved
Solution Approach 2:
Feature points are used for preliminary alignment actions that establish a good initial position quickly, improving efficiency. Then, finer adjustments using all measured data points refine the alignment to achieve sub-micrometer accuracy. The preliminary action with feature points prevents wasting computational resources on already-corrected misalignments
3Measurement precision
If iterative coordinate transfer is performed, then the form error calculation becomes more accurate, but the computation time increases significantly
Solution Approach 1:
The iterative coordinate transfer is segmented into a fixed sequence of three non-linear optimization steps: translation alignment, rotation alignment, and fine adjustment. By segmenting the iteration into distinct phases with clear convergence criteria at each stage, the method achieves accurate form error calculation while controlling total computation time through systematic progression
Solution Approach 2:
Translation and rotation alignments are performed as preliminary actions before fine adjustment iterations. These preliminary actions eliminate major sources of error first, allowing subsequent fine adjustment iterations to converge faster and with fewer iterations. This reduces total computation time while maintaining high form error accuracy
4Reliability
If the measured surface is pre-located using rotation and movement, then the systematic error is eliminated, but the alignment complexity increases
Solution Approach 1:
The pre-location process is segmented into systematic steps: translation alignment using centroid, rotation alignment using principal moments of inertia, and fine adjustment. Each segment addresses specific types of systematic errors (translation errors, rotation errors, and residual errors respectively), eliminating systematic errors comprehensively while maintaining procedural clarity and manageability
Solution Approach 2:
Translation and rotation alignments are performed as preliminary actions to eliminate major systematic errors before detailed measurement and analysis. This preliminary elimination of systematic errors ensures reliability of subsequent measurements while keeping the overall procedure organized and manageable through clear separation of error correction stages
Data Source
AI summary
Ultra-precision freeform surfaces are important to the development of complex and micro-optical-electro-mechanical devices used in many photonics and telecommunication products such as F-theta lenses for laser printers. These surfaces are complex and large scale surface topologies with shapes that generally possesses no rotational symmetry. Due to the geometrical complexities of these ultra-precision freeform surfaces, it is difficult to characterize the form accuracy and surface quality of freeform optical surfaces. The method of this invention is based on feature-point pre-fixture, and iterative precision alignment algorithm, which can provide sufficient capability of form characterization for ultra-precision freeform surfaces with form accuracy down to below sub-micrometer range