Reconstruction of a conic-section surface from autocollimator-based deflectometric profilometry

Area of Science:

• Optical Engineering
• Metrology
• Surface Science

Background:

• Autocollimator-based deflectometry is crucial for measuring large optical surfaces.
• Limited angular range necessitates rotating the optic, creating unknown coordinate frames for each scan.
• Reconstructing a coherent surface from misaligned scans is a significant metrology challenge.

Purpose of the Study:

• To present a novel method for reconstructing large conic-section optical surfaces from 1D line scans.
• To address the challenge of unknown coordinate reference frames between scans.
• To achieve accurate surface reconstruction despite measurement system limitations.

Main Methods:

• Utilizing a 6N+2 dimensional optimization approach, where N is the number of scan lines.
• Employing gradient-based nonlinear least squares fitting.
• Implementing a multistart global-search strategy for robust convergence.

Main Results:

• Successfully reconstructed best-fit conic-section surfaces from misaligned 1D line scans.
• Demonstrated a method to overcome the unknown coordinate frame problem inherent in deflectometry.
• Achieved high accuracy in surface reconstruction through careful problem formulation and optimization.

Conclusions:

• The developed method provides an effective solution for reconstructing large optical surfaces using autocollimator deflectometry.
• Accurate surface metrology is achievable even with rotational misalignment between scans.
• This technique enhances the capabilities of optical testing for large optics.