Freeform optics characterization with surface registration and fitting algorithms for optical point-based spatial...

Area of Science:

• Optical Engineering
• Metrology
• Computational Geometry

Background:

• Accurate form error characterization is crucial for freeform optics manufacturing and performance evaluation.
• Current surface registration and fitting algorithms struggle with the complexity of freeform optics.
• Optical point-based spatial path 3D topography metrology requires precise surface analysis.

Purpose of the Study:

• To develop improved surface registration and fitting algorithms for freeform optics.
• To enhance the accuracy of form error characterization in 3D topography metrology.
• To address limitations in current methods for freeform optics metrology.

Main Methods:

• B-spline surface description for freeform optics.
• Point orthogonal projection algorithm using the first-order Newton method.
• Lie algebra registration parameters for iterative coordinate adjustment.
• Least squares B-spline fitting method to improve upon the Zernike method.

Main Results:

• The proposed registration algorithm demonstrates good convergence and improves accuracy by one to two orders of magnitude compared to existing methods.
• Experiments show significant improvements in peak-to-valley and RMS accuracies for freeform prisms compared to the stylus method.
• The method effectively characterizes mid-to-high frequency form errors (around 200 nm) in freeform prisms.

Conclusions:

• The developed B-spline based algorithms offer a substantial advancement in freeform optics form error characterization.
• The improved accuracy and capability to detect finer errors are vital for advanced optical manufacturing.
• This work provides a more robust and precise solution for metrology of complex optical surfaces.