Generation of Reference Softgauges for Minimum Zone Fitting Algorithms: Case of Aspherical and Freeform Surfaces

Area of Science:

• Optical engineering
• Metrology
• Surface metrology

Background:

• High surface quality optical aspherical lenses are crucial for applications in medicine, synchrotrons, and vision.
• Accurate form error extraction from measured data relies on least squares (LS or L2-norm) or minimum zone (MZ) fitting algorithms.
• Minimum zone (MZ) fitting, also known as Chebyshev or L∞-norm, offers higher accuracy by minimizing peak-to-valley (PV) error compared to L2-norm.

Purpose of the Study:

• To develop a unique, robust approach for generating reference softgauges for complex optical shapes.
• To mathematically formulate and implement a non-vertex solution for creating these reference softgauges.
• To evaluate the performance of implemented MZ fitting algorithms (HTR and EPF) using the generated reference softgauges.

Main Methods:

• A novel robust approach based on a non-vertex solution was mathematically formulated and implemented.
• Reference softgauges were generated for complex shapes using the new approach.
• Two minimum zone (MZ) fitting algorithms, HTR and EPF, were tested on the generated reference pairs.

Main Results:

• The implemented non-vertex solution approach successfully generated reference softgauges.
• The HTR and EPF minimum zone (MZ) fitting algorithms were successfully tested on the generated reference pairs.
• The performance evaluation of the MZ fitting algorithms was conducted using metrics for degree of difficulty and performance measure.

Conclusions:

• The developed robust approach provides a reliable method for generating reference softgauges for complex optical shapes.
• The testing validates the effectiveness of the HTR and EPF algorithms in conjunction with the new softgauge generation method.
• This work contributes to guaranteeing the traceability, accuracy, and robustness of MZ fitting algorithms in optical manufacturing.