Least-squares fitting of Hartmann or Shack-Hartmann data with a circular array of sampling points

Area of Science:

• Optical Engineering
• Metrology
• Aberration Analysis

Background:

• Accurate characterization of optical aberrations is crucial for high-performance imaging systems.
• Traditional methods may lack precision or comprehensive analysis of various aberrations.
• The Hartmann and Shack-Hartmann tests are standard techniques for optical testing.

Purpose of the Study:

• To introduce a refined least-squares procedure for quantifying optical aberrations.
• To analyze the impact of sampling point distribution on aberration measurement accuracy.
• To provide a detailed mathematical analysis of different sampling configurations.

Main Methods:

• Utilized a least-squares fitting procedure based on transverse aberration measurements.
• Employed the Hartmann or Shack-Hartmann test for data acquisition.
• Investigated sampling point distributions in a ring pattern within the optical system's pupil.
• Analyzed configurations with 3, 4, 5, 6, or more sampling points.

Main Results:

• The described least-squares procedure effectively determines tilts, curvature, astigmatism, coma, and triangular astigmatism.
• Analysis reveals the properties and characteristics of different ring sampling configurations.
• Enhanced mathematical rigor provides deeper insights compared to prior work.
• The method demonstrates improved accuracy and detail in aberration analysis.

Conclusions:

• The proposed least-squares method offers a robust approach for optical aberration analysis.
• Ring sampling strategies, particularly with optimized point numbers, enhance measurement precision.
• This work advances the understanding and application of Hartmann-based optical testing techniques.