The evaluation of the variance of the wave-aberration difference function

Area of Science:

• Optical Engineering
• Image Science

Background:

• Designing high-quality optical systems requires managing wave-aberration differences.
• Hopkins' tolerance theory emphasizes minimizing the variance (K) of the wave-aberration difference function.

Purpose of the Study:

• To present a method for calculating wave-aberration variance (K) using universal coefficients.
• To provide a criterion for evaluating optical system performance across the entire field of view.

Main Methods:

• The study introduces universal coefficients P(i,j;s), Q(i,j;spsi), and R(i,j;spsi).
• These coefficients enable the calculation of variance K for both axial and extra-axial images.
• The calculation relies on known wave-aberrations of specific rays.

Main Results:

• Demonstrated that variance K can be calculated using the defined universal coefficients.
• Showcased the determination of these coefficients based on wave-aberration polynomial functions and ray tracing patterns.
• Presented examples of the calculated coefficients.

Conclusions:

• The developed method simplifies the calculation of wave-aberration variance for optical system design.
• The universal coefficients offer a practical tool for assessing and optimizing image quality.
• This approach aids in achieving desired optical performance by minimizing aberration variance.