Relating wavefront error, apodization, and the optical transfer function: on-axis case: comment

Area of Science:

• Optics
• Image Science
• Optical Engineering

Background:

• A previous study proposed a linear expansion for calculating the optical transfer function (OTF) based on wavefront errors.
• The prior method claimed rapid OTF calculation through recursive coefficient determination.

Purpose of the Study:

• To present an alternative, faster method for calculating the optical transfer function (OTF).
• To introduce non-recursive, closed-form basis functions for OTF computation.
• To demonstrate the efficiency of a digital autocorrelation approach for OTF calculation.

Main Methods:

• Development of closed-form basis functions for OTF expansion.
• Implementation of digital autocorrelation of the pupil function for OTF calculation.
• Comparative analysis of computational speed against recursive methods.

Main Results:

• The proposed closed-form basis functions offer a direct approach to OTF calculation.
• Digital autocorrelation of the pupil function demonstrates superior speed.
• The computational advantage remains consistent across varying wavefront complexities.

Conclusions:

• The digital autocorrelation method provides a significantly faster alternative for OTF calculation.
• Closed-form basis functions eliminate the need for recursive calculations.
• This approach enhances the efficiency of optical system analysis and design.