Effects of defocus and other quadratic errors on OTF

Area of Science:

• Optics and Photonics
• Image Science

Background:

• The optical transfer function (OTF) is crucial for characterizing imaging system performance.
• Exact analytical solutions for the OTF are often unavailable, especially for complex aberrations.

Purpose of the Study:

• To develop a simple and accurate approximation for the OTF of defocused systems.
• To extend this approximation to other quadratic aberrations, such as astigmatism.

Main Methods:

• Utilizing a straightforward approximation technique.
• Applying the method to a circular pupil under defocus conditions.
• Generalizing the approach for quadratic aberrations.

Main Results:

• A simple, accurate approximate expression for the OTF of a defocused system was derived.
• The approximation method was successfully generalized to include astigmatism and other quadratic aberrations.
• Demonstrated the utility of the approximation for non-trivial optical aberrations.

Conclusions:

• The proposed approximation offers a practical solution for calculating the OTF in systems with defocus and other quadratic aberrations.
• This method simplifies the analysis of image quality in optical systems where closed-form solutions are lacking.
• Provides a valuable tool for optical design and performance evaluation.