Point spread function of an optical system with defocus and spherical aberration-analytical formulas

Area of Science:

• Optics and Optical Engineering
• Computational Physics

Background:

• Optical systems are susceptible to aberrations like defocus and spherical aberration, which degrade image quality.
• Accurate Point Spread Function (PSF) calculation is crucial for understanding and correcting these aberrations.

Purpose of the Study:

• To develop an analytical procedure for calculating the PSF in optical systems with defocus and spherical aberration.
• To derive explicit formulas for approximating the PSF, accommodating spherical aberration up to the ninth order.

Main Methods:

• Analytical calculation of the Point Spread Function (PSF).
• Derivation of explicit approximate formulas for PSF incorporating spherical aberration.
• Application and validation of derived formulas on specific optical system examples.

Main Results:

• A novel procedure for the analytical calculation of PSF in aberrated optical systems is established.
• Explicit formulas are derived for approximating the PSF with spherical aberration up to the ninth order.
• The method's applicability is demonstrated through examples involving third-order spherical aberration.

Conclusions:

• The developed analytical method provides an efficient way to approximate the PSF in optical systems with aberrations.
• The derived formulas offer a valuable tool for optical designers and researchers working with complex optical systems.
• This work contributes to improved image quality prediction and correction in optical instrumentation.