Ray and wave aberrations revisited: a Huygens-like construction yields exact relations

Area of Science:

• Optics and Photonics
• Optical Engineering
• Aberration Theory

Background:

• Optical system aberrations are described by wave aberrations (departure from ideal wavefront) or ray aberrations (deviations in image plane).
• The classical relationship between wave and ray aberrations is an approximation whose error has not been analytically quantified.

Purpose of the Study:

• To derive exact analytical equations for computing wavefront and ray aberrations from wave aberrations (Optical Path Difference - OPD).
• To precisely define conditions for a function to be an OPD function and analyze the error of the classical approximation.

Main Methods:

• Derivation of exact analytical equations relating OPD to wavefront surface and aberrated ray directions.
• Establishing precise conditions for a function to be a valid OPD function.
• Numerical simulations to illustrate results and quantify approximation errors.

Main Results:

• Exact equations derived for wavefront surface, aberrated ray directions, and transverse ray aberrations in terms of OPD.
• Precise conditions identified for a function to be an OPD function, with each having an associated wavefront.
• Quantification of approximation error, showing it increases with large numerical apertures and strong OPD gradients.

Conclusions:

• The classical approximation connecting wave and ray aberrations has a quantifiable error.
• Strict conditions for small approximation errors are established, highlighting the impact of numerical aperture and OPD gradient.
• The derived exact equations provide a more accurate framework for analyzing optical aberrations.