Double-Conjugation Law in Geometrical Coherent Imaging. Application to Gaussian Beams

TL;DR

This paper derives a double-conjugation law in geometrical optics for coherent imaging of spherical caps, extends magnification concepts, and demonstrates that Gaussian beams follow these laws precisely.

Contribution

It introduces a geometrical optics-based derivation of the double-conjugation law and extends magnification concepts to finite distances, applying these to Gaussian beams.

Findings

Gaussian beams obey geometrical optics laws exactly.

The double-conjugation law is derived from geometrical optics principles.

A new magnification law for spherical caps is proposed.

Abstract

A centred system forms the coherent image of the optical field on a spherical cap, taken as an object, on another spherical cap, whose vertex and curvature center are the respective paraxial images of the vertex and center of the object cap. That ``double-conjugation'' law, usually obtained in the framework of a scalar theory of diffraction, is deduced from concepts of geometrical optics. A magnification law between radii of conjugate spherical-caps extends the notion of longitudinal magnification to finite distances, and generalizes the longitudinal Lagrange-Helmholtz formula. Applying the double-conjugation law to imaging Gaussian beams shows that those beams perfectly obey geometrical optics laws.