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

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.