  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.

Optics