Formulae for the geometrical propagation of a beam of light

The geometrical propagation of a beam of light is treated in this paper using aberration theory. Stop shifting on the aberration function and on the irradiance function provides insight into how the geometrical field changes as it propagates in free space. The formulae discussed in this paper give as a function of the field and aperture of an optical system, and to the sixth order of approximation, the wavefront deformation and, to the fourth order, the irradiance at the exit pupil plane of the system. The use of the formulae is illustrated with a lens design for uniform illumination that is nearly insensitive to the location of the illuminated surface.