Designing afocal achromatic doublet lenses

A method for designing afocal achromatic doublet is presented. We have implemented an exact ray trace through a separated doublet lens considering a plane wavefront propagating along the optical axis. The analytic equation of both the caustic surface and the back focal length for separated doublet lenses are provided. Demanding that the back focal length tends to infinity, we impose the conditions to design afocal optical systems, obtaining sixth and fourth degree polynomials as a function of the radii of curvature. In order to produce an afocal achromatic optical system, we solve numerically a set of two nonlinear equations assuming two spectral lines. Therefore, we have two unknowns which are the curvature radii for both the front surface and the rear surface. The contribution of this work is to provide simple formulas for designing optical beam expander or reducer devices based on separated doublets.