Nonlinear ray tracing in focused fields, part 3. Monochromatic wavefront aberration: tutorial

Using the flux tracing algorithm developed in the previous two parts, we examine the nonlinear rays that pass through the focus of a lens containing monochromatic aberrations. Lens aberration is modeled differently in the numerical propagation algorithms relating to the thin lens and the ideal lens cases. For the former, an additive phase term is applied to the transmission function of the thin lens, which describes a distortion in the thickness function of the lens, and for the latter an additive phase term is added to the pupil function of the lens (the Fourier transform of the image plane). In both cases, the Zernike polynomials are applied to model various aberrations including spherical, defocus, comatic, astigmatism, trefoil, and quadrafoil. Despite the different methods of modeling aberration for the two types of lenses, remarkably similar results are obtained for both cases. A discussion is also provided on the relationship between classical wavefront aberration theory and nonlinear tracing. This paper demonstrates the extraordinary potential of nonlinear ray tracing to gain insights into complex optical phenomena.