Off-axis conic surfaces: Interferogram simulation algorithm and its use in stressed mirror polishing

Off-axis conic sections optimizes the design of optical instruments, allowing unrestricted access to the focal point, and making possible to analyze the deflected light without disturbing the incident beam. In this paper are derived, as a first aim, a set of equations representing all kind of conical surfaces and their off-axis sections. With these analytical expressions, we found the associated wavefront coming from the off-axis sections. To complete this analysis, an algorithm was developed to obtain simulated interferograms for off-axis optical surfaces and was used in combination with interferometry to optical test this kind of surfaces in a quantitative way, an important aspect in optical fabrication, specifically the stressed mirror polishing technique. To test the algorithm and the derived equations, we compared experimental interferograms against interferograms calculated with our algorithm. Finally, we found that our method can calculate the aberration coefficients for any off-axis conical surface in a satisfactory manner, giving us the necessary data to control the fabrication process.