Fourier Theory Of Conical Scan Demodulation

Abstract

Conical scanning of a laser beam can be effectively used to measure the pointing offset of that laser beam from a point-reflective target such as a retro-reflector. The conical scan measurement method codes the lower frequency pointing error onto a carrier at the frequency of the conical motion. It then reduces the time varying, measured reflected beam intensity by a phase sensitive demodulation technique. Previous analyses of the conical scan measurement method have assumed a laser beam shape that is Gaussian. In practice the laser beam is often not Gaussian, leaving open the question of how well this method works for realistic beams. The present report describes a beam shape independent analysis of the conical scan laser pointing offset measurement process. A formulation is given that represents the process as an infinite series of differential operators acting on the beam shape function. This series is found to be rapidly convergent for unimodal beam shapes and small scan' radii.