Surface figure measurement based on the transmitted wavefront with reverse raytracing

Abstract

A method of surface figure measurement is described based on the transmitted wavefront of an optical element obtained from a Mach-Zehnder interferometer. Given known values for the refractive index and center thickness, along with the sample's transmitted wavefront, the unknown surface profile is reconstructed in a deterministic way. The technique relies on knowledge of one of the surfaces of the element, such as an easy-to-measure plano or spherical surface, and is well suited for testing aspheric surfaces. Reverse raytracing is used to bring the transmitted wavefront from the detector to the unknown surface considering the refraction at the surfaces in the system. Reverse raytracing also removes the effects of transmission through a thick lens and the induced aberration associated with the interferometer. In the interferometer, the wavefront transmitted through the sample is tested against a plano reference. This method also has the ability to make measurements on multiplexed surfaces, such as a lenslet array, which traditionally cannot be measured without moving the sample. The surface profile of a plano-convex lens has been produced and verified against other metrology techniques for calibration purposes. Surface measurements on a cylindrical lens and a lenslet array are also presented.