Analytical investigation of the parasitic diffraction orders of tilt carrier frequency computer-generated holograms

Computer-generated holograms (CGHs) are commonly used to test aspheric surfaces. In order to eliminate the influence of spurious diffraction orders, adequate carrier frequency is applied to CGHs to separate the overlapping orders. This paper describes a paraxial parametric model for separating the parasitic diffraction orders of a tilt carrier frequency CGH placed outside the interferometer focus. The approximate analytical expression for the disturbing field on the filter plane is derived using the paraxial model. This expression provides a recipe for determining the amount of tilt carrier frequency needed to eliminate the disturbing orders, and is applicable to concave weak aspheric surfaces with large f-numbers of the best-fit spheres, where paraxial approximation is valid. CGH design examples are provided.