Modeling an uncompensated Michelson interferometer for freeform optical analysis

Optical characterization and measurement of freeform optical surfaces are challenging as fast and high-resolution optical testing techniques are required. In this paper, we present an analytical model describing the formation of the interference pattern using an uncompensated Michelson interferometer that is illuminated by freeform wavefronts. These wavefronts are formed by the refraction of an on-axis parallel beam of monochromatic light by a freeform refractive surface. Since the interference pattern is characterized by the shape of the optical surface, this model may contribute to the development of algorithms for efficient surface reconstruction. The developed model is based on the decomposition of the freeform-illuminated Michelson interferometer's layout into several layouts, each based on a specific gaussian beamlet, and its associated reference ray paths. Formulas are derived for one layout and are applicable to all layouts after taking into consideration the reference parameters of each layout. To demonstrate the developed methodology, simulation examples are provided and discussed.