Design and Performance Analysis of Complex Optical Devices Using Symbolic Computation

The design of a complex optical instrument, such as an interferometer, leads to the study of a very large model represented as a set of equations that relate the parameters of the instrument. The problem is then to nd some optimal values of these parameters with respect to some performances. Due to the complexity of the models involved, there is no completely automatic method to solve this optimal design problem. We show below how computer algebra can be an invaluable tool to express some parameters or performances as functions of other parameters, and then to generate a dedicated numerical code when a symbolic treatment is no longer possible. We present a computer algebra package that we have developped to help the design and performance analysis of optical instruments.