Modifications to Matrix Optics to Support the Use of the Periaxial Approximation in the Interferometry of Cylindrical Surfaces

Interferometers are the gold standard for the precise measurement of small distances. For flat surfaces, interferometry can usually be conducted using the paraxial approximation. When the geometry of the surface cannot be treated as approximately flat, the paraxial approximation generally must be abandoned, but in special cases small modifications can preserve it. Once such modification, designed to maintain the use of the paraxial approximation when working with a cylindrical surface for the precision measurement of the universal gravitational constant, will be presented.