Method for reconstruction of complex surface shapes from a reflection-based non-null interferometric measurement

Complex surface forms are becoming increasingly prevalent in optical designs, requiring advances in manufacturing and surface metrology to maintain the state of the art. Non-null interferometry extends the range of standard interferometers to test complex shapes without the need for complicated and expensive compensating elements. However, non-null measurements will accumulate significant retrace errors, or interferometer-induced errors, which can be difficult to isolate from surface figure errors. Methods discussed in the literature to correct for retrace errors in a reflection-based interferometer are computationally intensive and limited in spatial resolution. A method is presented for reconstructing complex surface shapes in a reflection-based non-null interferometer configuration, which is computationally efficient, easy to implement, and can produce high spatial resolution surface reconstructions. The method is verified against simulated surfaces that contain more than 200   μ m of surface departure from a null configuration. Examples are provided to demonstrate the effects of measurement noise and interferometer model uncertainties, as well as an experimental validation of the method.