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 μm 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.