Approaching optical metrology with multiple light sources and compressive sensing

Complex optical surfaces such as aspheres and freeforms are used in optical systems to reduce aberrations or to achieve high optical performance with a compact design and less optical surfaces. Due to limited acceptance angles of conventional interferometric techniques, there is still no satisfactory solution for their form measurement that is at the same time precise, flexible, and fast. Often these surfaces are surveyed by pointwise measurement, or the aperture problem is overcome by elaborately compensating wave front deviations either through compensator lenses or computer-generated holograms. Alternatively, several subapertures are used to capture the whole surface. These, however, have to be recorded in sequence since the superposition of multiple independent wave fields cannot be assigned a time-independent wave front. Instead, we present a compressive sensing approach for Multiple Aperture Shear-Interferometry (MArS) which captures multiple overlapping subapertures simultaneously and allows a flexible measurement of aspheres with multi-spot illumination. MArS uses the mutual intensity as the primary measurand which is still well defined for superposed mutually incoherent wave fields. The mutual intensity is sparse in phase space for there are only a finite number of distinct wave fields at every surface point. Utilizing this sparsity, the presented compressive sensing approach avoids superflously large space-bandwidth products and significantly reduces the number of necessary measurements.