Advanced iterative algorithm for phase calibration ofspatial light modulators integrated in opticalinstrumentation in a vibration environment

We present a method to obtain the phase modulation characteristic curve of a spatial light modulator (SLM) under severe vibration conditions. The procedure is based on the well-known advanced iterative algorithm (AIA), which allows wavefront extraction from unknown phase-shifted interferograms. Generally, AIA is used to determine the wavefront and the determined phase shifts are of little interest. In contrast, in our method, the main goal of using AIA is to determine the unknown phase shifts induced by an SLM during the calibration procedure. Using a segmented approach to calibration, AIA enables successful calibration even in the presence of additional random phase shifts due to environmental changes. This method has the potential to calibrate SLMs integrated in complex optical instruments with little to no modifications to the optical setup, no matter the environmental conditions. We demonstrate our technique by calibrating an SLM under vacuum conditions (10−5mbar) in a common-path configuration compatible with usage of an SLM as a wavefront modulator at the pupil plane of an instrument. Our technique compensates for the vibrations produced by the vacuum pumps and reduces an order of magnitude the root-mean-squared error of the calibration curve evaluated with vibration errors. Our technique enhances the potential use of SLMs in complex optical systems, including aerospace optical instrumentation.