Speckle reduction in far field holograms using spatial light modulators

Reducing speckle in an hologram reconstruction setup requires precise calibration of both the spatial light modulator and the aberrations in the optical system. We calibrate the system using a physically interpretable digital twin implemented as a neural network with a camera-in-the-loop calibration scheme. In combination with a gradient-based optimizer and a loss function that enforces a smooth phase, this calibration allows us to demonstrate far-field projections without speckle in the predefined target area. In addition, we compare the gradient-based method with a method based on a speckle-free initial phase, which is computed using optimal transport. We investigate how the diffraction efficiency influences the image quality for both methods and how the modeled aberrations, or the absence of modeled aberrations, influence the image quality. With the method that uses the smoothed phase, local aberrations at the SLM appear as global deviations in the far field, as is typically the case for far-field holograms that use a random phase for initialization. For the method starting with the phase computed with optimal transport, local aberrations at the SLM plane appear as local deviations in the far field.