Phase retrieval via SLM phase modulation in 4 f optical setup : numerical inverse imaging with sparse regularization for phase and amplitude

1 The 4f optical setup is considered with a wave …eld modulation by SLM (spatial light modulator) located in the focal plane of the …rst lens. Phase as well as amplitude of the wave …eld are reconstructed from noisy multiple intensity observations. The reconstruction is optimal due to a constrained maximum likelihood formulation of the problem. The proposed algorithm is iterative with decoupling of the inverse of the forward propagation of the wave …eld and the …ltering of phase and amplitude. The sparse modeling of phase and amplitude enables the advanced high accurate …ltering and sharp imaging of the complex-valued wave …eld. Artefacts typical for the conventional algorithms (wiggles, ringing, waves, etc.) and attributed to optical di¤raction can be suppressed by the proposed algorithm.

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