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Holographic wave-shaping has found numerous applications across the physical sciences, especially since the development of digital spatial-light modulators (SLMs). A key challenge in digital holog- raphy consists in finding optimal hologram patterns which transform the incoming laser beam into desired shapes in a conjugate optical plane. The existing repertoire of approaches to solve this inverse problem is built on iterative phase-retrieval algorithms, which do not take optical aberrations and deviations from theoretical models into account. Here, we adopt a physics-free, data-driven, and probabilistic approach to the problem. Using deep conditional Generative-Adversarial-Networks (cGAN) and conditional Variational Autoencoder (cVAE) architectures, we approximate posterior distributions of holograms for a given target laser intensity pattern. In order to reduce the cardinality of the problem, we train our models on a proxy mapping relating an 8 × 8-matrix of complex-valued spatial-frequency coefficients to the ensuing 100 × 100-shaped intensity distribution recorded on a camera. We discuss the degree of ’ill-posedness’ that remains in this reduced problem and challenge our generative models to find holograms that reconstruct given intensity patterns. Finally, we study the ability of the models to generalise to synthetic target intensities, where the existence of matching holograms cannot be guaranteed. We devise a forward-interpolating training scheme aimed at provid- ing models the ability to interpolate in laser intensity space, rather than hologram space and show that this indeed enhances model performance on synthetic data sets.

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