  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 holography 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 models such as
Generative-Adversarial Networks (cGAN) or Variational Autoencoder (cVAE), we
approximate conditional 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 8x8-matrix of complex-valued
spatial-frequency coefficients to the ensuing 100x100-shaped intensity
distribution recorded on a camera. We discuss the degree of 'ill-posedness'
that remains in this reduced problem and compare different generative model
architectures in terms of their ability to find holograms that reconstruct
given intensity patterns. Finally, we challenge our 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
providing 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.
