  Optical holography has undergone rapid development since its invention in
1948, but the accompanying speckles with randomly distributed intensity are
still untamed now due to the fundamental difficulty of eliminating intrinsic
fluctuations from irregular complex-field superposition. Despite spatial,
temporal and spectral averages for speckle reduction, it is extremely
challenging to reconstruct high-homogeneity, edge-sharp and shape-unlimited
images via holography. Here we predict that holographic speckles can be removed
by narrowing the probability density distribution of encoded phase to
homogenize optical superposition. Guided by this physical insight, a
machine-learning-assisted probability-shaping (MAPS) method is developed to
prohibit the fluctuations of intensity in a computer-generated hologram (CGH),
which empowers the experimental reconstruction of irregular images with
ultralow speckle contrast (C=0.08) and record-high edge sharpness (~1000 mm-1).
It breaks the ultimate barrier of demonstrating high-end CGH lithography, thus
enabling us to successfully pattern arbitrary-shape and edge-sharp structures
such as vortex gratings and two-dimensional random barcodes.
