Phase-probability shaping for speckle-free holographic lithography

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.