Phase-probability shaping for speckle-free holographic lithography

Optical holography has undergone rapid development since its invention in 1948, but the accompanying speckles with alternating dark and bright spots of randomly varying shapes are still untamed now due to the intrinsic fluctuations from irregular complex-field superposition. Despite spatial, temporal and spectral averages for speckle reduction, holographic images cannot yet meet the requirement for high-homogeneity, edge-sharp and shape-unlimited features in optical display and lithography. Here we report that holographic speckles can be removed by narrowing the probability density distribution of encoded phase to homogenize optical superposition. Guided by this physical insight, an Adam-gradient-descent probability-shaping (APS) 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). These well-behaved performances revitalize CGH for lensless lithography, enabling experimental fabrication of arbitrary-shape and edge-sharp patterns with spatial resolution of 0.54λ/NA.