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Article History

Received: 1 November 2022

Accepted: 19 September 2025

First Online: 24 October 2025

Competing interests

: The authors J.H., Z.L., and F.S. declare no competing financial interests. The authors D.Z., W.F., and K.H. declare the following competing interests. D.Z., K.H., and W.F. have filed one patent application related to this work through the University of Science and Technology of China. This patent (D.Z., K.H. and W.F., “A method of phase-probability shaping for eliminating speckles in holography”, 2022113559812(2022), under review) applied by University of Science and Technology of China refers to the design algorithms of Adam-gradient-descent phase-probability shaping for speckle-free holograms. D.Z. and K.H. have filed two patents application related to this work through University of Science and Technology of China. The first patent applied (D.Z. and K.H., “A phase-type diffractive optical element and system for computer-generated-holography lithography in dry circumstance”, 2023100401398 (2023), under review) by University of Science and Technology of China refers to the binary-phase/amplitude CGH lithography in air. The second patent applied (D.Z. and K.H., “A diffractive optical element and system for computer-generated-holography lithography in liquid circumstance”, 2023100400821 (2023), under review) by University of Science and Technology of China refers to the binary-phase/amplitude CGH lithography in liquid.