Complex 3D Holographic Projection via Adaptive Gradient Descent Optimization

Volumetric holographic projection is widely used in applications such as optical beam shaping for laser fabrication, optical trapping, and image reconstruction. Adaptive beam forming is typically achieved by displaying computer-generated holograms on spatial light modulators. However, the design process must fully account for the physical constraints of these devices and aim to maximize the utilization of their finite pixel array. The limited number of pixels restricts the range of spatial frequencies that can be encoded, thereby constraining the dimensionality of the space spanned by the Fourier basis used to synthesize arbitrary wavefronts. This study introduces a novel approach for optimizing three-dimensional field projection from a spatial light modulator by incorporating an adaptive gradient descent algorithm into the computer-generated hologram design process, aiming to enhance image quality through speckle noise reduction. Experimental validation demonstrates an enhancement in spot intensity uniformity by 11 % and a tenfold reduction in speckle noise relative to holograms produced via the conventional Gerchberg–Saxton algorithm. By quantifying the spatial bandwidth product of the reconstructed fields, we derive the fundamental resolution requirements for spatial light modulators and provide actionable insight into the efficient orchestration of sequential image projection and high-precision multi-spot laser targeting in advanced manufacturing systems.