Multi-beam phase mask optimization for holographic volumetric additive manufacturing

The capability of holography to project three-dimensional (3D) images and correct for aberrations offers much potential to enhance optical control in light-based 3D printing. Notably, multi-beam multi-wavelength holographic systems represent an important development direction for advanced volumetric additive manufacturing (VAM). Nonetheless, searching for the optimal 3D holographic projection is a challenging ill-posed problem due to the physical constraints involved. This work introduces an optimization framework to search for the optimal set of projection parameters, namely phase modulation values and amplitudes, for multi-beam holographic lithography. The proposed framework is more general than classical phase retrieval algorithms in the sense that it can simultaneously optimize multiple holographic beams and model the coupled non-linear material response created by co-illumination of the holograms. The framework incorporates efficient methods to evaluate holographic light fields, resample quantities across coordinate grids, and compute the coupled exposure effect. The efficacy of this optimization method is tested for a variety of setup configurations that involve multi-wavelength illumination, two-photon absorption, and time-multiplexed scanning beam. A special test case of holo-tomographic patterning optimized 64 holograms simultaneously and achieved the lowest error among all demonstrations. This variant of tomographic VAM shows promises for achieving high-contrast microscale fabrication. All testing results indicate that a fully coupled optimization offers superior solutions relative to a decoupled optimization approach.