Intensity-coupled multi-beam phase retrieval for holographic volumetric additive manufacturing

Multi-beam holographic projection is a promising yet underexplored avenue for advanced volumetric additive manufacturing (VAM) systems to control image focus in 3D, compensate for aberrations, and overcome resolution anisotropy. Nevertheless, there is currently no formal method to jointly optimize multiple holographic projections for maximum reconstruction fidelity of the printed object. 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 and time-multiplexed scanning beams. Among all demonstrations, a special test case of holo-tomographic patterning achieved the lowest error with 128 simultaneously optimized holograms, highlighting its potential in high-contrast microscale fabrication. All testing results indicate that a fully coupled optimization offers superior solutions relative to a decoupled optimization approach.