  Recently developed iterative and deep learning-based approaches to
computer-generated holography (CGH) have been shown to achieve high-quality
photorealistic 3D images with spatial light modulators. However, such
approaches remain overly cumbersome for patterning sparse collections of target
points across a photoresponsive volume in applications including biological
microscopy and material processing. Specifically, in addition to requiring
heavy computation that cannot accommodate real-time operation in mobile or
hardware-light settings, existing sampling-dependent 3D CGH methods preclude
the ability to place target points with arbitrary precision, limiting
accessible depths to a handful of planes. Accordingly, we present a
non-iterative point cloud holography algorithm that employs fast deterministic
calculations in order to efficiently allocate patches of SLM pixels to
different target points in the 3D volume and spread the patterning of all
points across multiple time frames. Compared to a matched-performance
implementation of the iterative Gerchberg-Saxton algorithm, our algorithm's
relative computation speed advantage was found to increase with SLM pixel
count, exceeding 100,000x at 512x512 array format.
