  This publication extends the HoloTile framework to three dimensions,
introducing the ability to generate arbitrary dynamic patterns composed of
extended depth-of-field non-diffractive beamlets with theoretically 100%
diffraction efficiency. In particular, we demonstrate experimentally the
generation of speckle-reduced reconstruction patterns, consisting of spatially
multiplexed extended Bessel-like beamlets, implemented on a phase-only spatial
light modulator (SLM). Due to the inherent separation of the tiled subhologram
and the point spread function shaping hologram in HoloTile, we show that the
reconstruction amplitude can be expressed as a simple convolution of the
contributions from the two holograms. This results in a discretely sampled
reconstruction, with each spatial frequency component exhibiting long DoF with
characteristic Bessel beam properties. This separation facilitates spatial and
temporal multiplexing of both contributions, and allows for real-time dynamic
patterning with extended DoF. Additionally, a geometric analysis is included,
allowing for the direct calculation of the propagation characteristics of the
beamlets.
