Lookup tables for phase randomisation in hardware generated holograms

• Main Authors: Christopher, Peter J, Wilkinson, Timothy D
• Format: Journal Article
• Language: English
• Published: 31-03-2020
• DOI: 10.48550/arxiv.2004.04049

The rise in virtual and mixed reality systems has prompted a resurgence of
interest in two-dimensional and three-dimensional real-time computer generated
holography. Phase randomisation is an integral part of holographic projection
as it ensures independence in sub-frame techniques and reduces the edge
enhancement seen in flat-phase images. Phase randomisation requires, however,
the availability of a pseudo-random number generator as well as trigonometric
functions such as cos and sin. On embedded devices such as field programmable
gate arrays and digital signal processors this can be an unacceptable load and
necessitate the use of proprietary intellectual property cores. Lookup tables
are able to reduce the computational load but can run to many megabytes for
even low-resolution systems.
This paper introduces the use of lookup tables (LUTs) in the context of two
common algorithms used for real-time holographic projection: Gerchberg-Saxton
and One-Step Phase-Retrieval. A simulated study is carried out to investigate
the use of relatively small lookup tables where random numbers are repeated in
sequence. We find that the increase in error is low and tunable to under 5\%
even for small look up tables. This result is also demonstrated experimentally.
Finally, the implications of this study are discussed and conclusions drawn.