  Computer representations of real numbers are necessarily discrete, with some
finite resolution, discreteness, quantization, or minimum representable
difference. We perform astrometric and photometric measurements on stars and
co-add multiple observations of faint sources to demonstrate that essentially
all of the scientific information in an optical astronomical image can be
preserved or transmitted when the minimum representable difference is a factor
of two finer than the root-variance of the per-pixel noise. Adopting a
representation this coarse reduces bandwidth for data acquisition,
transmission, or storage, or permits better use of the system dynamic range,
without sacrificing any information for down-stream data analysis, including
information on sources fainter than the minimum representable difference
itself.
