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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 thedoi:10.1086/651009 fatcat:3dpctypu6fblzi5laitkaf4vge