Sampling density and quantitative microscopy.

The sampling densities required for the quantitative analysis of digitized microscope images is discussed. It is shown that the Nyquist sampling theorem is not the proper reference point for determining the sampling density when the goal is measurement, although it may be a proper reference point when the goal is image filtering and reconstruction. The problems associated with signal truncation--the use of a finite amount of data--and the finite amount of time available for computation make it impossible to reconstruct an arbitrary image, even if it is bandlimited. Two examples taken from straightforward measurement problems exhibit the fundamental problems associated with the measurement of analog quantities from digital data and the role played by the sampling density.