General sampling theorem and application in digital holography

Abstract

The most common sampling theorem is Shannon-Whittaker sampling theorem. While this theorem has been found very useful in many domains, there are cases in which it fails to determine the correct minimal sampling rate. Such a case is encountered in digital holography. It has been previously shown that a sampling rate that is lower than Nyquist rate can be applied in digital holography without loss of information. In this work we develop a generalization of the classical sampling theorem based on an analysis of the sampling process in Wigner domain. The generalized sampling criterion obtained is more widely applicable than Nyquist criterion. In particularly we demonstrate the application of this theorem in digital holography.