Three-dimensional shift-invariant pattern recognition in digital holographic microscopy

This paper reports a three-dimensional (3D) analysis of shift-invariant pattern recognition applied to holographic images reconstructed digitally from holographic microscopes. It is shown that the sequential application of a 2D filter to plane-by-plane reconstructions of an optical field is exactly equivalent to the application of a more general filter with a 3D impulse response. We show that any 3D filter with arbitrary impulse response can be implemented in this way. The process is illustrated (in 3D) by filtering a holographic image of different sized glass spheres suspended in water.