True optical spatial derivatives for direct phase gradient measurements

Abstract

This paper shows analytically and numerically that a vortex plate coupled to a neutral density filter can deliver a true optical spatial derivative when placed at the focal plane of a 2f lens pair. This technique turns any intensity or phase variations of coherent light into an intensity that is proportional to the square of the norm of the initial variation gradient. Since the optical derivative removes the uniform background, it is possible to measure the mode numbers of spatial phase gradients or fluctuations optically, without using any interferometer.