The statistical properties of the spatial derivatives of the phase of a monochromatic speckle pattern are studied. Initially, a one-dimensional probability density function for the derivative of the phase is obtained and compared with the solution for the analogous problem concerning instantaneous frequency of narrow-band Gaussian noise. Subsequently, a two-dimensional probability density function is derived that depends on the two first and three second spatial moments of the illumination intensity distribution of the scattering object. Some sample intensity distributions are considered for which explicit expressions for the probability density function are given.
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