When image plane speckle intensity integrated over a finite aperture is submitted to a logarithmic transformation, the noise becomes additive and signal independent. The first- and second-order moments of the probability distribution are derived. It is found that the logarithm of speckle noise approaches a normal distribution much faster than speckle intensity. The properties of speckle noise are different from those of filmgrain noise; for example, neither Nutting’s law nor Selwyn’s law is satisfied by speckle.
© 1976 Optical Society of America
H. H. Arsenault and G. April, "Properties of speckle integrated with a finite aperture and logarithmically transformed," J. Opt. Soc. Am. 66, 1160-1163 (1976)