The statistics of the derivative of intensity for partially developed speckle patterns have been investigated. The probability density function of the intensity derivative is given by an infinite series of modified Bessel functions of the second kind. The effect of integrating over space and time has also been discussed. The approximate form for the probability density function of the integrated intensity of the differentiated partially developed speckle pattern is also given by an infinite series of modified Bessel functions of the second kind. In the special case of fully developed speckle patterns, the probability density functions derived in this paper reduce to those given by Ebeling [ Opt. Commun. 35, 323 ( 1980)].
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