The van Cittert-Zernike theorem in pulsed ultrasound-implications for ultrasonic imaging

A classical theorem of statistical optics, the van Cittert-Zernike theorem, is generalized to pulse-echo ultrasound. This theorem fully describes the second-order statistics of the spatial fluctuations (the spatial covariance) of the field produced by an incoherent source. As a random scattering medium is insonified, it behaves as an incoherent source. The van Cittert-Zernike theorem can thus predict the spatial covariance of the pressure field backscattered by a random medium. Experimental results obtained with a linear array are in good agreement with theoretical expectations. The implications of this theorem in speckle reduction and in focusing in nonhomogeneous media are discussed