About the application of the van Cittert-Zernike theorem in ultrasonic imaging

The specific circumstances under which the van Cittert-Zernike theorem applies in ultrasonic imaging systems are examined through analysis and computations. Expressions are obtained for the mutual coherence function of an incoherent source when the signals are discrete in time and space and have finite lengths. Expressions are also obtained for statistics and effective signal-to-noise ratios that describe the error in the assumption of an incoherent source with finite signal lengths. Images of a one-dimensional source are reconstructed for different signal lengths and different pulse windows. The results show that ultrasonic signals with a relatively long effective length are needed to satisfy the incoherence requirement for image reconstruction based on the van Cittert-Zernike theorem. Consequently, although the van Cittert-Zernike theorem may be used to estimate the coherence length of ultrasonic signals in the aperture of an imaging system, special data acquisition techniques are needed for satisfactory reconstruction of ultrasonic images when depth resolution like that in current b-scans is required.