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 a nd computations, Expressions are obtained for the mutual coherence fun ction of an incoherent source when the signals are discrete in time an d space and have finite lengths, Expressions are also obtained for sta tistics and effective signal-to-noise ratios that describe the error i n the assumption of an incoherent source with finite signal lengths, I mages of a one-dimensional source are reconstructed for different sign al lengths and different pulse windows, The results show that ultrason ic signals with a relatively long effective length are needed to satis fy the incoherence requirement for image reconstruction based on the v an Cittert-Zernike theorem, Consequently, although the van Cittert-Zer nike theorem may be used to estimate the coherence length of ultrasoni c signals in the aperture of an imaging system, special data acquisiti on techniques are needed for satisfactory reconstruction of ultrasonic images when depth resolution like that in current b-scans is required .