The estimation of yields the direct calculation of displacement in the sample. There exist various methods for the estimation of , also called Doppler methods, which vary in accuracy and noise reduction. Consider two consecutive complex-valued A-line signals Display Formula
(3)where represents the magnitude, is the phase of the signal at two consecutive instants and , and . A direct way to estimate the phase difference can be achieved by Display Formula
(5)where is the complex conjugated version of , and and are the imaginary and real-part operators of a given vector, respectively. The main problem with this approach lies in its high instability and sensitivity to noise. Based on the study developed by Pinton et al.,22 we chose the Loupas et al.23 2-D autocorrelation as the motion estimation method. Loupas’ algorithm uses depth and lateral samples to calculate displacement. When we take two samples within the axial range, can be represented as Display Formula
(6)where is the element ’th along the -axis, , and , and is the size of the window in the axial direction in which the phase estimation is performed for a given . For an intensity vector of 1025 elements, a window size significantly reduces the noise without a strong resolution loss. Applying Eq. (6), the displacement can be calculated more accurately than with the classic method [Eq. (5)].