Although $D(i,j)$ is a discrete approximation of the closed-line integral, it has a special distinguishing characteristic. Studies have shown that the circulation approaches zero (ignoring noise) in the case where no singularity exits in the contour region; however; if there is net topological charge within the ($i0\u2032,j0\u2032$)-th lenslet aperture, then the circulation $D(i0,j0)$ approaches its local maximum, and its eight neighbors $D(i0+k,j0+l)$$(k=\xb11,l=\xb11)$ tend to have nonzero values. Furthermore, the circulations of the eight neighbors depend on the location of the singular point: If the singular point is at the center of the ($i0\u2032,j0\u2032$)-th lenslet aperture, the circulation $D(i0,j0)$ is a local maximum, and its eight neighboring circulations are approximately half of the local maximum. In contrast, when the OV is displaced away from the center, the circulation $D(i0,j0)$ is almost constant, but its eight neighbors tend to vary linearly with the distance from the center. This characteristic is quite different from that using a $2\xd72$ contour.^{16}