This is to show the E(k) to P(k) matching for the various single annuli. Here the case of J-band PSF #4 is shown. The plots start from the innermost #1 to #5 (as specified in the top label). As already written, annulus #7 is the "Mean" annulus. The shape of annuli is circular, their parameters are given in Table 1. In each panel, the E(k) to P(k) fit is shown in the upper inset. The lower inset shows instead the P0 fits (as in Figure 3). The middle inset is the residual obtained using the median P0 derived from the best-P0 interval shown in between vertical dashed lines in the lower panels.