The LLPE and LQPE for the centers of the looks [t.sub.L] = [LT.sub.s] are given by
The LLPE grows while going from the center of the multilook processing interval, and the LQPE is constant.
From (42) and from the LQPE acceptable error criteria (29) we find that for a large number of looks the LLPE dominates over the LQPE.
The LLPE and LQPE of the harmonic error at the moment of time [t.sub.L] are given by
The maximum LLPE is reached when the LQPE is zero (the most shifted looks are not defocused), and vice versa, the maximum LQPE is reached when the LLPE is zero (the most defocused looks are not shifted).
The extreme values of the LLPE and LQPE observed on the multilook processing interval are [+ or -][[alpha].sub.Emax] and [+ or -][[beta].sub.Emax],
Since the maximum LLPE and LQPE are determined only by the amplitude and the frequency of the phase error, the defocusing effect of the harmonic phase error does not depend on the number of looks.
The resolution is the function of two variables: the frequency [[alpha].sub.p] and the LLPE [[alpha].sub.Emax] From Fig.
Strictly speaking, the assumption of the uniform distribution of the LLPE shifts used to derive (39) is not valid for the harmonic error.
The single-look SAR images are shifted with a higher probability closer to the extreme values determined by the maximum LLPE (50a).
The new approach is proposed to characterize the influence of the phase error in terms of its local linear and local quadratic phase errors (LLPE and LQPE).
In order to analyze the defocusing effect of the LLPEs, we shall assume that all single-look SAPs are defocused by the same LQPE [[beta].sub.E] which corresponds to the worst LQPE defocusing effect among all SAR looks.