The probability that the normalized sidelobe level, r, does not exceed a specified limit, R, is then given by, The integral in equation (13) has been tabulated and is available from the literature (reference 23). Selecting a particular probability, say 99.99%, equation (13)and available tabulations enable the determination of the corresponding sidelobe level. For example, Figure 6 compares the 99.99% confidence limit with the same expected pattern shown in Figure 5. With only a 10° rms phase error and 10% rms amplitude error, the 99.99% limit for the first sidelobe is within 1.5 db of that of the average level. However, the upper confidence limit for the far sidelobes is significantly higher than the average level reflecting the greater variance of the sidelobe level in this region and the greater uncertainty as to what form the sidelobe pattern of a particular system might be. The maximum sidelobe level is of interest in determining the power density to which a surrounding population might be exposed to on a continual basis. Alternatively, the sidelobe envelope can be used to determine the required diameter of a surrounding restricted region outside of which the continuous exposure level would be below some specified value. As indicated above this specification must be done on a statistical basis. For example, if the peak power density in Figure 6 were 23 mw/cm , a restricted region of about 18 km diameter would insure that the population outside this region
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