NOVEMBER d@/dx+O as 2 . 4 , a condition which is not met by those modes possessing odd symmetry about r=O.In his letter, Mr. Kondrat'ev also pointed out an error made in my paper and gave the correct dispersion equation. The presence of the 3 factor which Mr. Kondrat'ev noted resulted in the omission of the factor 4 on the left hand side of the same expression in mv paper. I am very grateful tohim for calling m i attention to-the error.The purpose of this correspondence is to determine an optimum decision strategy that can be applied to the reception of binary optical signals. The Ideal Observer criterion which directs the observer to minimize the total probability of error will be used to determine optimum detection thresholds.'The photoelectrons received in the binary communication process are emanating from tmo disjoint sources, a signal or data source and a nonsignal source. Assuming the number received from either source in a given time period is governed by a Poisson distribution, Le., the probability of receiving m photoelectrons in a time interval T is PT(m) = -ame-" m ! a = the average number of photoelectrons received in the time interval T. The probability density function PDF on the signal source is [b(s) if 8 = 0 or no signal pulse I if 8 = 1 or a signal pulse = the average number of signal photoelectrons received when a signal is present.The PDF on the nonsignal source isii = the average number of nonsignal photoelectrons received. The combination of signal and nonsignal photoelectrons is additive. Let their sum be equal to V. The PDF on V when the signal is absent: 01

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