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The probability of a miss in the detection of a signal in an optical communications system through the turbulent atmosphere using intensity modulation is studied. The turbulence of the atmosphere causes scintillation of the received signal intensity which is treated as a lognormal random process. The received background radiation and electronic noise in the receiver is treated as additive white Gaussian noise (AWGN). A Chernoff bound is derived. For practical values of the signal-to-noise power ratio (SNR), a series solution for the characteristic function of the lognormal random variable is used to find the probability of miss. Simulation results agree with theoretical results. The method developed in this paper can be used by the system designer to choose the proper signal length and meet the system specifications for signal detection.