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The shot noise which occurs in photoelectric detection is calculated utilizing fully quantum mechanical procedures. The results which are obtained in this paper include the effects of photon bunching and they differ considerably from classical results which are obtained on the assumption of Poisson statistics. In some cases the Poisson-based classical results lead to shot-noise powers that are in error by as much as an order of magnitude. The results reveal the existence of a relative minimum in the plot of shot noise vs input signal to noise ratio. This suggests the possibility of optimum input signal to noise ratios within certain restricted ranges of the input signal to noise ratio. A plot of the shot noise which is in excess of that predicted by Poisson-based statistics vs input signal to noise ratio reveals a maximum at an input signal to noise ratio of approximately 1.5. This suggests that the enhancement of the Hanbury-Brown and Twiss effect that is obtained when coherent radiation is superposed upon chaotic radiation will be maximized at a coherent-to-chaotic ratio of approximately 1.5.
Gerard Lachs (1968) studied this question.