Optical Communications, 2nd Edition

3.4 PHOTOCOUNTING WITH RECEIVER FIELDS

When the impinging field on the photodetector surface is the focused field of the optical aperture, the previous counting theory can be directly applied. We consider the following examples.

3.4.1 Constant Point Source Fields

Let the received field be that due to the far field of a point source transmitting an unmodulated plane wave, producing the field at the receiver area A,

with receiver power P_r = (|a|²)A. This field is focused to the detector Airy pattern f_d(t, u, ν) on the photodetector surface A_d, producing the resulting count rate process of the photodetector

or, from Eq. (3.3.25),

The resulting mean count over any (0, T) is then

and the Poisson count probability is then

Thus a point source plane wave with a constant envelope field produces a constant count rate in the photodetector, and a Poisson count probability with mean αP_rT. Note that the mean count is directly proportional to the counting time length T, and is independent of when ...