Shot-noise formula for time-varying photon rates: a general derivation

An expression describing the variance of shot noise is derived for deterministic, time-varying photon rates on a semiclassical basis. This is done both for the case with and without postprocessing in the electrical regime. It is shown how the results are related to the traditional shot-noise formula and under which (restricted) conditions the well-known formula may be applied. This becomes significant when signal-to-noise ratios have to be calculated. An example related to optical heterodyning demonstrates similarities and differences between the traditional formula and the new results.