The time-dependent physical spectrum of light*

TLDR

The bandwidth of the physical spectrum cannot be taken arbitrarily narrow. The study defines a time‑dependent physical spectrum of light based on photodetector counting rates and identifies conditions for approximating earlier spectra, providing correction terms. The authors define the physical spectrum via photodetector counting rates.

Abstract

We investigate the time-dependent spectrum of light from an observational point of view and define a time-dependent “physical spectrum” of light based on the counting rate of a photodetector. The tunable element, the filter, that allows observation of different spectral components of the light is shown to play an essential role in the time-dependent spectrum. Its bandwidth cannot be taken arbitrarily narrow. We establish the connection between our physical spectrum and other time-dependent spectra associated with Page, Lampard, Silverman, and Kolmogorov, as well as with the Wiener-Khintchine power spectrum. Also, we show the conditions under which these earlier definitions can be used as the first approximations to the complete physical spectrum, and give an expression for the correction terms.