In a number of optical heterodyne systems it may happen that the signal power is so low that only a few, or even fractions of, photons enter the receiver in a characteristic time interval. As the heterodyne receiver basically employs the beating e ect, such intricate questions as`is there still a beating between the (many) local oscillator photons and the few return photons?' or how can a single photon produce an intermediate frequency?' arise. We show that the semiclassical theory, which provides exact results as long as optical ®elds with an adequate classical description are used, is capable of answering those questions. The term`photon' must thereby be assigned its (semiclassically) correct meaning, which is an abbreviation for`discrete interaction of light and matter'. We illustrate our discussion by providing a numerical example related to a space-borne CO2 Doppler wind lidar instrument.
IntroductionAt present, a major problem of space-borne (coherent) Doppler wind lidar systems is the limited transmitter pulse energy in combination with the weak atmospheric backscattering, since this results in only a few photons per measurement interval at the receiver front end. As the receiver basically consists of a heterodyne arrangement, it relies on the beating e ect of two electromagnetic ®elds, a process that is well understood in terms of classical ®eld theory. In the case where only a few signal photons are present at the receiver input, however, the picture of two beating ®elds becomes hard to imagine and thus has to be reconsidered; some fundamental and intricate questions such as is there still a beating between the (many) local oscillator photons and the few return photons?',`how can a single photon produce an intermediate frequency?' or when, within one intermediate frequency period, does the return photon arrive?' arise.It is the purpose of this paper to answer these questions by clarifying the physical principles that govern a coherent receiver at extremely low light levels at its input. After de®ning the term`photon' in a (semiclassically) correct way, we shall show that great care has to be taken in asking questions related to quantum theory; we shall see that some questions cannot be answered in principle. Having correctly described the process of light detection, we shall ®nally specialize our results for the heterodyne receiver and provide a numerical example for a typical CO2 Doppler wind lidar instrument.