Coherent lidar at low signal powers: Basic considerations on optical heterodyning

Abstract

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 effect, 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 fields 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 CO1 Doppler wind lidar instrument.

Phase-error estimation and image reconstruction from digital-holography data using a Bayesian framework

“…After detection, we demodulated the signal to remove the spatial-frequency offset from the reference beam, low-pass filtered to isolate the signal of interest, and decimated to obtain a 256 × 256 data array. 1 The resulting data was represented by Eq. (2) after vectorization.…”

“…Detection involves measuring the modulation of a strong reference field by a potentially-weak signal field. This modulation allows for the detection of signals with energies equivalent to a single photon or less [1].…”

Shot noise statistics and information theory of sensitivity limits in frequency-modulated continuous-wave ladar

“…Working with classically correlated coherent laser states, the semi-classical and full quantum optical descriptions give identical results [2]. For linearly chirped optical fields, the balanced heterodyne setup produces a real differential photocurrent consisting of a deterministic and a stochastic component as…”

“…This rule can be derived semi-classically [2] or with a full quantum mechanical treatment [3], and it applies to coherent detection receivers when the shot noise of the local oscillator (LO) field summed with the signal field is the dominant source of noise. Applying this rule to frequency-modulated continuous-wave (FMCW) ladar, which uses coherent detection, indicates that FMCW ladar has a sensitivity level of one photon per second per hertz of bandwidth.…”

Contradictions between a Quantum-Mechanical Model of the photon and the Detection Principle of FMCW Measurements

“…This raised the question of whether a photon can change its frequency over its course 1 . Another study that delves into the exploration of FMCW detection in the quantum regime can be found in 2 .…”