Abstract

The three principal paradigms for high-sensitivity photodetection—direct detection, homodyne detection, and heterodyne detection—all have well-accepted quantum descriptions.¹ Neglecting polarization and spatial characteristics, these descriptions are as follows: Unity-quantum-efficiency direct detection (continuous-time photon counting) of a photon-units positive-frequency field operator $\widehat{E}\left(t\right)$ produces a classical-impulse-train stochastic process whose statistics are identical to those of the photon-flux quantum measurement, ${É}^{†}\left(t\right)\widehat{E}\left(t\right)$. Homodyne detection of this same field operator yields a classical stochastic process proportional to the quadrature-operator quantum measurement, $\mathrm{Re}\left[{\widehat{E}}_S\left(t\right)e^{-\iota {\theta }_{\text{IF}}}\right]$, where ${\widehat{E}}_S\left(t\right)$ is the complex envelope of $\widehat{E}\left(t\right)$ bandlimited to B Hz and θ_IF is the local-oscillator phase. Heterodyne detection of É(t) produces a classical passband stochastic process proportional to $\mathrm{Re}\left\{\left[{\widehat{E}}_S\left(t\right)+{\widehat{E}}_I^{†}\left(t\right)\right]\exp \left(-i2\pi v_{IF}t\right)\right\}$, where ${\widehat{E}}_I\left(t\right)$ is the B Hz image-band complex envelope and v_IF is the intermediate frequency.

© 1997 Optical Society of America