Unified theory of ghost imaging with Gaussian-state light

The theory of ghost imaging is developed in a Gaussian-state framework that both encompasses prior work—on thermal-state and biphoton-state imagers—and provides a complete understanding of the boundary between classical and quantum behavior in such systems. The core of this analysis is the expression derived for the photocurrent-correlation image obtained using a general Gaussian-state source. This image is expressed in terms of the phase-insensitive and phase-sensitive cross correlations between the two detected fields, plus a background. Because any pair of cross correlations is obtainable with classical Gaussian states, the image does not carry a quantum signature per se. However, if the image characteristics of classical and nonclassical Gaussian-state sources with identical autocorrelation functions are compared, the nonclassical source provides resolution improvement in its near field and field-of-view improvement in its far field.

Figure 1

(Color online) A simple ghost-imaging setup.

Figure 2

(Color online) Photodetection model.

Figure 3

(Color online) Isocontours corresponding to the $e^{-2}$-attenuation levels for the phase-sensitive and phase-insensitive correlation functions in the near-field and the far-field regimes.

Figure 4

(Color online) Ghost-imaging setup with relay optics.