![(Color online) Light from a spatially-incoherent optical source—either a type-II phase matched SPDC or a laser rendered spatially incoherent by passage through a rotating ground-glass—is separated into signal and reference beams by a beam splitter. For the pseudothermal (laser) case, this is a 50-50 beam splitter. For the SPDC, this is a polarizing beam splitter. The reference beam travels $L\,$m to the CCD camera, while the signal beam travels $L\,$m to the target, and the reflected light travels $L\,$m to the bucket detector. The image is then formed by cross correlation between the photocurrents obtained from the bucket detector and the high spatial-resolution (CCD camera) detector.[]{data-label="fig:setup"}](Setup.pdf){width="3.5in"}

Setup {#sec:Setup}
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Optical Sources
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We are interested in ghost imaging with classical pseudothermal light, and the nonclassical output of an SPDC. In both cases our signal and reference beams will be represented quantum-mechanically as $\sqrt{\mbox{photons/m$^2$s}}$-units, $+z$-going, positive-frequency, field operators—${\hat{E}}_S({\bm\rho},t)e^{-i\omega_0t}$ and ${\hat{E}}_R({\bm\rho},t)e^{-i\omega_ot}$, as functions of transverse-coordinate vector ${\bm\rho}$ and time—at the output of the Fig. \[fig:setup\] beam splitter. Their baseband field operators have the canonical commutation relations $$\begin{aligned}
\label{eq:Comm1}&[{\hat{E}}_J({\bm\rho}_1,t_1),{\hat{E}}_K({\bm\rho}_2,t_2)] = 0, \\[.05in]
\label{eq:Comm2}&[{\hat{E}}_J({\bm\rho}_1,t_1),{\hat{E}}^\dagger_K({\bm\rho}_2,t_2)] = \delta_{JK}\delta({\bm\rho}_1-{\bm\rho}_2)\delta(t_1-t_2),\end{aligned}$$ for $J =  S,R$ and $K = S,R$, where $\delta_{JK}$ is the Kronecker delta, and $\delta(\cdot)$ is the 