detection is important for quantifying and comparing the performances of different target detection protocols.\

The Signal-to-noise Ratio Figure Of Merit
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For intensity correlation protocols, one way to construct the target detection signal is to directly define it as the covariance between the output of the probe and reference detectors. In reference [@Lopaeva:2013; @He:2018] the target detection signal is defined as the covariance between the number of photons that are detected on the probe and the reference detector: $$\begin{gathered}
S_{COV} = N_pN_r - {\langle N_p \rangle}{\langle N_r \rangle}\end{gathered}$$ where $N_p$ and $N_r$ stand for the number of collected photons and reference photons detected in a pair of probe and reference wave packet. The angle brackets stand for statistical averages over multiple SPDC pump pulses. A unique feature of this definition is that the average value of ${\langle S_{COV} \rangle}$ is always zero when the target object is absent. Therefore ${\langle S_{COV} \rangle}$ is resilient to the fluctuation of environment noise power. The signal-to-noise ratio (SNR) of the target detection is quantified as the contrast of $S_{COV}$ (normalized by its standard deviation) when the target object is present or absent: $$\begin{gathered}
\text{SNR}_{COV} = \frac{{\langle S_{COV} \rangle}_{in}-{\langle S_{COV} \rangle}_{out}}{\sqrt{{\langle \Delta^2S_{COV} \rangle}_{in}+{\langle \Delta^2S_{COV} 