analysis could be found in [@He:2018]. []{data-label="PowerSNR"}](fig3.pdf){width="0.6\columnwidth"}

A more straightforward definition of target detection signal for intensity correlation protocols is the rate of coincidence detections ($N_c = N_pN_r$), which is defined as the probability of detecting photons on both the probe and reference detectors in a pair of probe and reference wave packet [@england2019quantum]. The definition of the target detection signal is chosen in this manner since coincidence detections directly reflect the paired-generation nature of probe and reference photons. The target detection SNR is quantified as the contrast of $N_c$ when the target object is present or absent: $$\begin{gathered}
\text{SNR}_{NC} = \frac{{\langle N_c \rangle}_{in}-{\langle N_c \rangle}_{out}}{{\langle N_c \rangle}_{out}}\end{gathered}$$ where, as before, the subscript $in$ and $out$ stand for the presence and absence of the target object and the angle brackets stand for statistical averages. It could be shown that, under this figure of merit, the correlation enhancement of the intensity correlation protocol, as compared to the CI protocol with direct intensity detection only, is given by the second-order cross-correlation function $g^{(1,1)}$ of the probe and reference light [@england2019quantum]: $$\begin{gathered}
g^{(1,1)}= \frac{{\langle N_pN_r \rangle}}{{\langle N_p \rangle}{\langle N_r \rangle}}\end{gathered}$$ Since $g^{(1,1)}$ is inversely proportional to the number of probe and reference photons 