Fast remote spectral discrimination through ghost spectrometry

Assessing the presence of chemical, biological, radiological, and nuclear threats is a crucial task which is usually dealt with in spectroscopic measurements by analyzing the presence of spectral features in a measured absorption profile. The use of quantum ghost spectroscopy opens up the enticing perspective to perform these measurements remotely without compromising the measurement accuracy. However, in order to have the necessary signal-to-noise ratio, long acquisition times are typically required, hence subtracting from the benefits provided by remote sensing. In many instances, though, reconstructing the full spectral lineshape of an object is not needed and the interest lies in ascertaining the presence of a spectrally absorbing object. Here, we present an experimental investigation on the employ of the hypothesis testing framework to obtain a fast and accurate discrimination, carried out by ghost spectrometry. We discuss the experimental results obtained with different samples and complement them with simulations to explore the most common scenarios.

Figure 1

Conceptual scheme. A ghost-spectrometry scheme is implemented using frequency-correlated photon pairs: one photon is directed toward the supposed location of the spectral object, and detected with a bucket detector, while the other photon is analyzed in frequency. By comparing the recorded coincidences at low SNR with a reference measurement using a Kolmogorov-Smirnov test, it is possible to asses whether the two profiles are samples drawn from the same distribution or not.

Figure 2

(a) Experimental setup: A cw 403-nm laser is used to generate photon pairs through SPDC with a 3-mm type-I BBO crystal. One photon is sent through a spectrometer and detected with an intensified CCD camera, while the other photon is sent through a spectral object [either a SGF (orange)] or a solution of gold nanorods (AuNRs) and is detected using a bucket detector. A GBPF (green) acts as a reference. The GBPF is never removed from the setup throughout the two experiments. (b) Recorded coincidences for the reference. (c) Example of recorded coincidences for AuNRs at an accumulation time t = 10 s. The wavelength axis refers to the object arm.

Figure 3

Results with super-Gaussian filter. (a) Measured $p$-values obtained from a KS test between the reference (blue inset) and the signal measured with the super-Gaussian filter inserted in the beam at different accumulation times $t$. The blue dashed and solid lines are the rejection confidence level at 0.05 and 0.01, respectively. (b) and (c) recorded coincidence counts at $t$ = 1 s and $t$ = 10 s. The wavelength axis refers to the object arm.

Figure 4

Nanorod profiles. (a) Reference measurement (blue) and AuNRs absorbance (orange). The absorbance was measured using an UV/VIS spectrophotometer. (b)–(d) $C_1$ coincidence measurements at $t$ = 5, 25, and 50. (e)–(g) $C_2$ coincidence measurements at $t$ = 1, 5, and 10. (b) and (e) correspond to a rejection rate of 0.3, (c) and (f) to a rejection rate of 0.7 for $C_1$ and 0.8 for $C_2$, and (d) and (g) to a rejection rate of 0.95. The wavelength axis refers to the object arm.

Figure 5

Results of AuNRs: (a) KS rejection rate for concentration $C_1$ and $C_2$. Green bars indicate the successful rejection. Pink bars indicate acceptance of the null hypothesis. (b) $p$-values for $C_1$ and (c) $p$-values for $C_2$. Blue dashed line: 0.05 confidence level; blue solid line: 0.01 confidence level; the box center indicates the average value, while the box edges indicate the 25th and 75th percentile; the whiskers extend to all measured values.

Figure 6

Simulation broad absorption on a structured reference. (a) Blue: reference, yellow dashed lines: spectral object transmission; purple: signal obtained with the yellow transmission profile. (b) Simulated reference and (c) simulated signal for $\alpha =0.016$ at the level of signal resulting in a $100\%$ rejection rate.

Figure 7

KS rejection rate for different values of $\alpha$ and resources $N_T$. Green bars indicate the successful rejection. Pink bars indicate acceptance of the null hypothesis.

Figure 8

$p$-values (a) $\alpha =0$, (b) $\alpha =0.004$, (c) $\alpha =0.006$, (d) $\alpha =0.008$, (e) $\alpha =0.010$, (f) $\alpha =0.012$, (g) $\alpha =0.014$, and (h) $\alpha =0.016$. Dashed blue line: 0.05 confidence level; solid blue line: 0.01 confidence level. The box center (black dot) indicates the average value, while the box edges (dark solid pink) indicate the 25th and 75th percentile; the whiskers extend to all measured values.

Figure 9

Simulation for broad reference and narrow absorption. (a) Blue: reference; dashed lines: spectral object transmission; purple: signal obtained with the yellow transmission profile. (b) simulated reference and (c) simulated signal for $\sigma =6$ nm for $N_T=15k$, resulting in a $100\%$ rejection rate.

Figure 10

KS rejection rate for different values of $\sigma$ and resources $N_T$. Green bars indicate the successful rejection. Pink bars indicate acceptance of the null hypothesis.

Figure 11

$p$-values (a) $\sigma =0$ nm, (b) $\sigma =1$ nm, (c) $\sigma =1.5$ nm, (d) $\sigma =2$ nm, (e) $\sigma =3$ nm, (f) $\sigma =4$ nm, (g) $\sigma =5$ nm, and (h) $\sigma =6$ nm. Dashed blue line: 0.05 confidence level; solid blue line: 0.01 confidence level. The box center (black dot) indicates the average value, while the box edges (dark solid pink) indicate the 25th and 75th percentile; the whiskers extend to all measured values.