Single-Pixel Imaging with Heralded Single Photons

11 Traditional remote sensing applications are often based on pulsed laser illumination with a narrow linewidth and characteristic repetition rate, which are not conducive to covert operation. Whatever methods are employed for covert sensing, a key requirement is for the probe light to be indistinguishable from background illumination. We present a method to perform single-pixel imaging that suppresses the effect of background light and hence improves the signal-to-noise ratio by using correlated photon-pairs produced via spontaneous parametric down conversion. One of the photons in the pair is used to illuminate the object whilst the other acts as a temporal reference, allowing the signal photons to be distinguished from background noise. This heralding method shows how the noise regime is key to producing higher contrast images.


13
The ability to covertly illuminate a scene is a sought-after goal within remote sensing. For covert imaging, there is a requirement 14 that the probe photons be indistinguishable from the fluctuations of the background light. Using a pulsed laser makes this 15 disguise difficult since the defined wavelength and repetition rates allows the source to be distinguished from the background 16 light. In contrast a source based on spontaneous parametric down conversion (SPDC) creates photons over a range of 17 wavelengths at random times, making it a much better candidate for a covert system 1 . There have been recent developments in 18 producing high-flux photon-pair light sources with a broad gain bandwidth that enable this covert probing of a scene to be 19 performed 2 . 20 Using quantum correlations to improve the signal-to-noise (SNR) of imaging has been the subject of significant study 3-6 21 and with array sensors it has been possible to demonstrate sub-shot noise measurements using a photon-pair light source 7-9 . 22 These correlated photons have also been utilised to distinguish signal photons from the noise photons in the background light 23 and has been applied in a LIDAR system for range finding 10 . Indeed, a further advantage of this approach is since it is based 24 upon random, albeit correlated, events that two or more similar systems can operate in the same environment and not suffer 25 from cross-talk 2, 11 .

26
Here we quantify the improvement in SNR in a single-pixel imaging (SPI) system 12, 13 by utilising the correlations from a 27 photon-pair light source. SPI has been demonstrated at a variety of wavelengths 14-16 , for high speed applications 17, 18 , and 28 performing depth measurements 19 . In SPI a series of patterns are projected onto a target, the total power of the corresponding 29 transmitted or back-scattered light is measured using a single-pixel detector revealing the overlap between the projected pattern 30 and the object 20 . This method of using a single-pixel to image an unknown scene was developed alongside the field of ghost 31 imaging, where corrected photons were used to produce images with single element detectors as a heralding system with 32 a detector array used to identify the position of the anti-correlated photons 21 , this was also shown to also be possible with 33 classical sources 22 . 34 We demonstrate that there exists a noise regime where there is an improvement in the SNR of the images when using the 35 photon-pair, correlated, light source. This will enable the system to be used more covertly in the presence of background light. 36 We present a model and experimental measurements to demonstrate the operating regime where there can be an advantage via

39
In a classical SPI system a light source is used with an optical modulator to produce a structured illumination 23 or is used 40 with a detector to produce a structured detection 24 . In the system presented here SPDC is used to realise a photon-pair light 41 source. The photon-pairs are split such that one is directed to the heralding detector and the other to probe an object with a 42 second detector behind the object, in principle this would be applicable to the back-scattered imaging arrangement, but this is 43 technologically more challenging to implement due to the high losses involved. Outputs from the two detectors are used as 44 stop-start triggers for a coincidence counter. A key parameter to achieve an advantage for the heralding measurement is to 45 maximise the number of two-fold correlated photons. In principle the system can be used in two ways: firstly, the correlations 46 can be ignored and the signal can be read as the total photon count from the signal detector, or secondly the correlations can be 47 used such that the signal is read as only the counts recorded in the coincidence peak. In the first case the signal is maximised 48 but is also subject to being confused by any background light, in the second case, the time gating means most of the background 49 light is eliminated but at the expense of a reduced signal. It is the interplay between these two competing issues that determines 50 the regimes in which using the source correlation might bring an advantage.

51
The noise in the imaging system will be proportional to the noise from a non-imaging measurement, such that we can estimate the noise in our system. The SNR of our measurement for a given integration time is given by SNR = S √ S+N , where S is the number of counts due to signal photons and N is any additional counts arising from background noise. For the measurement where the correlations are not used (uncorrelated photons), the signal S is the total number of counts detected from the source and the noise is made up from detector dark counts N d , and the number of measured optical background counts N b . For any real-world measurements outside of a laboratory the background levels will fluctuate due to varying frequencies of electronics and movement in position of illumination sources, this is included as temporal changes in the background level. To emulate these temporal fluctuations a fluctuation term γ is added, where γN b is the standard deviation in the background level with a mean value of N b . The addition of this fluctuation will result in a larger variance than measured from a Poissonian noise source. Therefore, the SNR of our uncorrelated measurement is given by The advantage of using the correlation peak is minimising this background noise due to the gate time associated with the peak, the fraction of the noise falling within the gate time is ε. The coincidence ratio, the fraction of the coincidence counts divided by the total number of counts, is given by h. When using the correlation peak the number of signal counts is reduced to hS. Including the correlation ratio and the time-gating noise reduction enables the correlated SNR to be estimated as The SPI experimental set up. The SPDC crystal produces 2-photons, one of which is measured by a SPAD detector as a heralding arm, the other is reflected from the DMD acting as a transparency mask, the photons transmitted through the target are recorded with a PMT. The coincidence measurement is made with a coincidence counter.
An example of the temporal measurement of the correlated photons is shown in figure 1(a), with h calculated as the counts 52 contained in the grey period divided by the total number of counts. Figure 1(b) shows the SNR calculated for a range of measurement will have a higher SNR than the uncorrelated case. As figure 1(b) shows, the correlated measurement does not 56 outperform the uncorrelated measurement for all possible parameters. The advantage for the correlated measurement is most 57 apparent when the coincidence ratio h is sufficiently large relative to the inverse gate width ε. For the experimental parameters 58 we report in this paper, we find there is no measurable advantage when using a static background signal (γ = 0) for noise levels 59 lower than 8 times the signal level.