1. Introduction

Optical imaging through strongly scattering media has long been a quest of importance in many areas, with vivid examples found in light detection and ranging (LIDAR) in foggy environments and in vivo biomedical imaging through human soft tissues. To this end, coherent wavefront correction of low-order spatial and temporal distortion by multiple scattering has been shown to improve penetration depth, energy delivery and imaging [1–5]. Nevertheless, controlled wavefront shaping using adaptive optics typically requires tedious feedback controls [2,4,6] or guides-star reference [7,8], whose applications in realistic scenario are overly restricted. Another way of imaging through scattering media is by identifying the singly scattered ballistic photons from the target over those scattered by the media that could be dominating by far. At this front, optical coherence tomography by the means of coherence gating can considerably extend the imaging depth over conventional microscopic imaging [9–11], becoming an essential diagnostic tool in multiple areas. Unfortunately, it does not suffice, hence requires collective accumulation of image acquisitions and significant effort in image reconstruction [12] when the medium is much thicker than its scattering mean free path ($l_s$), where only very few ballistic photons are measurable, while still be swarmed by non-ballistic photons [13–15]. The third approach is to exploit the “memory effect" for speckle correlation [16] or autocorrelation of the speckle field [4] to reconstruct fine image features from multiply scattered photons with elegant algorithms. Despite the intriguing advantage of harvesting scattered light without any wavefront correction, this approach is limited by the memory effect range and axial decorrelation of the speckle effect [7,17]. It therefore proves inadequate for imaging through or inside thick multi-scattering human tissue [7].

Besides those purely optics techniques, one can leverage on the deeper penetration of acoustic waves and their interaction with optical waves, either by measuring acoustic modulated optical signals or detecting optically excited acoustic waves. This has led to the emergence of hybrid deep-tissue imaging techniques to take advantage of the optical diffraction limit and acoustic penetration depth, for photoacoustic tomography [18], acoustic-opto tomography [19,20] and ultrasound guided optical imaging [8,21,22]. However, they rely on complex wavefront-shaping in acoustic or optical domains to break the acoustic diffraction limit for optical diffraction-limited imaging.

All those conventional approaches for imaging through scattering medium commonly suffer from a fundamental shortcoming, lack of photon detection sensitivity, to perform imaging at single photon level. Limited sensitivity is a fundamental limitation prohibiting biomedical imaging through extended imaging depth or ophthalmic imaging with low illumination power for safety concerns, where returning ballistic photons are rare. Moreover, for non-invasive imaging of an object behind an obstacle by backscattering, it is crucial to detect and isolate the ballistic photons returning from the object. These ballistic photons, however, are usually obscured by orders of magnitude more photons (multiply) scattered by the obstacle, which can share the same spectrum and arrival time and thus are indistinguishable to single photon detectors. This is in contrast to transmissive imaging where the forward propagating ballistic photons take the shortest path, and are thereby separable from multiply scattered ones by their earlier arrival time [23]. In practice, however, the applications of transimissive imaging are overly restricted to those with access to detection behind the target and obstacle.

To address the above challenges, we demonstrate a single photon sensitive imaging modality based on optical gating enabled by quantum frequency conversion (QFC) of few picosecond optical pulses in a periodically poled lithium niobate (PPLN) waveguide for non-invasive 3D imaging through strongly scattering medium. By preparing the QFC driving pump in proper picosecond pulses, only signal photons in a single spatiotemporal mode can be converted efficiently. Undesirable photons in other modes, even if they spectrally and temporally overlap with the signal, are converted with much less efficiency [24,25]. It is a nascent quantum measurement technique that utilises mode-selective quantum frequency conversion in a $\chi ^2$ nonlinear waveguide to discount single photons on overlapping but orthogonal mode bases [26] in quantum information processing [27], thus also called quantum parametric mode sorting (QPMS) [25]. The QPMS has been shown to achieve a 40 dB advantage in detection signal to noise over a typical linear-optical photon counting system, or 11 dB over the theoretical limit of an ideal matched filter [25,28]. Crucially, the pump pulses create a picoseconds photon detection window independent of detector’s timing jitter and its associated electronics, isolates backscattered photons from the target, and creates a mechanism to distinguish such photons arriving only picoseconds apart. It thus enables non-invasive diffraction-limited imaging with single-photon sensitivity through a visually opaque, strongly scattering media, or where the background is orders of magnitude stronger than the signal [29]. Additionally, the picoseconds photon detection window, created from the pump pulse optical gating, is well below the timing jitter of the detector and its associated timing electronics, while minimizing pileup distortions, dead time, and detector saturation otherwise plaguing applications based on single photon detection [30]. We note that the same advantages are not replicable by the methods based on optical parametric amplification [31], due to a ultra-low signal level with much less than one photon received per pulse.

2. Methods

2.1 Imaging setup

The experimental setup for single photon imaging is shown in Fig. 1(d). Two nearly transform-limited, 6 ps pulses at 1554.1 nm (probe) and 1565.5 nm (pump) are carved out from the MLL using a pair of cascaded 200 GHz dense-wavelength-division multiplexing (DWDM) filters each. Collimated signal probe pulses (Gaussian beam diameter: 2.2 mm) at 1554.1 nm are transmitted toward the scene through a transceiver. An optical fiber circulator separates the outgoing signal pulses and the incoming backscattered photons with a minimum isolation ratio of 55 dB. The transceiver of the imager is based on a simple monostatic coaxial arrangement using off-the-shelf telecom-grade optical components. The backscattered signal photon will be recombined with pump pulse via another DWDM and subsequently fiber coupled into the mode-selective upconversion detector. An FPGA is used as central processor for controlling the MEMS mirror and optical delay line, and acquiring the data from the USPD.

 

Fig. 1. (a) Schematic of the 3D imager showing the scattering obstacle (white block) and target (black cardboard and washers). (b) Propagation of speckle field captured by a CCD camera at a distance of 0 cm, 25 cm and 50 cm after a 5 mm scattering obstacle with optical thickness, $L$=4.3, to show the severity of scattering. (c) Illustrative comparison of ballistic photons (red) and multiscattered photons (black). (d) The complete experiment setup. MLL, mode-locked fiber laser (repetition rate = 50 MHz, center wavelength = 1560 nm); programmable MEMS (Micro-Electro-Mechanical Systems) mirror; ODL, programmable optical delay line; USPD, upconversion single photon detector; Si-APD, silicon avalanche photodiode; FPGA, field programmable gate array; WDM, wavelength-division-multiplexing; EDFA, erbium-doped fiber amplifier; FPC, fiber polarization controller.

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2.2 Upconversion single photon detector

The fiber coupled upconversion single photon detector (USPD) consists of a temperature controlled periodically poled lithium-niobate (PPLN) waveguide, aspheric lenses and a series of optical filters as shown in Fig. 2(a). The length of the waveguide is 1.96 cm, and temperature is stabilized at 58.45$\pm 0.1^\circ$C. With the aspheric lenses, input coupling efficiency from a single mode fiber is 34$\%$ and output coupling to a multimode fiber (MMF) is 76$\%$. After the output coupling lens, a short pass filter (Cutoff wavelength: 950 nm, OD $>$ 5) is used to remove the residual pump pulses and three narrow bandpass filters (Center wavelength: 779.8 nm) were applied to provide out of band rejection of more than 140 dB. The series of filters are crucial to minimize the dark count of the upconversion module. To characterize the internal conversion efficiency and phase matching bandwidth of the PPLN, a continuous wave laser was coupled into the waveguide at transverse-electric polarization, and swept from 1554.1 to 1565.5 nm while measuring the second harmonic power. The measured phase matching curve is centered at 1559.8 nm with the FWHM bandwidth of 0.73 nm and maximum normalized internal conversion efficiency of 130% $W^{-1}$ $cm^{-2}$. The phase matching curve of PPLN waveguide is shown in Fig. 2(c) where measurement data lie on top of a $sinc^2$ ideal phase matching profile, from which the inverse group velocity mismatch between upconversion and fundamental (signal and pump) wavelengths is calculated to be 280 $ps \cdot m^{-1}$ for our numerical simulation of mode selectivity. The pulse shape of the picoseconds probe and pump pulses carved out from the MLL with WDM filters are measured using a Frequency Resolved Optical Gating (FROG HR–150) with 0.1 ps resolution. Both pulses are in a nearly Gaussian shape with FWHM 6.0 and 6.2 ps at 1554.1 nm and 1565.5 nm depicted in Fig. 2(b). Well understood amplitude and phase profile of pulses is crucial for the subsequent mode selective calculation. Thus, enables mode-selective and picoseconds optical time gating features that isolate backscattered photons from the target, and creates a mechanism to distinguish such photons arriving only picoseconds apart. The total detection efficiency of our system is measured to be 25$\%$, which includes the transmission loss of the filters, the free-space to fiber coupling loss (in the module), and the Silicon avalanche photodiode’s (Si-APD- MMF coupled) quantum efficiency of $\approx$ 70 $\%$.

 

Fig. 2. (a) The schematic diagram of the fiber coupled upconversion module, integrating temperature controlled periodically poled lithium-niobate (PPLN) and a series of optical filters. (b) Retrieved pulse shapes by the Frequency Resolved Optical Gating (FROG). The amplitude (green line) and phase (yellow line) profile of generated pump and signal pulses at 1565.5 nm and 1554.1 nm, respectively, are shown. (c) Phase matching curve of the PPLN waveguide, plotted against the frequency offset at center wavelength of 1559.8 nm with a FWHM of about 80 GHz. The red line is the curve fitting, and the blue dashed line is the experimental result.

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2.3 Characterization of scattering obstacles

Scattering media obstacles were made from epoxy resin and Titanium Oxide ($TiO_2$) pigment ($\sim$220 nm particle size). Four obstacles with constant opacity and varying thickness were measured using the setup in Fig. 3(a). Two iris, that define the beam’s width, were placed 30 cm before and directly after the obstacle. 1554.1 nm light passes through the setup and is measured using an optical power meter 50 cm from the obstacle [10]. The transmission, $T$, through the obstacle was measured and the scattering mean free path ($l_s$) was calculated as $l_s=L_{sample}/ln(T)$, where $L_{sample}$ is the thickness of the scattering sample. The optical thickness $L$ represents the total scattering of each sample in the unit of $l_s$. Figure 1(b) and (c) show an example of the propagation of the speckle field captured by a CCD camera after a Gaussian beam passes through an obstacle with an optical thickness of $4.3$ and an illustrative comparison of ballistic photons and multiscattered photons.

 

Fig. 3. (a) Setup to determine Optical Thickness (L). MLL: Mode Locked Laser, SM: Scattering Media, PM: Optical Power Meter. (b) Optical Thickness ($L$) in the unit of scattering mean free path ($l_s$) vs. the thickness of the scattering samples. Red dotted line is linear best fit.

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3. Results & discussion

The single photon 3D imager (Fig. 1) is implemented by using an upconversion single photon detector (USPD), shown in Fig. 2(a)) with near transform limited pump pulses at 1565.5 nm (FWHM: 6.2 ps) and probe pulses at 1554.1 nm (FWHM: 6 ps). Both are carved from a 50 MHz femtosecond mode-locked fiber laser (MLL) by using separate sets of cascaded spectral filters. The pulses’ intensity and phase profiles are characterized in both spectral and temporal domains (see Fig. 2(b)) with a frequency resolved optical gating device to ensure high quality and thus good mode selectivity (see Supplement 1) [25,28]. The probe pulses, collimated to a beam diameter of 2.2 mm with very low intensity of $<$ 1 mW/mm$^{2}$ (picojoules per pulse), are used to image the target behind scattering obstacle via a single-mode-fiber coaxial optical transceiver and a MEMS scanning mirror. The robust design of our transceiver imager reduces system footprint while allowing flexible, long working distance. Meanwhile, the pump pulses are sent to a programmable optical delay line (ODL), before combined with the returning signal photons and sent to the USPD. The total detection efficiency of the USPD is 25$\%$ and it has a low intrinsic dark count probability of 6$\times 10^{-5}$/pulse. The total noise of the current imager is limited by optical pulse’s extinction-ratio. The signal-to-noise ratio (SNR) for photon counting is given as, $N_{\textit {SIG}}/\sqrt {N_{\textit {SIG}}+N_{\textit {DC}}}$ [32], where $N_{\textit {SIG}}$ and $N_{\textit {DC}}$ are the backscattered signal photon counts and total background counts, respectively. This means that our imager needs only 2$\times 10^{-5}$ detected photons/pulse to achieve a SNR of 15 for each pixel with a 50 MHz MLL. This exceptionally low noise yet single photon sensitive imager may pave the way for ophthalmic imaging with mean photon number $<<$1. The key parameters of the single photon imager is given in Table 1. To reconstruct the 3D image of the target behind the strongly scattering media, we perform time-resolving single photon counting, while raster steering the probe beam across the scene. A single time-resolving measurement is performed by scanning the ODL while counting the number of detections over a fixed dwell time. The scattering media used in this experiment are common tissue phantom made of epoxy resin and TiO$_2$ pigment ($\sim$220 nm particle size) [33].

Table 1. Key parameters of the single photon 3D imager

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The crux of our 3D imager is the mode-selective single photon counting that rejects multiscattered photons and allows us to identify backscattered photons arriving at different times. To demonstrate the 3D capability of our single photon imager, we perform 3D imaging with 800 pixels through a 7.5$l_s$ phantom placed 1.3 meter away from the transceiver. Depicted in Fig. 1 (a), the phantom was a 1.5 cm thick slab of epoxy resin and TiO$_2$ pigment, and the target was two metal washers (1 mm and 1.5 mm thick) mounted on a piece of black cardboard. Figure 4(a) shows the recovered 3D image of the two washers with their transverse features intact and their the 0.5-mm difference in thickness well resolved. Figure 4(c) shows time-resolving measurements of a target placed behind phantoms 0.5 cm and 2 cm thick, corresponding to optical thickness, $L$, of 4.3$l_s$ and 9.4$l_s$, respectively. As seen in the figure, distinct peaks are formed from single photons backscattered from different interfaces of the phantom and target. The width of all peaks is about 10 picoseconds, as defined by the pump and signal pulse widths. The absence of pulse width spreading indicates near perfect elimination of the multiscattered photons. In addition, there are also lots of single photons backscattered from the front surfaces of the phantom. If entering the detector, these photons are enough to completely saturate and blind it for true signal photons from the target arriving $<$0.5 ns later. Thanks to the picoseconds time gating, the strong background and weak signal will not fall in the same detection window. As a result, our system can measure the signal with single photon sensitivity without suffering the pileup, dead time, and saturation effects common to other single photon detection systems [30]. Beyond retrieving the surface morphology information via photon arrival time, the imaging system can be further expanded for mapping the optical absorption information of the target by measuring pixel-wise differential photon count in the same spirit as differential optical absorption imaging [34].

 

Fig. 4. (a) 3D image of the target behind a 1.5 cm obstacle, constructed with ${6.0\times 10^{-4}}$ detected photons per pulse per pixel. A line graph of the pixels show the depth resolution. (b) A 25 $\times$ 25 pixels 3D image of the target behind a 3 mm chicken breast with optical thickness of 7.5$l_s$ with total acquisition time of 10 s. (c) (Top) Time resolved photon counting results for a 5 mm scattering obstacle with L=4.3$l_s$, and (Center) a 20 mm scattering obstacle with L=9.4$l_s$. Inset: Solid line is zoom-in of the single photon counting peak (target) for 9.4$l_s$, dotted line is the peak (shifted and normalized) for 4.3$l_s$. FS/BS: front/back surface of the obstacle. (Bottom) Time resolved photon counting results of direct detection by using 1-ns gated commercial InGaAs single photon detector (ID Quantique-ID210) with $<$ 200 ps timing resolution.

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As discussed in [29], the longitudinal ranging resolution of our 3D imager is about 100 $\mu$m, decided by the pump pulse width and the ODL step size used in the time-resolving measurements. As long as there are sufficient photon counts, this resolution remains the same and independent of the multiscattering strength as there is no pulse width spreading in the returning single photons. Similarly, the transverse spatial resolution of our 3D imager can maintain diffraction limited, as primarily determined by the angular resolution of the transceiver. In our setup, the transceiver is comprised of a single mode fiber (SMF) coupled to an aspheric lens, providing diffraction limited collimation of the probe laser beam. Thus, the field of view is intrinsically matched to the point spread function (PSF) of the scanning probe beam. This makes the current transceiver configuration ideal for achieving diffraction limited 3D imaging while maintaining efficient coupling into a SMF for the subsequent frequency upconversion in the PPLN waveguide.

By Rayleigh criterion, the angular resolution of our 3D imager is given as

To validate this, we compare the lateral resolution of our imager, with and without a phantom with an optical thickness of 7.5$l_s$, using a positive United States Air Force (USAF) resolution target that consists of chrome lines plated on a thin piece of clear glass. In both cases, we raster scan a 12$\times$98 pixel grid over a section of the USAF target that has 2 mm line width and spacing. The chrome lines are distinguished from the glass by the number of peaks in the time-resolving photon counts. Pixels falling on the glass show peaks representing single photons returning from both the front and back interfaces of the glass, while pixels falling on the chrome only show a single peak because photons are prevented from reaching the back interface. Note that the ODL scanning parameters used prevent the detection of multiscattered photons returning from the scattering medium. Figure 5(b) shows the recovered 2D image through the 7.5$l_s$ phantom where the 2 mm target elements are clearly resolved. To compare the lateral resolution with and without the phantom, we construct 1D plots by averaging the 12 pixels along each of the 98 columns. From these plots, depicted in Fig. 5(d) and (e), it is evident that the resolving power of this 3D imager is unaffected by the scattering phantom in the photon path. This resilience stems from its ability to isolate single photons from the non-ballistic ones. In Fig. 5(e), the uncertainty in lateral resolution increased slightly when imaging through a sample with an optical thickness of 7.5$l_s$. This is because, with a significantly lower number of detected single photons, the detector dark counts become more pronounced, which raise the Poisson noise for each pixel and hence the slightly distorted 2D image in Fig. 5(b).

 

Fig. 5. (a) Picture of the USAF resolution target under test. Lines are 2 mm wide with 2 mm separation. (b) Reconstructed image of the target occluded by scattering obstacle with optical thickness of 7.5$l_s$. (c) A time resolved measurement on clear glass of the USAF target, showing both the front and back surfaces. (d) Spatially resolved lines from the USAF target without obstacle. (e) Spatially resolved lines from the USAF target occluded by an obstacle with an optical thickness of 7.5$l_s$. (Blue bars are ground truth for reference) (f) A time resolved measurement on the opaque bar of the USAF target.

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4. Conclusion

In conclusion, a non-invasive 3D imager has been demonstrated by selectively detecting the backscattered photons via picoseconds optical gating enable by mode selective frequency up-conversion in a nonlinear waveguide. With this, we demonstrate diffraction-limited imaging through strongly scattering media with up to 9.5$l_s$ optical thickness, using only few picojoule probe pulses. This single-photon 3D imaging approach is non-interferometric and allows long working distance, thus may be highly applicable in light-susceptible ophthalmic imaging. Our technique is highly versatile and applicable with other contrast mechanisms and imaging geometries, including acoustic-opto imaging [35] and long range imaging [36]. By extending the probe pulse into the mid-IR [37,38] wavelength, it can further assist a variety of imaging applications, particularly in vivo measurements through deep living tissues upon few detected ballistic photons.