1. INTRODUCTION

The time-correlated single-photon counting (TCSPC) technique originates from the measurement of excited molecules. The TCSPC technique is always used with very low-intensity photon signals. The time interval between the triggering signal and the correlated photon signal is recorded to form a histogram. In this way, the time of flight could be measured with time accumulation. Because the width of the time bin for the histogram can reach a few picoseconds, the TCSPC technique can provide a high temporal resolution. To avoid the distortion of the time-of-flight (TOF) signal, the number of photons arriving in each period should be less than 1. Nowadays, the TCSPC plays an important role in the measurement of the fluorescence lifetime at the single-photon level ^[1,2]. In recent years, TCSPC has also been widely used in the photon-counting laser ranging and imaging (LiDAR) ^{[3–12" target="_self" style="display: inline;">–12]}. The depth information can be obtained by the TOF measurement. The implementation of a highly sensitive single-photon detector in photon-counting LiDAR allows the possibility of long-distance ranging with low laser emitting powers ^{[1315" target="_self" style="display: inline;">–15]}. Photon-counting LiDAR systems usually use a pulsed laser with a certain repetition rate as the transmitter and a single-photon detector as the receiver ^[16,17]. This kind of system is simple and robust, but it usually takes quite a long time to have a high-resolution scanning on the targets with such systems to form a three-dimensional (3D) image. On the other hand, 3D photon-counting imaging can be realized by using a multi-beam transmitter with a multi-pixel single-photon detector array ^{[1820" target="_self" style="display: inline;">–20]}, and the imaging system could easily achieve a large field of view with multi-pixel detectors ^[21,22]. However, these instruments always cost a lot due to the difficulty in fabrication of the single-photon detector array with highly integrated numerous pixels of balanced detection efficiency and noise level.

Here we propose and demonstrate a multi-beam LiDAR using one single-pixel single-photon detector with the frequency-multiplexing photon-counting method. Sixteen pulsed laser diodes were triggered by 16 individual frequency sources at different repetition rates around 1 MHz. Only one single-pixel single-photon detector based on a Geiger-mode Si avalanche photodiode (Si APD) was used to register all the returning photons. According to the strong correlation between the laser pulses and the returning photons that were emitted by that unique laser source, TOF information could be acquired for each laser beam at a repetition rate. In this way, frequency multiplexing was realized. Due to the application of the single-pixel single-photon detector, the receiver part of the system was largely simplified in this multi-beam LiDAR. The scale and cost of the system could be decreased significantly as well, leading to a practical photon-counting LiDAR system for airborne applications.

2. PRINCIPLE OF FREQUENCY-MULTIPLEXING PHOTON-COUNTING LIDAR

In the TOF measurement based on TCSPC, the synchronization signal of the laser pulse will be connected to the “START” channel of the TCSPC, and the output of the single-photon detector will be connected to the “STOP” channel. Then, the interval between the “START” and the “STOP” will be recorded to form a histogram with the accumulation time increasing. The temporal cross-correlation between the triggering laser pulse and the detected returning photons can be written as where N is the number of periods, fi is the synchronization signal of the laser pulse with repetition rate of i, I is the detected returning photon signals, and τ is the time delay. Only in the case that the repetition rate of the detected returning photons is identical to that of the synchronization signal or to the ratio of that and the time delay between them is stably fixed, could the strong correlation peak be observed in the measurement, which can be used for the TOF information. Otherwise, if the repetition rate of the detected photons varies a little from that of the laser pulse, the photons will be regarded as background noise, and no correlation peak could appear. Therefore, it is possible for the frequency-multiplexing technique to be implemented in the photon-counting LiDAR.

Suppose that we have several spatially separated pulsed laser sources operating at different repetition rates, and the laser beams arrive at different spots on the target. Then, the scattered photons in all directions from different laser beams will be mixed in space and detected by the same single-photon detector (SPD). If we measured the time correlation between the signal from the SPD and the synchronization signal from only one of the laser sources, we will observe the correlation peak in the histogram formed by the returning photons from exactly that laser source. Meanwhile, the detected photons from the other laser sources will be considered as noise in the measurement since there is no correlation between them. By using the synchronization signal from different laser sources, TOF measurements on different laser beams on the target can be achieved simultaneously.

To verify the possibility of implementation of the frequency-multiplexing technique in photon-counting LiDAR, we ran a simple test. Sixteen pulsed laser diodes (LD1-LD16) emitting at 850 nm were triggered at different repetition rates around 1 MHz from 16 randomly selected frequency sources (Sync 1-Sync 16). The repetition rates of the frequency sources were measured by a frequency counter (Agilent 53131A Universal Counter) and are listed in Table 1. It is obvious that there were very tiny differences in the repetition rate among different laser sources.

The output beams from the laser diodes are aimed at the target with equal angles. An SPD based on Si APD was used to detect all the returning photons. The detection efficiency of the detector was measured to be around 60% at 850 nm, with the dark count rate of 300 counts per second (cps).

In the test, the background noise without any LD emission was about 1×105cps. We took Sync 8 as the synchronization signal for the “START” channel of the TCSPC (Hydraharp 400, PicoQuant, Germany) and connected the output of the SPD to the “STOP” channel. First, we switched on all 16 LDs. The counting rate of the SPD was about 2.27×105cps, including the background noise. The high count rate could lead to a pile-up and distortion of the signal in the TCSPC measurement, but in our experiment, the linear dynamic range of the detector was up to 10 Mcps, and the after-pulsing probability was less than 1%. Therefore, the high count rate has little effect on this LiDAR performance.

The temporal resolution of the TCSPC was set at 64 ps. The correlation peak rose up quickly in the measurement as shown by the red curve in Fig. 1(a) with 1000 s accumulation. The system showed very good long-term stability during the whole acquisition procedure. Note that there were no other peaks in the curve, indicating that though all the detected photons carried regular repetition rates, there was no correlation between the photons and the synchronous trigger if the repetition rates were not identical. Then, we switched off the LD8 and kept the other LDs on. The counting rate of the SPD decreased to 2.2×105cps due to the absence of LD8. No peak was found in the TCSPC measurements as shown by the black curve in Fig. 1(a) because there was no correlation between the detected photons and the synchronous clock Sync 8. The test also verified that there was no crosstalk among the detection of all the beams. As a result, the laser beams at different repetition rates could work simultaneously and independently in the photon-counting LiDAR.

Fig. 1. (a) Correlation between Sync 8 and all the returning photons with (red) and without (black) LD8. (b) SBR as a function of the total photon counts.

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We used the ratio between the maximum peak height and the background level as the signal-to-background ratio (SBR) ^[7] to evaluate the discrimination limit of the TCSPC measurements. Though the photons from other LDs only contributed to the background offset in the correlation measurement, the correlation peak would be buried if the background offset was too high. Then the SBR would be decreased with the increasing number of multiplexing beams. We left only LD8 working while exposing the whole system to a white-light continuous-wave LED lamp. The SBR of the LiDAR decreased gradually with the increase of the background noise from the LED lamp light as shown in Fig. 1(b). When the total photon-counting rate was up to 1×106cps, the SBR was still better than 8. Considering the photon count from each frequency channel was about 7×103cps and the stray light background noise was about 1×105cps, the background noise from the LED was equivalent to 128 beams for frequency multiplexing. As shown in Fig. 1(b), even when the background noise was about 7.4×106cps, the SBR was above 1, indicating that the discrimination on the correlation peak is possible with a large number of multiplexing channels up to 1043.

3. EXPERIMENTAL SETUP

Here we demonstrate a frequency-multiplexing photon-counting imaging LiDAR with only one SPD as the receiver. The schematic of the system is shown in Fig. 2. The whole system, including the transmitter and the receiver, was mounted on a 2D rotational stage. Sixteen fiber-pigtailed laser diodes emitting at 850 nm were used as the multi-beam transmitter. The laser diodes were driven at different repetition rates by 16 different frequency sources around 1 MHz as listed in Table 1. The synchronous signal from each frequency source was connected to the “START” channels of the TCSPC module. The average optical power of each laser beam was about 7.3 μW, corresponding to a single energy per pulse to be about 7.3 pJ. The pulse width of the laser was approximately 1.7 ns. The output laser pulses from the fiber ends were collimated by a concave mirror by aligning the end faces of the fibers at the focus of the concave mirror as shown by the inset of Fig. 2. The focal length of the concave mirror was 75 mm. After the concave mirror, all the laser beams were collimated, and the diameter of each was around 5 mm. The 16 beams were arranged horizontally in a line with a separation angle between the adjacent two beams of around 9.3 mrad, covering a total angle of ±70mrad. The divergence angle in the vertical direction of each beam was about 0.5 mrad. The returning photons were detected directly by the SPD. To get a larger field of view, there was no collecting lens in front of the detector. An interference bandpass filter (850FS10-25, Andover Corporation, USA) was inserted to extract the signal photons from the background noise. The output of the SPD was connected to the “STOP” channel of the TCSPC module. The TCSPC module was based on a field-programmable gate array (FPGA) board with 16 independent channels of “START” and only one “STOP” channel, indicating that all the “START” signals shared the same “STOP” signal simultaneously in the TOF measurement. The time bin width of each channel was set at 64 ps. The TCSPC module was connected to a computer via a USB cable. The computer played the roles of TOF information collector and 2D rotational stage controller.

Fig. 2. Schematic of the multi-beam frequency-multiplexing photon-counting LiDAR. LD1–LD16: laser diodes operating at different repetition rates around 1 MHz. Fiber Array, 16 multi-mode optical fibers in an array; BPF, interference bandpass filter at 850 nm with a bandwidth of 10 nm; SPD, single-pixel single-photon detector; TCSPC, 16-channel time-correlated single-photon counter module. Inset: zoom-in of the beam collimation part. CM, concave mirror.

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First, we tested the depth resolution and the precision of the whole imaging system. Using one of the laser beams aimed at the target at a distance of 10 m, the TOF measurement was recorded. In the test, the temporal resolution τTCSPC of the TCSPC was set at 64 ps. Taking into account the laser pulse duration τLaser (∼1.7ns) and the timing jitter of the SPD τSPD (∼800ps), the temporal resolution of the system should be Δt=τTCSPC2+τLaser2+τSPD2+τSync2, where τSync is the time jitter of the synchronous signal (∼10ps). Therefore, the temporal resolution of the system was calculated to be 1.87 ns. Accordingly, the depth resolution should be about 28.0 cm. The full width at half-maximum (FWHM) of the TOF measurement by the system was about 1.9 ns, corresponding to a depth resolution of about 28.5 cm, in good agreement with the prediction. For each laser beam, we repeated the test 50 times. The standard deviation of the average peak value was regarded as the depth precision of each beam, which was about 48 mm.

The photon-counting imaging LiDAR was placed in the middle of the hall entrance. Figure 3(a) shows the architectural drawing of the hall with markers on the distance measured by a tapeline. In the experiment, the system worked in the line-by-line scanning mode. When the laser beams scanned the targets, the rotation plate holding the whole system scanned in the vertical direction with a resolution of 8.7 mrad/step. Due to the limitation of the height from the floor to the ceiling at 15 m, the motor scanned 261.8 mrad in 30 steps in the vertical direction. In the horizontal direction, the scanning resolution was 149.3 mrad/step, corresponding to a spatial resolution of 9.3 mrad/channel. The total coverage angle in the horizontal direction was 2.98 rad in 20 steps. The accumulation time for the scan was set at 0.4 s/step. It took about 4 min for the whole acquisition process to form an image of 30×(20×16) pixels. Taking into account the movement time of the rotational stage, the whole scanning time was about 40 min. The total photon counts of the SPD were about 4.2×105cps, including the signal photon-counting rate of about 3.2×105cps and the background noise of around 1.0×105cps. The background noise was mainly caused by an LCD screen at the corner on the wall.

Fig. 3. (a) Map of the hall where the experiment was carried out. (b) The rebuilt image of the hall from the top view acquired by the multi-beam frequency-multiplexing 3D photon-counting laser imaging system. (c) The reconstructed 3D image of the hall from the side angle. Dashed line box: the horse model with its shadow on the wall. (d) Detail of the horse model image in the black dashed line box in (c).

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4. RESULTS AND DISCUSSIONS

Since the laser was rotated in horizontal and vertical directions, the LiDAR was placed at the origin of the polar coordinate system. The distance between the targets and LiDAR D was calculated with the flight time of the photon and the speed of the light in the air. To obtain the image in the Cartesian coordinate system, the image was corrected by where θ and φ denote the scanning angle of the laser in the horizontal and vertical directions, respectively, corresponding to the position in the polar coordinate system, and X, Y, Z are the positions in the Cartesian coordinate system.

Figure 3(b) shows the top view of the reconstructed image. The round dot in the image stands for the LiDAR, which is manually added in the figure. Due to the scanning angle, some of the objects in the shadow of others are not displayed in the image. Other than that, the reconstructed image and the measured distance matched very well with the architectural drawing of Fig. 3(a). Figure 3(c) is the rebuilt image seen from another viewing angle. Figure 3(d) shows the detail of the horse model together with the shadow on the wall marked in the black dashed line box in Fig. 3(c). The shape of the tail and the hind legs were imaged quite well.

In typical multi-beam 3D laser imaging systems ^{[1820" target="_self" style="display: inline;">–20]}, multi-pixel detector arrays are usually employed so that each detection pixel receives the photons from one beam. Crosstalk in the detection arrays between different detection pixels could not be avoided. Moreover, with the increase of the emitting beam number, the number of detection pixels should increase accordingly. Therefore, the cost of the system, which depends a lot on the receiver, will become high. The multi-beam frequency-multiplexing photon-counting 3D laser imaging system here used only one single-photon detector. As a result, no crosstalk will occur in such a system. In addition, the frequency-multiplexing method can be applied to the multi-beam laser imaging systems with even more laser beams. There is no need to add detectors in the receiver part when the number of laser beams increases. Of course, the number of TCSPC channels should be increased, which only involves the electronic devices.

Compared to wavelength-division multiplexing LiDAR ^[11], in this frequency-multiplexing photon-counting technique, there was no control on the wavelengths of different laser diodes in the transmitter part, and neither were there special narrow bandpass filters before the photon detectors in the receiver part, which much simplified the photon-counting LiDAR system, paving the way to a compact but large-scale three-dimensional imaging system for airborne LiDAR. Moreover, since the laser diodes in the emitter part were of almost the same wavelength, dispersion in the air could be ignored, which also simplified the calibration of the LiDAR system.

5. SUMMARY

In conclusion, we demonstrated a multi-beam LiDAR with only a single-pixel single-photon detector as the receiver by frequency multiplexing. Using a multi-channel TCSPC module, the sole detector can discriminate signals from 16 independent signal sources simultaneously, reducing the scale and the cost of the multi-beam photon-counting LiDAR. A 3D image of a hall of about 20.2m×15.6m was acquired with such a compact system to demonstrate the reliability. The frequency-multiplexing method can be easily applied to the existing multi-beam LiDAR system. This kind of system shows great potential in multi-beam LiDAR applications.