1. Introduction

A single-photon detector has substantial advantages: a single-photon sensitivity (due to nonlinear avalanche effect), high-accuracy timing (due to a sharp leading edge of the avalanche pulse), direct digital output, no need for a post-amplifier, small size, low power, and high stability [1–3]. It offers a novel way to detect extremely low-level light signals, and has been widely used among lidar systems. This novel lidar system often referred to as photon counting lidar, which possesses ultrahigh sensitivity and ranging accuracy [4–6]. By adding scanning optics system [7,8] or using single photon avalanche diode (SPAD) array [9,10], the 3D range images are obtained with resolutions high enough to identify objects in the range of kilometers [11,12].

At the beginning, the application of photon counting lidar is mainly based on 3D range image, and the obtained information of target is relatively simple. Researchers try to extend the function of photon counting lidar and obtain more information for a wider application. A compact direct detection Doppler lidar based on one upconversion single-photon detector is demonstrated for wind velocity detection in the atmospheric boundary layer [13,14]. A Micro-pulse polarization lidar at 1.5 µm using a single superconducting nanowire single-photon detector is demonstrated for atmospheric observation [15].

Increasing the acquired information will become the main development direction of photon counting lidar in the future. Based on this, we uses the piecewise statistical method to improve the conventional photon counting lidar. This improved system can acquire radial range, velocity and acceleration of target in the case of photon starved scenes, even less than one photon in each received pulse.

2. Working principle of the improved photon counting lidar

System diagram of the improved photon counting lidar is shown in Fig. 1(a). Firstly, signal generator produces a series of electric pulses that are divided into two channels: one channel is used to drive Laser to emit laser pulse (called emitted signal); the other channel is transmitted to oscilloscope as the initial signal. Emitted signal is collimated to illuminate the target, with an adjustable attenuator for simulating the detection of remote weak signal. The target is a flat reflector fixed on the transmission belt. The transmission belt is controlled by a motor, and its rotation velocity w and acceleration $\alpha$ are adjustable. The radius of the motor wheel is r, and thus in the direction of laser beam the velocity and acceleration of the target (the flat reflector) are $v\ =\ wr$ and $a = \alpha r$, respectively. Then, laser pulse is reflected by the target and back to the receiving system, called the received signal. With a narrow band filter removing the solar background noise, the received signal is gathered by lens and is detected by a single-photon detector (Gm-APD). Finally, the detection results of Gm-APD and the initial signal are collected by an oscilloscope and output to a computer for signal processing.

 

Fig. 1. Working principle of the improved photon counting lidar. (a) System diagram of the improved photon counting lidar. (b) Schematic diagram of emitted and received signals. (c) Schematic diagram of radial range, velocity and acceleration estimation.

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As shown in Fig. 1(b), the emitted signal is a pulse sequence with equal time interval $\Delta T$. Pulse sequence is divided into several statistical segments according to the length of time T, and thus each statistical segment corresponds to K signal pulses. Through a series of round-trip time $\{{\Delta {t_i}} \}$, signal pulses return to the receiving system ($\Delta {t_i} < \Delta T$ is satisfied for the avoidance of range ambiguity). Each signal pulse has a certain probability to trigger Gm-APD, and thus in a statistical segment M out of K signal pulses are detected with the recorded information $\{{\Delta {t_1},\Delta {t_2} \cdot \cdot \cdot \Delta {t_i} \cdot \cdot \cdot \Delta {t_M}} \}$. The detection results in each statistical segment are averaged as $\overline {\Delta t} = \frac{1}{M}\sum\limits_{i = 1}^M {\Delta {t_i}}$, and a series of average results are obtained as $\{{\overline {\Delta {t_1}} ,\,\overline {\Delta {t_2}} \cdot \cdot \cdot \overline {\Delta {t_i}} \cdot \cdot \cdot } \}$. According to the range formula of lidar $R\ =\ {{c\Delta t} \mathord{\left/ {\vphantom {{c\Delta t} 2}} \right.} 2}$, we obtain a series of range values $\{{\overline {{R_1}} ,\,\overline {{R_2}} \cdot \cdot \cdot \overline {{R_i}} \cdot \cdot \cdot } \}$, which correspond to a series of time points $\{{T,\,2T \cdot \cdot \cdot iT \cdot \cdot \cdot } \}$. These data of range $\{{\overline {{R_1}} ,\,\overline {{R_2}} \cdot \cdot \cdot \overline {{R_i}} \cdot \cdot \cdot } \}$ and time $\{{T,\,2T \cdot \cdot \cdot iT \cdot \cdot \cdot } \}$ are plotted on the coordinates as shown in Fig. 1(c), and then radial range R, velocity v and acceleration a of the target can be estimated simultaneously by the curve fitting method according to the motion equation $R = {R_0} + vt + {{a{t^2}} \mathord{\left/ {\vphantom {{a{t^2}} 2}} \right.} 2}$.

3. Experiment and result analysis

Figure 2 is the photo of the experiment system of the improved photon counting lidar that is built in our laboratory according to the working principle block diagram of Fig. 1. The signal generator (Tektronix AFG3252) has two outputs, with one as the driving signal of the laser and the other one as the initial signal of timing. Under the control of the driving signal, a 532 nm semiconductor laser generates an equidistant laser pulse sequence with repetition frequency of 10 KHz and pulse width of 1 ns. Attenuator can achieve adjustable attenuation of 1db-100db, in order to simulate weak signal detection.

 

Fig. 2. The photo of the experiment system of the improved photon counting lidar.

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The Gm-APD module is used for the detection of received signals, including three main components: a narrow-band filter, optical receiving system and Gm-APD detecter. (i) A narrow-band filter (the center wavelength is 532 nm, the full width at half-maximum is 10 nm, and the center transmittance is 65% @532 nm), which is used to filter background noise. (ii) Optical receiving system (The optical aperture is about 25 mm, and optical transmittance is about 85%), which is used to collect the received signal and focus it onto the photosensitive surface of detector. (iii) A single-point Gm-APD detector (LASER COMPONENTS COUNT-50C; the photon detection efficiency at 532 nm is about 65%; the dead time is 50 ns; the timing jitter is about 800ps), which is used to detect weak received signal. The dead time of 50 ns is greater than the pulse width of 1 ns, so each pulse echo can only respond to a count event at most. Besides, this dead time is less than the interval of 100 µs between adjacent pulses (10KHz repetition frequency laser), and there is no effect between adjacent pulses. 16 channels photon count card (Becker & Hickl GmbH DPC-230; the time resolution is 164.61ps), which is used for high-accuracy timing. Finally, signal processing and display are performed by computer.

Considering the detection of stationary target, the round-trip time of each signal pulse is the same, a clear and accurate signal peak can be obtained through conventional photon counting statistics, as shown in Fig. 3(a). However, for the detection of motion target, the round-trip time of each signal pulse is different, conventional photon counting statistics will produce a severe broadening of signal peak with the same statistical time of 0.5s as the stationary target. Thus, on the one hand, the ranging accuracy will become worse; on the other hand, it can only obtain the range information of target, losing the velocity and acceleration information. Therefore, we propose the piecewise statistical method, as shown in Fig. 3(c). This method divides the time axis into some equal small statistical segments, each of which is processed separately, and then according to the time-varying results of each statistical segment, radial range, velocity and acceleration of the target are estimated simultaneously. Here, the total statistical time of 0.5s is divided into 50 segments, with 0.01s for each segment. Each segment is counted separately, and then a series of discrete signal peaks are obtained. Obviously, it can be seen that signal peaks are moving with time, which contains radial range, velocity and acceleration of the target. We make statistics of discrete signal peaks according to time, as shown in Fig. 3(d), and then use the quadratic motion equation $R = {R_0} + vt + {{a{t^2}} \mathord{\left/ {\vphantom {{a{t^2}} 2}} \right.} 2}$ to fit the data, and finally radial range, velocity and acceleration of the target are obtained, that are ${R_0}\, = 10.003,\,v = 1.023,\,a = 0.962$.

 

Fig. 3. Experimental results and analysis. (a) the signal peak of stationary target with conventional photon counting statistics of 0.5s; (b) the signal peak of motion target (radial velocity $v = 1\,\textrm{m/s}$ and acceleration $a = 1\,\textrm{m/}{\textrm{s}^2}$) with conventional photon counting statistics of 0.5s; (c) the signal peak of motion target (radial velocity $v = 1\,\textrm{m/s}$ and acceleration $a = 1\,\textrm{m/}{\textrm{s}^2}$) using our improved piecewise statistics of 0.5s, which includes 50 statistical segments with 0.01s for each statistical segment; (d) radial range R, velocity v and acceleration a of the target is estimated simultaneously by the curve fitting method.

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Next, the accuracy of this improved method is analyzed. First, considering range accuracy, it is directly related with pulse width (that is expressed as the full width half maximum of pulse, FWHM) and cumulative number of successful detection. For our system, pulse width is $FWHM = 1ns$, and cumulative number of successful detection is ${N_D} = N \cdot P$. Here, the number of emitted pulses N is the product of the laser repetition frequency F and the total detection time ${T_{sum}}$, namely $N = F \cdot {T_{sum}}$. The probability of successful detection P satisfies the Poisson probability model [16], namely $P = 1 - \exp ( - {N_s} \cdot \eta )$, with ${N_s}$ the received signal intensity (the average number of photons per received signal pulse) and $\eta$ quantum efficiency of Gm-APD detector. Thus the theoretical range accuracy can be expressed as ${\sigma _R}\ =\ {{FWHM \cdot c} \mathord{\left/ {\vphantom {{FWHM \cdot c} {\left( {2\sqrt {{N_D}} } \right)}}} \right. } {\left( {2\sqrt {{N_D}} } \right)}}$, while the experimental range accuracy can be expressed as the standard deviation of the results of 1000 repeated experiments. Figure 4(a) shows experimental range accuracies with different number of emitted pulses N and different received signal intensity ${N_s}$. Here, the different number of emitted pulses are changed by adjusting the total detection time, with other parameters remained the same (e.g., laser repetition frequency is still 10KHz and each segment is still 0.01s). On the one hand, with the increase of the number of emitted pulses N, range accuracy gradually gets better; on the other hand, with the increase of received signal intensity ${N_s}$, range accuracy also gets better. Essentially these two factors affect the cumulative number of successful detection ${N_D} = N \cdot P = N[{1 - \exp ( - {N_s} \cdot \eta )} ]$, and then affect range accuracy. This point has been well proved by basically the same range accuracies of point A and point B in Fig. 4(a). In the case of point A, with 10000 emitted signal pulses and ${N_s}\ =\ 0.8$, the probability of successful detection is $P = 1 - \exp ( - {N_s} \cdot \eta ) = 1 - \exp ( - 0.8 \times 0.65) \approx 40\%$, and then the cumulative number of successful detection ${N_D} = N \cdot P = 10000 \times 40\%= 4000$. While in the case of point B, with 4000 emitted signal pulses and the received signal intensity ${N_s} \to \ +\ \infty$, the probability of successful detection is close to 100%, and then the cumulative number of successful detection ${N_D} = N \cdot P = 4000 \times 100\%\ =\ 4000$. Due to the same cumulative number of successful detection of point A and point B, their range accuracies are basically equal. This also indicates that when the pulse width and other system hardware conditions are the same, the cumulative number of successful detection can directly and effectively evaluate range accuracy. Beyond that, like point C and point D in Fig. 4(b), or like point E and point F in Fig. 4(c), they all have the same cumulative number of successful detection, and therefore velocity accuracy and acceleration accuracy are also basically equal, respectively.

 

Fig. 4. Accuracy analysis. (a) Range accuracy. (b) Velocity accuracy. (c) Acceleration accuracy.

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For our system, whose pulse width is $1\,ns$ and repetition frequency is 10 KHz. With the received signal intensity ${N_s}\ =\ 0.8$ and 10000 emitted signal pulses, we can realize the simultaneous measurement of radial range, velocity and acceleration, with range accuracy of $6.6\,mm$, velocity accuracy of $0.04\,\,m/s$, and acceleration accuracy of $0.10\,m/{s^2}$. In practical application, the detection performance can be effectively improved by shortening pulse width and increasing repetition frequency of the laser.

4. Conclusions

In this paper, a novel imrpoved photon counting lidar based on the piecewise statistical method is proposed. This system can realize the simultaneous measurement of radial range, velocity and acceleration, without increasing the system hardware complexity. The scheme and working principle of our proposed system are described in detail. Then experimental researches are carried out for principle verification and performance study, and the accuracies of radial range, velocity and acceleration are analyzed through a large number of repeated experiments. Two main factors that influence the measurement accuracy, including the received signal intensity and the emitted signal pulses number, are synthesized as the cumulative number of successful detection. Thus, the cumulative number of successful detection is more convenient and effective to directly evaluate the change trend of measurement accuracy of range, velocity and acceleration. Finally, the experimental results show that radial range, velocity and acceleration can be obtained simultaneously in the case of photon starved scenes (Average number of photons per received signal pulse is 0.8).