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Abstract
To avoid echo photons to be submerged in noise in rough terrain or dynamic applications, a single photon imaging mechanism with multi-scale time resolution is proposed in this paper. Combining with adaptively thresholding technique, multiple histograms with different time resolutions are produced to cluster the echo photons into a time bin and then separate them from the noise. With microsecond-scale resolution, uncertainty in the position of an object can be reduced from several kilometers to 300 meters, and therefore the computational overheads are saved by only investigating depths with picosecond-scale resolution where an object is present. Reconstructed results of the two near surfaces show that the depth accuracy is less than 0.15 m in the conditions of 8 echo photons and 1 Mcps background count rate, even though the pulse width of laser source reaches 3.5 ns (equivalent to an uncertainty of 0.525 m). In addition, the echo can be distinguished from the noise clearly when the background count rate varies from 200 kcps to 1 Mcps. The proposed method is suitable for implementation in digital signal processor (DSP) due to low data volumes and computational overheads.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Single photon detection can provide extremely high sensitivity to collect the weak optical signals [1–3], which promotes widespread applications, such as biological imaging [4,5], Non-line-of-sight (NLOS) imaging [6,7], vibration sensing [8,9], and so on. Due to its excellent sensitivity, distance to be measured is extended from tens of kilometers [10,11] to hundreds of kilometers [12–14], or lower power laser source is allowed to be used in long range applications [15,16]. Applying statistical measurement technique (time-correlated single photon counting, TCSPC) [17,18], the needed photon flux is significantly lower than classical linear detection [19,20].
In general, when the echo photons and the noise photons are collected by a single photon avalanche diode (SPAD), a large number of photon events are triggered accordingly. By repeatedly recording the photon events against the emission time of associated pulsed laser, a histogram can be produced [17,21]. However, time resolution of the histogram may affect both the depth resolution and the signal-to-noise ratio (SNR). In this case, sub-picosecond time resolution, combining with sub-picosecond pulsed laser source, was applied for single photon lidar in the past few years, resulting in the noise of less than one count for each time bin under daylight conditions [22]. For instance, to avoid pileup distortion and improve depth accuracy, sub-picosecond photon-efficient 3D imaging was demonstrated [23]. Using a sub-picosecond timing accuracy for pulsed light sources with a full width at half maximum (FWHM) wider than 50 ps, the system was proved to be operated across a wide dynamic range, from low-flux to high-flux measurements. Recently, a QPMS-based 3D imager was reported with exceptional detection sensitivity and noise tolerance [24], where sub-picosecond timing resolution and quantum parametric mode sorting (QPMS) allowed to perform 3D imaging with weak returning signal at 0.0006 mean photon detection per pulse despite strong background noise. Unfortunately, motion of the object or the platform might cause the echo photons to be discretely distributed in multiple time bins, which would degrade the sensitivity of detection. Filtering out the noise remained a challenging work since it was difficult to distinguish whether the photon event was generated by the echo photon or noise photon [25]. To suppress the false alarm probability, a returned light was split into two Gm-APD (Geiger mode avalanche photodiode) arrays, from which an AND gate was used to compare the arrival time of the electrical signals. The false alarm probability was drastically decreased, because the noise distributed randomly in time domain was filtered out [26]. Based on the fact that the echo photons of adjacent pixels would arrive at the photosensitive surface of the detector at almost the same time, a Gm-APD array was divided into many elementary units and a proper threshold was used to decide whether there existed echo photons or not. In this case, a clear 3D image was taken from the experimental system in spite of strong background noise in sunny day [27]. An adaptive single photon detection method was proposed to handle the fluctuating background noise, where the histogram was compared with an adaptive threshold to implement a desired false alarm probability. In this case, the single photon lidar could be operated under fluctuating background noise environments [28]. Combining single photon detection with outstanding computational techniques, such as unmixing signal and noise [29], machine learning [30], and long-range-tailored computational algorithm [31], high-quality 3D structure and reflectivity can be reconstructed at low signal-to-background ratio (SBR).
The returned light may be broadened in rough terrain or dynamic applications. In this case, the echo photons may be discretely distributed in multiple time bins in a histogram, which will make the echo photons be submerged in the noise. In order to implement photon-sensitive detection in noisy environments, a single photon imaging mechanism with multi-scale time resolution is proposed in this paper. Multiple histograms, whose time resolutions range from hundreds of picoseconds to several microseconds, are produced to cluster the echo photons into a time bin and separate them from the noise. Afterwards, uncertainty in the position of an object can be reduced significantly, and therefore the computational overheads are saved by only investigating depths where an object is present.
2. Multi-scale single photon detection
When at least one echo photon or noise photon appears and triggers a photon event, the detection probability of single pulse echo ($P_{DS}^{{T_R}}$) can be determined [32,33]. Specially, when the pulsed laser is shut down, no echo photon is collected. In this case, the false alarm probability of single pulse echo ($P_{FAS}^{{T_R}}$) can be obtained from simplifying $P_{DS}^{{T_R}}$. Finally, the detection probability and the false alarm probability of single pulse echo are given by
Since the echo photons can’t be distinguished from the noise photons with single pulse echo, the TCSPC technique is applied to improve the sensitivity in single photon detection. Assuming that M pulse echoes are accumulated to produce a histogram, the detection probability and the false alarm probability of M pulse echoes ($P_D^{{T_R}}$ and $P_{FA}^{{T_R}}$) can be represented as
In rough terrain or dynamic applications, time resolution of the histogram should be degraded so as to cluster the echo photons into a time bin. Unfortunately, lower time resolution may result in lower SNR because the mean number of the noise photons (${n_n}$) increases accordingly. Furthermore, lower time resolution may result in lower depth accuracy as well. To cluster the echo photons into a time bin, improve the signal-to-noise ratio and the depth accuracy simultaneously, multiple histograms with different time resolutions are introduced in single photon detection. Here, these histograms are named as: basic-histogram, micro-histogram, and macro-histogram, corresponding to a basic-resolution (400 ps), micro-resolution (20 ns), and macro-resolution (2 us), respectively.
Schematic of the multi-scale single photon detection is shown in Fig. 1. Firstly, a basic-histogram is prepared for every pixel by performing M pulse accumulation. In order to reconstruct the depth information of the central pixel, it needs to cooperate with its surrounding pixels to form a pixels-block. As shown in Fig. 1(a), each pixels-block contains a central pixel and eight surrounding pixels. Due to the spatial correlation of the pixels-block, it is possible to cluster the echo photons into a time bin in the macro-histogram. Secondly, a micro-histogram is produced by performing binning operation to respective basic-histogram for each pixel in the pixels-block. Thirdly, an adaptive threshold is determined according to the count rate (background noise) in real time [28]. When the background noise fluctuates, the count rate varies accordingly. Subsequently, the threshold is updated to obtain a desired false alarm probability. Each micro-histogram is individually compared with the threshold. If the count in the micro-histogram exceeds the threshold, the time bin is set to 1 and otherwise it is set to 0. Subsequently, a thresholding sequence can be produced (see Fig. 1(b)). Fourthly, all thresholding sequences in a pixels-block are accumulated to produce a macro-histogram by performing binning operation as well. Subsequently, index of the echo in the macro-histogram can be determined according to the principle of peak discrimination. Finally, a sub-basic-histogram, corresponding to the index of the echo, is chosen from the basic-histogram to perform depth reconstruction. It should be noted that the echo photons may be discretely distributed in multiple time bins in the sub-basic-histogram. In this case, counts in the sub-basic-histogram need to be weighted in conjunction with the intensity distribution of the pulsed light, so as to obtain a superior depth.
Fig. 1. Schematic of multi-scale single photon detection. (a) A pixels-block is designated to produce multiple histograms; (b) each micro-histogram is individually used to produce a thresholding sequence in the pixels-block; (c) all thresholding sequences are accumulated to produce a macro-histogram; (d) a sub-basic-histogram, corresponding to the index of the echo, is chosen from the basic-histogram to perform depth reconstruction.
During threshold determination for the micro-histogram, a desire false alarm probability is limited to 0.1%. It means that, there is approximately 1 time bin whose counts are larger than the threshold within 1000 time bins. Therefore, “1” is sparse in the thresholding sequence. Besides, binning operation of 100 time bins in the thresholding sequence is required to produce a macro-histogram, because their time resolution is given by 20 ns and 2 us, respectively. In this case, the detection probability of single thresholding sequence ($\hat{P}_{DS}^{Macro}$) can be obtained approximately from that of M pulse echoes ($P_D^{Micro}$). Similarly, the false alarm probability of single thresholding sequence ($\hat{P}_{FAS}^{Macro}$) can be obtained approximately from that of M pulse echoes ($P_{FA}^{Micro}$).
All thresholding sequences in a pixels-block are accumulated to produce a macro-histogram. Consequently, the detection probability of N thresholding sequences ($\hat{P}_D^{Macro}$) and the false alarm probability of N thresholding sequences ($\hat{P}_{FAS}^{Macro}$) can be given by
Compared with accumulating N basic-histograms directly, the macro-histogram obtained from accumulating N thresholding sequences can avoid the echo photon to be submerged in the noise and improve the signal-to-noise ratio. In addition, by weighting the counts in the sub-basic-histogram, depth accuracy can be improved when the pulse width of laser source reaches several nanoseconds (equivalent to around 0.5 m uncertainty) and it is broadened in rough terrain or dynamic applications.
In remote sensing applications, the distance to be measured is unknown and there is no prior information about the location of the object. In this case, uncertainty in the position of an object may range from several kilometers to tens of kilometers. With the macro-histogram, the location of the object can be determined to within an uncertainty of 300 m and no prior information is required. Apparently, the uncertainty can be greatly reduced and then the computational overheads are saved by only investigating depths where an object is present.
3. Experimental setup
A single photon lidar system is established to verify the proposed method with multi-scale time resolution in this paper. As shown in Fig. 2, a pulsed laser source with a wavelength of 1064 nm is used to illuminate the scene. When a pulsed light is emitted from the laser source, it is split into two parts: a synchronous light and an emitted light. The synchronous light is collected by a PIN diode to generate a “start” signal, which is connected to the TCSPC module (quTAG made by quTools). The echo photons and noise photons are collected by the optical system together and then coupled to the SPAD detector (SPCM-AQRH made by Excelitas). Afterwards, a “stop” signal is triggered and connected to the TCSPC module as well.
The main parameters of the single photon lidar system is given in Table 1. It should be noted that the quTAG module can provide excellent performance with a time resolution of 1ps. Therefore, multiple histograms with different time resolutions can be produced by binning operation.
Table 1. Main parameters of the single photon system.
Specifically, a basic-histogram is utilized to improve the depth accuracy. Since the time jitter of the SPAD is approximately 350 ps, the basic-resolution is set to 400 ps (a little larger than the time jitter) in our system. It should be noted that the echo photons may be discretely distributed in multiple time bins, which makes it difficult to extract the depth information from the basic-histogram. In this case, a macro-histogram is required to cluster the echo photons into a time bin. The macro-resolution is set to 2 us so as to cover an uncertainty of 300 m within a pixels-block in most terrain or dynamic applications. In order to suppress the false alarm probability, the macro-histogram is obtained from thresholding the micro-histograms in the pixels-block, instead of performing direct accumulation and binning operation to the basic-histograms. Hence, a micro-histogram is required to perform adaptively thresholding operation. The micro-resolution is set to 20 ns in our system, which lies in the basic-resolution (400 ps) and the macro-resolution (2 us).
4. Results and discussions
Two near surfaces are located in front of the single photon lidar system. One surface is placed 1 meter away from the other so that a comparison can be performed between the reconstructed distance and the true distance. In special case, when the light spot illuminates two surfaces at the same time, multiple echoes will occur in the basic-histogram while single echo is seen in the macro-histogram due to different time resolution. To highlight the superiority of our proposed method with multi-scale time resolution, macro-histograms are obtained in two different ways: one way is to accumulate N basic-histograms and then perform binning operation, and the other way is to accumulate N thresholding sequences.
The macro-histograms in Fig. 3(a) are obtained by performing accumulation and binning operation to the basic-histograms under the count rates of 200 kcps (counts per second, cps), 500 kcps, and 1 Mcps, respectively. As the count rate increases, the echo is more and more difficult to be distinguished from the noise. More seriously, the noise counts are higher than the echo counts when the count rate reaches 1 Mcps, which will result in an error-reconstruction of depth. Similarly, the macro-histograms in Fig. 3(b) are obtained by performing accumulation to the thresholding sequences under the count rates of 200 kcps, 500 kcps, and 1 Mcps, respectively. Due to the adaptively thresholding operation, the desired false alarm probability is limited to below 0.1% in the thresholding sequence. However, the actual false alarm probabilities are slightly different from each other under different count rates, resulting in distinguishing noise counts in the macro-histograms. Nevertheless, it can be seen from the Fig. 3(b) that the echo can still be distinguished from the noise clearly.
Fig. 3. The macro-histograms are obtained in two different ways. (a) is obtained by performing accumulation and binning operation to the basic-histograms under the count rates of 200 kcps, 500 kcps, and 1 Mcps, respectively. By contrast, (b) is obtained by performing accumulation to the thresholding sequences under the count rates of 200 kcps, 500 kcps, and 1 Mcps, respectively.
As shown in Table 2, statistical results of the detection probability (${P_D}$) and the false alarm probability (${P_{FA}}$) are obtained from a larger number of the macro-histograms. It can be concluded that a high detection probability and a low false alarm probability can be implemented by performing accumulation to the thresholding sequences.
Table 2. Statistical results of the detection probability and the false alarm probability.
According to the macro-histograms in Fig. 3(b), it is indicated that the echo is located in the first time bin, ranging from 0 to 2 us. In this case, only a few datasets (2 us) in the basic-histogram (corresponding to a time bin in the macro-histogram) is used for depth reconstruction, and the rest datasets will be discarded. This process will greatly reduce the data volumes and computational overheads in depth reconstruction. The reconstructed results of the two near surfaces are shown in Fig. 4. It can be seen from the figure that the distance between the surfaces I and II can be measured correctly under different count rates (200 kcps, 500 kcps and 1 Mcps). One surface is located approximately at 16 m while the other is located approximately at 17 m.
Fig. 4. Reconstructed depth of two near surfaces under different count rates. (a) The photograph is obtained from a commercial CCD camera with visible-band; (b), (c) and (d) are the 3D profiles reconstructed by using the sub-basic-histogram under the count rates of 200 kcps, 500 kcps and 1 Mcps, respectively.
A comparison between the experimental results and the true value is shown in Table 3. ${R_I}$ and ${R_{II}}$ are the distances between the surface I (II) and the single photon lidar system, respectively. $\Delta {R_{Meas}}$ and $\Delta {R_{True}}$ are the measured distance and the true value between the surface I and the surface II, respectively. Their mean values and root mean squares (RMS) are obtained by performing statistical operation to most of the pixels. Apparently, the measured distance between two surfaces is consistent well with the true value under different count rates. Moreover, the root mean squares of the measured distances are less than 0.15 m in the conditions of 8 echo photons and 1 Mcps background count rate, even though the pulse width of the laser source reaches 3.5 ns (equivalent to an uncertainty of 0.525 m).
Table 3. Comparison of the distances between the experimental results and the true value.
Another experiment is performed to capture the profile of the buildings. As shown in Fig. 5(a), a photograph is obtained from a commercial CCD camera with visible-band. To increase the number of pixels and extend the region that can be imaged, multiple pixels scanning is applied to form a larger-size image. The 3D profile of the buildings is shown in Fig. 5(b), corresponding to the selected area in Fig. 5(a). It can be seen from the profile that the reconstructed depth of the buildings ranges from 1000 m to 1200 m. Each building can be distinguished evidently, which is represented by different colors in the profile.
Fig. 5. Reconstructed depth of the buildings. (a) The photograph is obtained from a commercial CCD camera with visible-band, and (b) is the 3D profiles corresponding to the selected area in (a).
In our lidar system, the ranges of multiple histograms are designated as 50 us, which correspond to the pulse repetition frequency of 20 kHz. Even though the distance to be measured is extended from dozens of kilometers to hundreds of kilometers, the proposed multi-scale method can still limit the range of sub-basic-histogram to a time bin width of the macro-histogram (2 us), and therefore the data volumes and the computational overheads are saved in depth reconstruction.
5. Conclusion
A single photon imaging mechanism with multi-scale time resolution is proposed in this paper to avoid the echo photons to be submerged in the noise photons in rough terrain or dynamic applications. Combining with adaptively thresholding technique, multiple histograms with different time resolutions are produced to improve the performance of echo detection. By weighting the counts in the basic-histogram, depth accuracy can be improved when the pulse width of laser source reaches several nanoseconds (equivalent to around 0.5 m uncertainty) and it is broadened in rough terrain or dynamic applications. Besides, data volumes and computational overheads are saved by limiting the range of sub-basic-histogram to a time bin width of the macro-histogram, even though the distance to be measured is extended from dozens of kilometers to hundreds of kilometers. The proposed method is suitable for rough terrain or dynamic applications in real time.
Funding
National Natural Science Foundation of China (61805249); Youth Innovation Promotion Association of the Chinese Academy of Sciences (2019369).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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