A real-time noise filtering strategy for photon counting 3D imaging lidar

Zijing Zhang; Yuan Zhao; Yong Zhang; Long Wu; Jianzhong Su

doi:10.1364/OE.21.009247

1. Introduction

Gm-APD has substantial advantages in photon counting 3D imaging lidar: each range measurement requires a single detected photon because of its ultrahigh sensitivity, even single photon response; also, a sharp leading edge of avalanche pulse allows high-resolution timing; besides, the output signal of Gm-APD is digital and strong enough to drive the processing circuit without noise of analog-to-digital converter (ADC) and amplification. Photon counting 3D imaging lidar using Gm-APD as the detector has been extensively investigated by many research groups [1–7]. However the inevitable noise remains a significant challenge in analysis of the digital output data of photon-counting since there is no way to distinguish the avalanche events generated by signal or noise.

Daniel G. Fouche reported the false-alarm probability of the laser radar using Gm-APD detector. The coincidence processing of a few pulses is proposed to reduce the false-alarm probability. In his paper, the conditions of three pulses and five pulses are taken as examples, indicating that identifying the signal from only three pulses can reduce the false-alarm probability by orders of magnitude [8].

Hong Jin Kong divided a returned laser pulse into two Gm-APD arrays and used an AND gate to compare the arrival time of the electrical signals from two Gm-APD arrays. The false alarm probability is drastically decreased, because noise distributed randomly in the time domain is filtered out. The experimental measurement showed the new method of two Gm-APD arrays could reduce false alarms and obtain a clear 3D image [9].

Many methodologies of post processing for filtering out false alarms are presented by Applied Research Laboratories of University of Texas at Austin, such as the Modified Canny Edge Detection (MCED), the probability distribution function (PDF), and the Local Angle Mapping Technique (LAMT) [10]. MIT Lincoln Laboratory also developed a 3D imaging laser radar system with Gm-APD. They took time to obtain a clear 3D image through a series of complicated image processing algorithms that cleaned the raw detection data to be a clear 3D image of the target of interest with noise filtered out [11].

In summary, effective techniques that can filter out false alarms and obtain a clear 3D image must be developed. For the range measurement process of the imaging lidar, the ranges of the target surface areas corresponding to the adjacent pixels of the Gm-APD detector do not vary much due to the characteristic of the surface continuity for most targets of interest, and therefore the temporal difference of the echo signals on adjacent pixels is slight. According to this characteristic, we propose a new method to obtain a clear 3D image through filtering out false alarms in real time. We took some adjacent pixels as an elementary unit and used a proper threshold to distinguish signal and noise.

2. The working principle

First, the raw data characteristic of the photon counting 3D imaging lidar is analyzed. The outputs of some adjacent pixels in a m × n Gm-APD array are shown in Fig. 1. Considering the surfaces of most targets of interest are continuous, the ranges of the target surface areas corresponding to the adjacent pixels of the Gm-APD detector do not vary much, and therefore the temporal difference of the echo signals on adjacent pixels is slight. The echo signal of adjacent pixels will arrives at the detector surface at almost the same time, which is shown as the photon counting pulses in the dash box (blue) in Fig. 1. However noise will be randomly distributed on the whole time axis. By calculating the counting rate of these adjacent pixels, the echo signal will be distinguished from noise with a proper threshold in the counting rate.

Fig. 1 The raw data characteristic of the photon counting 3D imaging lidar. Due to the surface continuity characteristic of most targets of interest, considering the photon counting results of several adjacent pixels in the m × n Gm-APD array, signal (in the dash box) is comparatively centralized near the target position with its surface detail differences and noise (out of the dash box) is randomly distributed on the whole time axis.

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According to this feature of signal distinguishing from noise, a smart strategy is designed, which can filter out false alarms and obtain a clear 3D image of the target of interest in real time without wasting time in post-processing. As shown in Fig. 2(a), the m × n Gm-APD array is divided into many elementary units, each of which has N adjacent pixels (N = 9 for an example in this paper). Each elementary unit has the same processing circuit as shown in Fig. 2(b). The working principle of this circuit is shown in Fig. 2(c). The pulse-laser signal is transmitted at 0, and the master clock of the elementary unit starts timing from 0. At the same time, each pixel of Gm-APD array is set to Geiger mode and waits for the echo signal. The individual clock of each pixel doesn’t work by this time. When a Gm-APD pixel is triggered by signal or noise, the individual clock of this pixel starts timing from 0 and a logic high level whose time width is $Δ t$ is generated. The next triggered event (the avalanche event) will reset the individual clock of its own pixel until a stop signal. In each elementary unit, the logic levels of N pixels are added together in real time. When the total logic level of an elementary unit exceeds a proper threshold, a stop signal will be generated and stop all the clocks in this elementary unit. By this time, the master clock is $Δ τ$ and the individual clock of the $i^{t h}$ pixel is $τ_{i}$ . The round-trip time of the signal for each pixel is calculated by subtracting the result of the individual clock from the one of the master clock. For example, the timing result of the $i^{t h}$ pixel is $T_{i} = Δ τ - τ_{i}$ as Fig. 2(c). Thus false alarms generated by noise are well filtered out without exceeding the threshold due to the characteristic of its random distribution. We call this method as the unit-threshold method (UTM) in this paper.

Fig. 2 The working principle for an elementary unit. (a)a m × n Gm-APD array is divided into many elementary units of 3 × 3 pixels. (b) The timing circuit for an elementary unit. Each pixel has the individual clock, and an elementary unit has a master clock. (c) The signal processing flow for 9 pixels of an elementary unit. When the total logic level of all pixels of an elementary unit exceeds a certain threshold, the system considers of detecting the echo signal and all clocks are stopped. Then these counting points of the echo signal are recorded, and however other counting points that are generated by noise are not recorded due to total level (or the counting rate in $Δ t$ ) below the threshold.

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UTM utilized the statistics of the echo signals of 9 adjacent pixels to do the threshold adjustment. But the 9 pixels were not integrated into one image pixel. The elementary unit that consists of 9 adjacent pixels is just a distinguishing unit, and the 9 pixels in the same elementary unit have individual clocks. After the unit-threshold processing, the 9 pixels still have independent timing results.

3. The theoretical analysis

In this paper, $N_{s}$ is the mean number of the photoelectrons that is generated by a pulse-laser echo signal on each pixel; $N_{n}$ is the mean number of the photoelectrons that is generated by noise per nanosecond per pixel; $Δ t$ is the time width of the logic high level, which should be larger than the temporal difference of the echo signals on the adjacent pixels and make sure that the echo signal will not be filtered out. Thus the echo signals of all the pixels in the same elementary unit are concentrated in some $Δ t$ . When there is the echo signal of the target in $Δ t$ , the mean triggered probability of each pixel is expressed as $1 - \exp (- N_{s})$ ; when no echo signal in $Δ t$ , the mean triggered probability of each pixel is $1 - \exp (- N_{n} Δ t)$ by noise $N_{n}$ . $x$ is the number of pixels that is triggered in N pixels of an elementary unit in $Δ t$ . The counting rate of $x$ in $N$ pixels can be expressed as $P_{s} (x)$ and $P_{n} (x)$ , with and without the echo signal in $Δ t$ respectively.

P_{s} (x {)=C}_{N}^{x} {[1 - \exp (- N_{s})]}^{N} \exp {(- N_{s})}^{N - x}

P_{n} (x {)=C}_{N}^{x} {[1 - \exp (- N_{n} Δ t)]}^{x} \exp {(- N_{n} Δ t)}^{N - x}

According to the probability distribution differences of $x$ with or without signal, a proper threshold $Y$ is used to distinguish signal and noise. Any threshold is not ideal: (a) there is a certain probability of noise exceeding the threshold without the echo signal, which is called as the false-alarm probability; (b) there is a certain probability of signal below the threshold, which is called as the drop-out probability. The false-alarm probability and the drop-out probability are inevitable, and the sum of them is called the false-detection probability $H$ . It is a probability of incorrect signal and noise distinguishment, which is used to estimate reliability of this method.

H (N, Δ t, N_{s}, N_{n}, Y) = \sum_{x= Y}^{x= N} P_{n} (x) + \sum_{x= 0}^{x=Y-1} P_{s} (x)

The false-detection probability $H$ is decided by five variables $N$ , $Δ t$ , $N_{s}$ , $N_{n}$ and $Y$ . Next we discuss the relationship between $H$ and four variables ( $N$ , $Δ t$ , $N_{s}$ , $N_{n}$ ). After that, we research the method of selecting the proper threshold $Y_{p r o p e r}$ .

$H$ increases with the increase of $Δ t$ in Fig. 3(a). This is because the accumulated power of noise becomes strong with $Δ t$ increasing, which makes it difficult to distinguish signal from noise. Therefore $Δ t$ should be set to be short enough, when the temporal difference of the echo signal in an elementary unit is not larger than $Δ t$ . In Figs. 3(b) and 3(c), $H$ decreases with the increase of $N_{s}$ and the decrease of $N_{n}$ respectively. This is because it is easier to distinguish signal from noise due to the greater difference between them.

Fig. 3 The relationship between $H$ and four variables ( $N$ , $Δ t$ , $N_{s}$ , $N_{n}$ ).

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In Fig. 3, $H$ also decreases with the number of pixels in the elementary unit $N$ dramatically. However the selection of $N$ should not be too large, and just make the false-detection probability satisfy the application requirement. If $N$ is too large, it will make $Δ t$ increase due to the larger elementary unit corresponding to the greater difference of the target surface. Furthermore, too large $N$ will make the imaging results of the target edge become bad, when there exists a target in part of an elementary unit and no target in the other part. According to the data point of Fig. 3(a), when $N_{s} = 5$ , $N_{n} = 0.01 n s^{- 1}$ and $Δ t = 30 n s$ , an elementary unit $N = 9$ can make the false-detection probability $H$ decrease to 0.001. Furthermore the elementary unit of $N = 9$ is easy to be divided from Gm-APD array. Hereinafter taking $N = 9$ as an example, the experimental verification will be carried out in Section 4.

The probability distributions of the number of triggered pixels $x$ with different signal and noise intensities for an elementary unit of $N = 9$ are shown in Fig. 4. This picture more intuitively shows the differences between signal and noise than Eqs. (1a) and (1b). A threshold is employed to distinguish signal and noise: when the number of triggered pixels $x$ exceeds the threshold $Y$ , there is the echo signal in this $Δ t$ ; when $x$ doesn’t exceed $Y$ , no echo signal exists in this $Δ t$ . From the partial enlargement in the top left corner of Fig. 4, the proper threshold that is employed to distinguish signal from noise varies with the intensity of signal or noise. The selection of this proper threshold should make the false-detection probability minimum, taking Eq. (2) as

Fig. 4 The probability distribution of signal $N_{s}$ (blue lines) and noise $N_{n}$ (red lines). There are different probability distributions with different signal and noise intensities, and the proper threshold that is employed to distinguish them varies. A partial enlargement in the dash box is shown on the top left corner.

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H = \sum_{x= Y}^{x= N} P_{n} (x) + \sum_{x= 0}^{x=Y-1} P_{s} (x) \to \min

The proper threshold $Y_{p r o p e r}$ is obtained by the partial derivative method.

{\frac{\partial (H)}{\partial (Y)} |}_{Y = Y_{p r o p e r}} = {\frac{\partial (\sum_{x= Y}^{x= N} P_{n} (x) + \sum_{x= 0}^{x=Y-1} P_{s} (x))}{\partial (Y)} |}_{Y = Y_{p r o p e r}} = 0

Equation (4) is so complicated that it is difficult to obtain the analytical solutions, and therefore the numerical results are shown in Fig. 5. According to the different designs of $N$ and $Δ t$ , the proper threshold $Y_{p r o p e r}$ under different signal and noise intensities can be calculated in advance for application.

Fig. 5 The proper threshold $Y_{p r o p e r}$ with different signal and noise intensities. (The number of pixels in an elementary unit $N = 9$ and $Δ t = 30 n s$ ).

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4. The experimental results and analysis

An experimental system that is used to demonstrate UTM in this paper is established. The laser transmits a 532nm laser pulse, a small part of which is reflected into a PIN detector as a start signal by the beam splitter and the other part is transmitted to illuminate the target. The laser signal pulse returns to the lidar system through the atmospheric attenuation and the target reflection. A 532nm narrow-band filter, whose band width is 8nm and peak transmittance is 70% in the 532nm working wavelength, is used to decrease the background noise. The echo signal is received by the 3 × 3 fiber array and each channel is detected by Gm-APD (LASER COMPONENTS COUNT-50C; the photon detection efficiency at 532nm is above 60%; the dead time of Gm-APD is 50ns). Timing circuit as Fig. 2(b) is employed in the experimental system. With scanning, the experiment for demonstrating UTM is carried out and the experimental results are shown in Fig. 7. In our experiment, a daylight lamp is used to simulate the solar background noise and illuminate the target with intensity control. The noise photoelectron rate is set as $N_{n} = 0.01 n s^{- 1}$ per pixel, which is the noise intensity (that includes the solar background noise and also includes the dark count noise and so on) in the sunny day approximately. The echo signal photoelectron is controlled as $N_{s} = 5$ per pixel through regulating the power of each transmitting pulse-laser signal. The imaged target is shown in Fig. 7(a), in which the dash box is the detection area. The experimental results are shown in Figs. 7(b)-7(f).

Fig. 6 The experimental system diagram. BS: Beam Splitter, Timing module is shown as Fig. 2(b).

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Fig. 7 The imaging results. (a) The imaged target. (b) Without threshold. (c) Threshold $Y = 6$ . (d) Threshold $Y = 7$ . (e) Threshold $Y = 8$ . (f) The detail of Fig. 7(d)

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The imaging result without UTM processing is shown in Fig. 7(b), and it is not a clear and ideal 3D target image due to false alarms generated by noise. Under the same conditions, the UTM is employed to take a clear 3D target image with the threshold $Y = 6$ , $Y = 7$ and $Y = 8$ corresponding to Figs. 7(c)-7(e) respectively. From Fig. 5, the proper threshold is $Y_{p r o p e r} = 7$ under this experimental circumstance of $N_{s} = 5$ and $N_{n} = 0.01 n s^{- 1}$ per pixel. The imaging result of $Y_{p r o p e r} = 7$ shows that false alarms generated by noise are filtered out clearly and take a clear 3D image of the target successfully.

The imaging results that are deviated from the proper threshold $Y_{p r o p e r} = 7$ are shown in Figs. 7(c) and 7(e) with $Y = 6$ and $Y = 8$ respectively. When $Y = 6$ below the proper threshold, some false alarms generated by noise are not filtered out; when $Y = 8$ above the proper threshold, false alarms are filtered out totally, however some photon counting points of signal will be filtered out by mistake.

A detailed enlargement of the detection result is shown in Fig. 7(f), two surfaces can be distinguished clearly. We calculated the statistics of two target surfaces (the close target and the far target), whose results are shown in Figs. 8(a) and 8(b). The mean round-trip time of the close target is 367.3ns, and its standard deviation is 3.0ns; the mean round-trip time of the far target is 376.0ns, and its standard deviation is 2.2ns. According to the standard deviation, the range resolution is estimated as 0.45m.

Fig. 8 The range resolution analysis. (a) The ranging results of the close target that is the target A in Fig. 6(a). (b) The ranging results of the far target that is the target B in Fig. 6(a).

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The laser pulse width that is employed in this experiment is 8ns. Due to the high sensitivity of Gm-APD, it is almost all triggered by the photon of the leading edge of the echo laser-pulse signal, and therefore the experimental accuracy can be higher than the pulse width of the transmitting signal. If a narrower pulse laser signal is employed, the range resolution and the imaging results will be improved.

5. Conclusion

This paper presents a method that can efficiently reduce false alarms of noise and take a clear 3D image of the target of interest in real time. This method divides Gm-APD array into many elementary units and uses a proper threshold to decide if there exists the echo signal or not, which is called as the unit threshold method (UTM). In this paper, the operation flow of UTM is elaborated, and then the selection of the proper threshold is discussed for different application circumstances. For demonstrating UTM, we take 9 pixels as an elementary unit and build an experimental system. With $N_{n} = 0.01 n s^{- 1}$ (the background noise intensity with a narrowband filter in the sunny day) and $N_{s} = 5$ per pixel, the experimental results demonstrate that UTM can efficiently filter out false alarms generated by noise due to noise distributed randomly in the time domain and obtain a clear 3D image of the target of interest in real time.

Compared with the typical methods of solving noise problem, such as the multi-pulse accumulation method [8], the dual Gm-APD arrays method [9] and some image post-processing algorithms [10, 11], UTM don’t need to take extra time to accumulate multiple pulses or operate the image post-processing algorithms, and furthermore there are no losses in the detection probability for UTM without dividing a returned laser pulse. UTM can take a clear real-time 3D image efficiently despite noise and establish a foundation for Gm-APD photon counting technology application in the daylight.

Acknowledgments

This work was supported by “the Fundamental Research Funds for the Central Universities” (Grant No.HIT.KLOF.2010048).

References and links

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A real-time noise filtering strategy for photon counting 3D imaging lidar

Abstract

1. Introduction

2. The working principle

3. The theoretical analysis

4. The experimental results and analysis

5. Conclusion

Acknowledgments

References and links

Cited By

Figures (8)

Equations (5)

Optics Express