Differential time domain method improves ... - OSA Publishing

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Research Article

Vol. 55, No. 2 / January 10 2016 / Applied Optics

Differential time domain method improves performance of pulsed laser ranging and three-dimensional imaging JIE CAO,1,2 QUN HAO,1,* YANG CHENG,1 YUXIN PENG,2 KAIYU ZHANG,1 JIAXING MU,1

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PENG WANG1

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Key Laboratory of Biomimetic Robots and Systems, Ministry of Education, School of Optoelectronics, Beijing Institute of Technology, Beijing 100081, China 2 Department of Biomedical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117575, Singapore *Corresponding author: [email protected] Received 27 August 2015; revised 12 November 2015; accepted 1 December 2015; posted 2 December 2015 (Doc. ID 248622); published 8 January 2016

A ranging method based on the differential time domain method (DTDM) is proposed in order to improve ranging accuracy and the range of active measurement based on peak discriminator (PD). We develop mathematical models and deduce that zero-crossing sensitivity is an important factor, which affects the ranging error of DTDM. Additionally, zero-crossing sensitivity is determined by delayed time. We carried out relative experiments and obtained the smallest ranging error when delayed time is receiving pulse width. We also compare ranging, three-dimensional (3D) point clouds and depth images based on two methods under same testing conditions. The results show that DTDM is beneficial in improving performance of pulse laser ranging and 3D imaging. © 2016 Optical Society of America OCIS codes: (280.3400) Laser range finder; (150.6910) Three-dimensional sensing; (250.1345) Avalanche photodiodes (APDs); (040.1880) Detection. http://dx.doi.org/10.1364/AO.55.000360

1. INTRODUCTION Pulsed laser three-dimensional (3D) sensors have the advantages of simplicity of principle, high resolution, and long distance detection based on the active techniques of laser ranging [1,2]. Therefore, 3D sensors are widely used in many applications including robotics, terrain visualization, and vehicle navigation [3–5]. These 3D sensors emit the infrared narrow pulse to target and measure the time-of-flight (TOF) between start and stop signals at every pixel, in order to obtain the range data [6]. Ranging accuracy and dynamic range of measurement are the important performances of 3D sensors. However, low reflected light leads to the low signal to noise ratio (SNR) in measurement, which results in a low ranging accuracy. Concurrently, too much reflected light results in signal saturation, which limits the dynamic range of measurement [7]. Meanwhile, the key of acquiring accurate TOF is discriminating the exact arrival time of the echo pulse. Some methods have been used in acquiring TOF. For example, the leading edge discriminator (LED) is a simple approach, and the leading edge of the received pulse is detected as the signal crosses a certain threshold. LED is simple to carry out due to its simple electrical structure, but it produces a large walk error of a few nanoseconds [8]. Kong et al. proposed a method using two 1559-128X/16/020360-08$15/0$15.00 © 2016 Optical Society of America

Geiger-mode avalanche photodiodes (GmAPD) to obtain the acquisition of TOF, and the false alarm is decreased, and detection probability was increased because the noise was filtered out [9]. Lim et al. used four types of amplitude parameters, including slew rates, peak values, signal widths, as well as charge amounts [10], in order to correct the time error in the leading edge discriminator, respectively. The constant fraction discriminator (CFD) is used to enhance timing accuracy, and the walk error is less than 1 ps [11,12]. The peak discriminator (PD) is a typical approach to decrease walk error, but the disadvantage of this method is that the echo is easily affected by both background noise and broadening echo pulse. These result in poor performance in the condition of low SNR [13]. Our group has presented a laser ranging finder based on differential opticalpath method (DOPM) to suppress common-mode noise and improve SNR of systems [14], although the issues of a large volume of systems and difficulty with assembly and calibration limit the practical use. Based on the above summary, we present a differential time domain method (DTDM) based on circuital components instead of the optical method, in order to improve the performances of laser ranging and practicability of the system. The system uses common electrical components and is easily

Research Article implemented. We developed a ranging prototype and 3D system, and carried out many experiments to illustrate the advantages of DTDM. The remaining sections of the paper are organized as follows. First, the principle and mathematical models of DTDM are introduced in Section 2. Based on principle, in Section 3 we develop a ranging prototype and carry out ranging and 3D imaging experiments. Finally, conclusions are drawn in the last section. 2. METHODS The principle of DTDM is shown in Fig. 1, where a short pulse is triggered by the field programmable gate array (FPGA), and the moment of triggering signal is set as the start point. The pulse is collimated by transmitting lens (TL) and is used to illuminate the target. The scattered or reflected echo pulse (analog signal) is focused on the avalanche photo diode (APD) through the receiving lens (RL). The current is converted to voltage and then transformed into an echo signal P r1 (analog signal). Similarly, the delayed echo signal P r2 is obtained through the time delayer. The differential echo signal P rd P r1 − P r2 is obtained by an electrical comparator. A signal sampling module (SSM) is used to sample the differential echo signal P rd . The differential echo signal (P rd ) through the comparator is the analog signal. After the differential echo signal goes into the SSM (signal sampling module, i.e., A/D convertor), the analog differential echo signal converts into a digital signal. PD discriminates the peak point; however, the differential echo signal has a point of zero power, i.e., zero-crossing point, and it is set as the stop signal. TOF is determined between the start and stop signal, and it is obtained by the FPGA. The ranging data are sent to the computer. To illustrate the advantages of DTDM clearly, we used analog signals which are reconstructed from digital samples in the following experiments. Laser pulse is a temporal function of the Gaussian model, which is written as Ref. [15]. Based on Fig. 1, we analyze the echo signal as following. 2 Et −t ; (1) P t t pffiffiffiffiffi exp 2τ2 τ 2π where E t is the original pulse energy, and τ is transmitting pulse width. Compared with DOPM, DTDM does not decrease

Fig. 1. Schematic of a system based on DTDM: FPGA, field programmable gate array; TL, transmitting lens; RL, receiving lens; APD, Avalanche photo diode; TD, time delayer; and SSM, signal sampling module.


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echo power by half due to the nonuse of the beam splitter. Therefore, the theoretical formula of differential echo power is written as [14] 8 P rd t P r1 t − P r2 t > > 8 h > i 9 > > 1 2Rd 2 > > < = > t − −> − exp p ffiffi > c 2τ2r > 2E tp T ffiffi2a T o ηD ρr > · i h < π τr > exp − 1 t − 2R−d 2 ; > : ; 2 c 2τ2r > > > 2 2 z > > > τ2 τ2 tan θw > c2 > r h i > > : wz w 1 λz2 2 0 πw 0

where P rd t is received differential echo power on APD, T a is a one way atmospheric transmission, T o is the receiver optics transmission efficiency, ηD is the quantum efficiency, and R is the range between the system and the target, which has a tilt angle of θ · ρr is the reflectance of the target, τr is the received pulse width, c is the light speed, w0 is the waist radius of the laser, wz is the beam radius, and λ is the wavelength. Equation (2) shows that DTDM exists at the zero-crossing point due to the subtracting between two Gaussian echo signals, and the zero-crossing point is used to determine stop moment. Zero-crossing sensitivity is defined as the temporal change rate of echo power at the zero cross. Meanwhile, our group study shows the system obtains highest sensitivity when differential distance meets equations as follows [14]. d opt c · τr ;

(3)

where d opt is optimal differential distance. Therefore, we obtain that the optimal delayed time is the receiving pulse width (τr d opt ∕c) according to the relationship between range and time. 3. EXPERIMENTS AND RESULTS In order to test the properties of DTDM, we carried out experiments including ranging experiments and 3D imaging experiments. Experiments are designed from six aspects: (1) In order to compare the difference between PD and DTDM, we capture the echo pulse including single pulse based on PD and differential echo pulse based on DTDM; (2) Based on (1), we compare the echo pulse signals at different ranges; (3) We then studied the relationship between ranging error and zerocrossing sensitivity. Meanwhile, in order to obtain lowest ranging error at optimal zero-crossing sensitivity, we study the relationship between delayed time and zero-crossing sensitivity; (4) Ranging tests between PD and DTDM were carried out under different conditions to illustrate that DTDM can suppress effects from common-mode noise; (5) In order to illustrate that DTDM is beneficial in terms of improving the range of active measurement, we carried out comparative ranging experiments between PD and DTDM; and (6) We compare 3D point clouds (raw data) and depth images between PD and DTDM. A. Experimental Setup

Based on DTDM, we developed a prototype of the laser raging finder. In order to compare 3D image based on PD and DTDM, the scanning system is constructed by the use of

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the electrical-motor platform with four degree of freedom, shown in Fig. 2. The parameters of experimental setup are shown in Table 1. B. Comparative Echo Pulse between PD and DTDM 3

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50 W 1 kHz 905 nm 10 ns, full width at half-maximum 50 mm focal length, 20 mm diameter aperture, no antireflection coating Active area is 500 μm, Responsivity is 85 A∕W (at 905 nm), quantum efficiency >85% (at 905 nm) Minimum range is 2 m, and maximum range is 200 m. Square board, tank model Four degree of freedom, including x, y and z movement, and z-axis rotation. The resolution of platform less than 5 μm. Serial communication with computer, and controlled by platform controller.

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C. Echo Signals with respect to Range

According to Eq. (3), in order to obtain optimal range accuracy, the delay time can be obtained by adjusting the time delayer. Therefore, we study the differential echo signals with respect to the range, shown in Fig. 4. There are three groups of pulse

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Based on the experimental setup, under the condition of noise power 50 mW, we present the comparative results on echo pulse profiles between PD and DTDM at 100 m, shown in Fig. 3. From Fig. 3, we can see the peak area of echo signals is affected seriously by noise, and such an affection leads to difficulty in extracting peak point accurately. Different from PM, DTDM transforms PD into a zero-crossing point. The area of zero-crossing point is smoother than the peak area of PM. Therefore, DTDM is a benefit to obtain higher range accuracy than PD.

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D. Comparison of Laser Ranging Error under Common-Mode Noise

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In order to illustrate the effects of common-mode noise on ranging results, we introduce common-mode noise by the use of lasers of continuous wave (CW) in ranging tests. The power of the CW is 80 mW, and the wavelength is 532 nm. Meanwhile, the transmitting power is 60% of the laser source by the use of an attenuator. Based on the ranging experimental setup in Section 3.A., we carried out the ranging test 1000 times at 200 m. Figure 5 shows the results based on PD under the conditions of without common-mode noise and with common-mode noise. Under the conditions without CW, we find that the ranging results are not larger than 199.8 m and less than 200.2 m, which is shown in Fig. 5(a). Statically, the root-mean-square (RMS) of the ranging error is 82 mm. However, we can see the divergence of the ranging error is larger than in Fig. 5(a), and RMS is 145 mm, shown in Fig. 5(b). The results illustrate that the ranging error is decreased by common-mode noise. In order to illustrate the advantage of DTDM which suppresses common-mode noise, we carried out the comparative experiments between DTDM and PD. Based on DTDM, we carried out the ranging tests at 200 m under the same conditions of PD. The results are shown in Fig. 6, where the convergence of ranging results based on DTDM are better than PD. Statically, the RMS of the ranging error based on DTDM decreases from 145 to 98 mm. Therefore, DTDM can suppress the common-mode noise and improve ranging accuracy. According to the above analysis, the common-mode noise results in an increase of ranging error. Additionally, the ranging

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error increases with the decreasing of transmitting power because low transmitting power leads into low SNR. In order to illustrate that the DTDM is beneficial of obtaining ranging error under transmitting power lower than PD, we compare the ranging error between the two methods under different transmitting power. We use an attenuator to change transmitting power and record the RMS of the ranging error of the two methods. The results are shown in Fig. 7, and we do not plot ranging error below 20% of the original power because no echo signals are detected at that low frequency. From the trend of the two curves, we find that the RMSs of the ranging error based on two methods increase with the decreasing of transmitting power as shown in Fig. 7. We find that the RMSs of the ranging error based on two methods increase with the decreasing of transmitting power. However, the RMS of the ranging error based on DTDM is lower than the PD from beginning to end, and the descending rate of RMS of DTDM is slower than PD. For example, when the transmitting power is 90% of the laser source, the RMS of PD and DTDM are 82 and 55 mm, respectively. When the transmitting power is 30% of the laser source, the RMSs of PD and DTDM increase to 208 and 124 mm, respectively. The amount of increasing ranging error based on PD is 1.8208–82∕124–55 1.8 times as low as the DTDM. The results illustrate that DTDM is beneficial for obtaining lower ranging error under the low transmitting power than PD.

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profiles at different ranges (50, 100, and 200 m). We analyzed them from two aspects. First, with the increases of range, the fluctuations of single pulse profile are more serious than differential echo pulse. The area of the zero-crossing point is smother than the peak area, which agrees with the above analysis. Second, delay time is always equal to pulse width, regardless of the broadening pulse. From Fig. 4, with the increases of range, the width of the echo pulse is broadened from 10 to 16 ns. Although the echo pulse is broadened, the delayed time is always equal to the pulse width to obtain the optimum range accuracy. Therefore, the delay time can be adjusted according to variation of the pulse width, which is a benefit to obtain the optimum range accuracy.

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Second, we found that the ranging error increases dramatically when the delayed time is twice as large as the receiving pulse width. An example is the ranging tests at 100 m, depicted in Fig. 9. Given the consideration of receiving the echo pulse width is broadened, the zero-crossing sensitivity decreases dramatically when delayed time is larger than 25 ns, and the ranging error increases dramatically above this delayed time, shown in Fig. 8. The results are in accordance with the simulations presented in Ref. [14]. It is worth noting that such situations should be avoided for practical use due to the large ranging error. F. Laser Ranging of Active Range of Measurement Fig. 8. Relationship between delayed time and ranging error.

E. Experiments on Relationships among Ranging Error, Zero-Crossing Sensitivity and Delayed Time

In order to illustrate delayed time affects ranging error, we carry out experiments between the relationship of the delayed time and the RMS of ranging error, shown in Fig. 8. In order to validate optimal delayed time obtains the lowest ranging error, we carry out the ranging experiments based on the relationship between delayed time and zero-crossing sensitivity, shown in Fig. 9. The testing ranges between the square board and the system are 50, 100, and 200 m, respectively. We recorded 1000 times, at different ranges to calculate the RMSs of ranging error as changing delayed time. Figs. 8 and 9 illustrate the analysis results from the two aspects. First, we found that the RMS of ranging error decreases with increasing delayed time. Then, the ranging error increases with the increases of delayed time, and the optimal delayed time is equal to the receiving pulse width. For example, in ranging experiments at 200 m, the RMS of the ranging error decreases from 146.8 mm (at 1 ns delayed time) to 98 mm (at 16 ns delayed time). Then, it increases from 98 to 245 mm (at 31 ns delayed time). Meanwhile, we found that the zero-crossing sensitivity increases with the increase of delayed time, where sensitivity reaches its highest value at 16 ns, shown in Fig. 9. The results illustrate that DTDM achieves the lowest ranging error when delayed time is equal to the receiving pulse width.

As discussed above, DTDM transforms the peak position detection into a zero-crossing point detection, which improves the active range of measurement at short ranging. In order to illustrate that point, we carried out the comparative experiments at a short range. In the ranging experiment, the target was displaced at 2 m and without CW. The peak power of the pulsed laser was 50 W without an attenuator. Obviously, the echo signal is saturated because echo power is too strong, as shown in Fig. 10. We can see the area near the peak is flat. Therefore, the position of the stop moment is difficult to determine, resulting in a large ranging error. However, DTDM transforms peak into zero-crossing point, and decreases the uncertainty of PD, shown in the dark triangular line in Fig. 10. We found that the position zero-crossing point is determined to be more accurate than its peak point. Moreover, we compare the linear range of measurement for DTDM and PD, because linear range reflects the active range of measurement. In comparative experiments, the peak power of pulsed laser is also 50 W and does not use an attenuator. We record the ranging results as the distance between the target and system decreases from 80 to 2 m. The ranging results are shown in Fig. 11. During the saturation at short range (less than 10 m), we find that the relationship between range and TOF is nonlinear when the testing range is less than 5 m, which is shown in the amplification of Fig. 11. However, based on DTDM, the relationship between range and TOF is in accordance with a linear relation under the condition of 2 m ranging. According to the analysis of Fig. 10, PD cannot 3

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determine peak moment accurately because of flatness of the peak area. On the contrary, DTDM obtains zero-crossing point accurately by the use of a differential echo signal. The results show that DTDM improves the active range of measurement. G. Comparisons of 3D Imaging

Based on the experimental setup, we compare 3D image based on PD and DTDM. Two targets of white board (simple geometrical target) and a tank model (complicated geometrical target), shown in Figs. 12(a) and 12(b), were displaced at 30 m from the system. The white board is sampled with 100 × 100 pixels, and the tank model is sampled with 200 × 200 pixels. The point clouds (raw data) of two targets

Fig. 13. Range images of tank model based on PD and DTDM: (a) and (b) are side view images based on PD and DTDM, (c) and (d) are top view images based on PD and DTDM.

based on PD and DTDM are shown in Figs. 12(c)–12(f ). Compared with Figs. 12(c) and 12(e), the fluctuations of the point clouds based on PD are obviously larger than that of DTDM. The height of white board is 25 cm. Statically, the maximum point clouds based on PD is 29 cm, and ranging error is 40 mm. However, the maximum of point clouds based on DTDM is 27 cm, and ranging error is 20 mm. Moreover, we estimate the vibrations of ranging error based on point clouds. An example is the average of ranging error of PD is 28 mm, and DTDM is 13 mm. In the point clouds of a complicated geometrical target, shown in Figs. 12(d) and 12(f ), we find that DTDM is more convergent than PD. For example, compared with the area of dark circles between Figs. 12(d) and 12(f ), the 3D point clouds based on PD is more divergent than DTDM, which illustrates that ranging error based on DTDM is smaller than PD. Based on point clouds of the tank model, we compare the depth images of side view and top view based on PD and DTDM, respectively. The depth images are described by the use of pseudo color, shown in Fig. 13. Compared with Fig. 13(a), i.e., imaging based on PD, the depth image based on DTDM is much clearer and higher resolution, shown in Fig. 13(b). Furthermore, in Fig. 13(c) we can hardly distinguish the turret and the tank body in the top view image. However, we can distinguish turret and tank body clearly based on DTDM. The imaging results show that DTDM is beneficial for improving imaging quality. 4. DISCUSSION

Fig. 12. Comparisons of 3D point clouds based on PD and DTDM: (a) and (b) are simple and complicated targets, respectively, (c) and (d) are based on PD, (e) and (f) are based on DTDM.

Based on the experimental results, we find that DTDM is skilled in suppressing the effects from common-mode noise. To study features of DTDM, we discuss two important aspects. First, because range accuracy is affected by noise, we discuss the differential echo pulse affected by noise. Second, we discusse range resolution with respect to range.

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Fig. 14. Echo pulse profiles of PD and DTDM under different noise level; the noise power of (a)–(d) are 10, 30, 50, and 80 mW, respectively.

A. Echo Signals with respect to Noise

Based on experimental setup, we carried out the comparative experiments on echo pulse profiles of PD (single pulse profile) and DTDM (differential pulse profile) with respect to noise, shown in Fig. 14. We find that the fluctuations of single echo profiles are significant with the increases of noise level. Compared with Figs. 14(a) and 14(d), the fluctuations in pulse profile of (d) are obviously larger than (a). The positive maximum voltage of echo signal in (d) is 2.5 V, and the minus maximum voltage of echo signal in (d) is 2.2 V. Such fluctuations of pulse profiles result in low accuracy of PD. On the other hand, we found that DTDM suppresses such effects on the zerocrossing area and obtains high range accuracy. Even in high noise level [e.g., Fig. 14(d)], the zero-crossing point is extracted accurately. That is the basic reason why differential pulse profile is better than single pulse profile.

The results on range resolution with respect to range are shown in Fig. 15, in which the range resolution of DTDM is better than PD. For example, under the condition of 30 m, the range resolution of PD is 49 mm, and the range resolution of DTDM decreases to 29 mm. Therefore, the performance of the 3D image of the tank model based on DTDM is better than PD, shown in Fig. 13. Meanwhile, from the comparative profiles of single pulse and differential pulse, shown in Fig. 15, in which we find the area of the zero-crossing point is smoother than the peak area. The fluctuation in peak area of single pulse increases with the increases of target range, shown in the profiles at 30 and 200 m. However, the fluctuations in the zero-crossing area of DTDM are always smaller than the peak area, which illustrates that DTDM is beneficial to obtain higher range resolution. 5. CONCLUSIONS In order to conquer drawbacks of large ranging error resulting in common-mode noise, and to improve the active range of measurement based on PD, and to avoid complexity of DOPM, we proposed a ranging method based on DTDM. Based on the principle, we developed a laser ranging finder and carried out many experiments to verify the theory, including ranging and imaging experiments. We obtained important conclusions based on experimental results. First, DTDM suppresses the effects from common-mode noise, and the RMS of ranging error based on the DTDM is decreased from 145 to 98 mm under the same conditions of common-mode noise. Second, the DTDM transforms the peak discriminator into zero-crossing discriminator, and it improves the range of active measurement when compared with PD. Third, the system obtains the lowest ranging error when the system achieves highest zero-crossing sensitivity based on the experiments on relationship between ranging error and zerocrossing sensitivity. Meanwhile, the system obtains highest zero-crossing sensitivity when delayed time is receiving pulse width, i.e., the system obtains lowest ranging error when delayed time is receiving pulse width. Fourth, DTDM is beneficial for capturing clearer depth image when compared with depth images based on PD.

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Funding. National Natural Science Foundation of China (NSFC) (51327005, 61275003, 91420203).

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