Differential optical-path approach to improve signal-to-noise ratio of pulsed-laser range finding Qun Hao,* Jie Cao, Yao Hu, Yunyi Yang, Kun Li, and Tengfei Li School of Optoelectronics, Beijing Institute of Technology, Beijing, 100081, China * [email protected]
Abstract: A pulsed-laser range finding based on differential optical-path is proposed, and the mathematical models are developed and verified. Based on the method, some simulations are carried out and important conclusions are deduced. (1) Background power is suppressed effectively. (2) Compared with signal-to-noise ratio (SNR) of traditional method, SNR of the proposed method is more suitable than traditional method in long-range finding and large tilt angle of target. (3) No matter what the tilt angle of target is, it always has optimal sensitivity of zero cross as long as the differential distance is equal to the light speed multiplied by the received pulse length and there is an overlap between two echoes. ©2014 Optical Society of America OCIS codes: (280.3400) Laser range finder; (150.5670) Range finding; (140.3538) Lasers, pulsed; (040.1345) Avalanche photodiodes (APDs).
References and links 1. 2. 3. 4. 5. 6. 7.
8.
9. 10.
11. 12. 13. 14. 15. 16. 17.
R. D. Richmond and S. C. Cain, in Direct-detection LADAR Systems (SPIE, 2010). G. Berkovic and E. Shafir, “Optical methods for distance and displacement measurements,” Adv. Opt. Photonics 4(4), 441–471 (2012). B. Schwarz, “Mapping the world in 3D,” Nat. Photonics 4(7), 429–430 (2010). P. F. McManamon, “Errata: Review of ladar: a historic, yet emerging, sensor technology with rich phenomenology,” Opt. Eng. 51(6), 060901 (2012). M. Fridlund, “Future space missions to search for terrestrial planets,” Space Sci. Rev. 135(1-4), 355–369 (2008). B. Kaldvee, A. Ehn, J. Bood, and M. Aldén, “Development of a picosecond lidar system for large-scale combustion diagnostics,” Appl. Opt. 48(4), B65–B72 (2009). J. Yun, C. Gao, S. Zhu, C. Sun, H. He, L. Feng, L. Dong, and L. Niu, “High-peak-power, single-mode, nanosecond pulsed, all-fiber laser for high resolution 3D imaging LIDAR system,” Chin. Opt. Lett. 10(12), 121402 (2012). A. McCarthy, R. J. Collins, N. J. Krichel, V. Fernández, A. M. Wallace, and G. S. Buller, “Long-range time-offlight scanning sensor based on high-speed time-correlated single-photon counting,” Appl. Opt. 48(32), 6241– 6251 (2009). S. Pellegrini, G. S. Buller, J. M. Smith, A. M. Wallace, and S. Cova, “Laser-based distance measurement using picosecond resolution time-correlated single-photon counting,” Meas. Sci. Technol. 11(6), 712–716 (2000). S. Kurtti and J. Kostamovaara, “An integrated receiver channel for a laser scanner,” in Proceedings of IEEE Conference on Instrumentation and Measurement Technology (Congress Graz, Graz, Austria, 2012), pp. 1358– 1361. H. Lim, “Comparison of time corrections using charge amounts, peak values, slew rates, and signal widths in leading-edge discriminators,” Rev. Sci. Instrum. 74, 3115–3119 (2003). M. Lee and S. Baeg, “Advanced compact 3D lidar using a high speed fiber coupled pulsed laser diode and a high accuracy timing discrimination readout circuit,” Proc. SPIE 8379, 83790Z (2012). S. Mitchell, J. P. Thayer, and M. Hayman, “Polarization lidar for shallow water depth measurement,” Appl. Opt. 49(36), 6995–7000 (2010). T. R. Chevalier and O. K. Steinvall, “Laser radar modeling for simulation and performance evaluation,” Proc. SPIE 7482, 748206 (2009). H. J. Kong, T. H. Kim, S. E. Jo, and M. S. Oh, “Smart three-dimensional imaging LADAR using two Geigermode avalanche photodiodes,” Opt. Express 19(20), 19323–19329 (2011). Y. Qin, T. T. Vu, Y. Ban, and Z. Niu, “Range determination for generating point clouds from airborne small footprint LiDAR waveforms,” Opt. Express 20(23), 25935–25947 (2012). F. Wang, Y. Zhao, Y. Zhang, and X. Sun, “Range accuracy limitation of pulse ranging systems based on Geiger mode single-photon detectors,” Appl. Opt. 49(29), 5561–5566 (2010).
#201148 - $15.00 USD (C) 2014 OSA
Received 11 Nov 2013; revised 13 Dec 2013; accepted 16 Dec 2013; published 3 Jan 2014 13 January 2014 | Vol. 22, No. 1 | DOI:10.1364/OE.22.000563 | OPTICS EXPRESS 563
18. R. Agishev, B. Gross, F. Moshary, A. Gilerson, and S. Ahmed, “Simple approach to predict APD/PMT lidar detector performance under sky background using dimensionless parametrization,” Opt. Lasers Eng. 44(8), 779– 796 (2006). 19. Z. Zhang, Y. Zhao, Y. Zhang, L. Wu, and J. Su, “A real-time noise filtering strategy for photon counting 3D imaging lidar,” Opt. Express 21(8), 9247–9254 (2013). 20. J. Yang, L. Qiu, W. Zhao, and H. Wu, “Laser differential reflection-confocal focal-length measurement,” Opt. Express 20(23), 26027–26036 (2012). 21. S. Der, B. Redman, and R. Chellappa, “Simulation of error in optical radar range measurements,” Appl. Opt. 36(27), 6869–6874 (1997). 22. S. E. Johnson, “Effect of target surface orientation on the range precision of laser detection and ranging systems,” J. Appl. Remote Sens. 3(1), 033564 (2009). 23. T. Ishii, K. Otani, T. Takashima, and Y. Xue, “Solar spectral influence on the performance of photovoltaic (PV) modules under fine weather and cloudy weather conditions,” Prog. Photovolt. Res. Appl. 21, 481–489 (2011). 24. M. Jack, J. Wehner, J. Edwards, G. Chapman, D. N. Hall, and S. M. Jacobson, “HgCdTe APD-based linearmode photon counting components and Ladar receivers,” Proc. SPIE 8033, 80330M (2011).
1. Introduction Pulsed-laser range finding is an active remote sensing technique. The target is illuminated by short pulse emitted from a pulsed-laser source, and the distance is obtained by calculating time of flight (TOF) of echo from target. Supposing the light speed is c, and the round-trip time is t, the distance can be obtained with R = ct/2 [1, 2]. Since this method has advantages of simplicity, high accuracy and utility, it is widely used in the fields of both military and civilian [3–5]. Laser source with short pulse duration of nanosecond, picosecond or even femtosecond increase the range finding accuracy greatly [6–9]. The key of acquiring TOF is discriminating the exact arrival time of the echo pulse. Some methods have been used in acquiring TOF. 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 easy to carry out because of its simple electrical structure, but it produces large walk error of a few of nanosecond [10]. Hansang Lim et al used four kinds of amplitude parameters, including slew rates, peak values, signal widths, as well as charge amounts [11], to correct time error in the leading edge discriminator respectively. Constant fraction discriminator (CFD) is used to enhance timing accuracy, and it reduces the walk error to less than picosecond [12, 13]. Peak discriminator is an approach to decrease walk error, but the disadvantage of this method is that echo is easily affected by both background power and targets tilt angle, which results into poor performance in the condition of low SNR [14]. Recently, Hong Jin Kong et al proposed a method using two Geiger-mode avalanche photodiodes (GmAPD) to realize acquisition of TOF. The echo was divided into two beams by splitter and arrival time of the electrical signals from the GmAPDs were compared. Though intensity of echo is decreased by half, the false alarm was decreased and detection probability was increased because the noise was filtered out [15]. Actually, the sources of noise of range finding include speckle, thermal and background, etc. Among of them, background power is prime noise for long rang detecting and exists in most of optical system [16–18]. Meanwhile, it is constant and does not change with time. Other noises distribute randomly [19]. In general, the method of differential optical-path has the ability to suppress background power. The method uses two receiving channels, of which one is reference channel, and the other is signal channel. Background power is suppressed by subtracting them. For example, the structure of differential optical-path suppresses commonmode noise and improves measurement accuracy of the confocal microscopy [20]. In order to suppress background power and increase SNR of pulsed-laser range finding, a method based on differential optical-path is proposed. The principle and theoretical analysis are illustrated in Section 2. Simulations based on the method are carried out in section 3. Conclusions are listed in the last section, which suggest the proposed pulsed-laser range finding can suppress background power and gain high SNR at long range.
#201148 - $15.00 USD (C) 2014 OSA
Received 11 Nov 2013; revised 13 Dec 2013; accepted 16 Dec 2013; published 3 Jan 2014 13 January 2014 | Vol. 22, No. 1 | DOI:10.1364/OE.22.000563 | OPTICS EXPRESS 564
2. Methods and materials 2.1 Principle The system based on differential optical-path is shown as Fig. 1. A short pulse is triggered by field programmable gate array (FPGA) and collimated by TL. Then, the pulse is divided into two parts by beam splitter BS1. One is focused by CL and detected by PD, which generates the electrical start signal. The other is used to illuminate the target. The scattered or reflected light from the target is reflected by BS1 and divided into two beams by BS2. There are two same receivers consisting of an APD and the corresponding lens RL, respectively. APD A is illuminated by reflected light from BS2 and RL1, and generates echo signal Pr2. Similarly, APD B generates echo signal Pr1. The differential echo signal Pr2-Pr1 is obtained by subtraction in FPGA. The differential echo signal has a point of zero power, i.e. zero cross, and it is set as the stop signal. TOF is determined between the start and stop signal. The temporal change rate of the power at the zero cross in the differential echo signal is defined as the sensitivity of zero cross. It can be changed by adjusting differential distance between optical-path OA and OB. FPGA controls the stage using SC to change differential distance until the system acquire highest sensitivity of zero cross. Supposing the distance between BS1 and CL is l0, the distance between BS1 and BS2 is l1, the distance between BS2 and RLA is l2, the distance between BS2 and RLB is l3, differential distance between OA and OB is 2d. The positions of two receivers can be described as
l1 l2 l0 d . l1 l3 l0 d
(1) PD
CL
Air
Trigger
TL
Laser
BS1
Position B
FPGA
B
APD B
Target
O BS2
+
RL B
Pr1 Pr2
A RL A
SC1 Position A APD A SC2
Fig. 1. Pulsed-laser range finding system structure based on differential optical path. BS-beam splitter, TL-transmitting lens, RL-receiving lens, PD-photo detector, APD-avalanche photo diode, CL-convergent lens, SC- stage controller.
Figure 2 shows the difference of echo signal between proposed method based on differential optical path and peak discriminator. On the left side is the start signal from PD. The peak is easy to detect because of the high intensity and low background power, so it is set as the start timing moment. Traditional system includes only a single APD. In the long-range measurement, peak position of the echo is difficult to discriminate because of the background power and echo broadening. Meanwhile, the temporal change rate of echo power near the peak is very small, i.e. the sensitivity near peak is very low, which increases the difficulty of discriminating peak position. Different from peak discriminator, differential optical-path
#201148 - $15.00 USD (C) 2014 OSA
Received 11 Nov 2013; revised 13 Dec 2013; accepted 16 Dec 2013; published 3 Jan 2014 13 January 2014 | Vol. 22, No. 1 | DOI:10.1364/OE.22.000563 | OPTICS EXPRESS 565
method uses two APDs. Two receivers are moved by a distance of d symmetrically near or far from BS2. Compared with traditional method, although echo power is reduced by half in each detector, the background power can be suppressed by subtracting between two echo signals, Meanwhile, there is a zero cross in the differential echo signal and the sensitivity of zero cross is obviously higher than that of the peak in the original echo signal. t0=2R/c
I
traditional method proposed method
Start
Stop Pr
Pr2 (APD A)
Pr1 (APD B) 0
t Stop Prd=Pr2-Pr1
Fig. 2. Difference between differential echo and echo of peak discriminator.
2.2 Echo analysis Schematic diagram of laser range finding is shown in Fig. 3, left side is an system of transmitter and receiver, and right side is a target plane, which has a tilt angle of θ. R is the range between the system and the target. Laser pulse is with a temporal function of Gaussian model, which is written as [1]
Pt t
t 2 Et exp 2 , 2 2
(2)
where Et is the original pulse energy, τ is transmitting pulse width. Traditional receiver includes a single detector and echo signal power expression is written as [1, 20]
X
Transmitter /Receiver
O
Z R
Y Fig. 3. Schematic diagram of pulsed-laser range finding.
#201148 - $15.00 USD (C) 2014 OSA
Received 11 Nov 2013; revised 13 Dec 2013; accepted 16 Dec 2013; published 3 Jan 2014 13 January 2014 | Vol. 22, No. 1 | DOI:10.1364/OE.22.000563 | OPTICS EXPRESS 566
1 2 R 2 E T 2T Pr t t a o D r exp 2 t c 2 r 2 r tan 2 w2 z 2 2 , r c2 z 2 w z w0 1 2 w0
(3)
where Pr(t) is the received power on the detector, Ta is the one way atmospheric transmission, To is the receiver optics transmission efficiency, ηD is quantum efficiency, ρr is the reflectance of the target, τr is the received pulse width, w0 is the waist radius of the laser, w(z) is the beam radius, and λ is the wavelength. According to Fig. 1, Eqs. (1) and (3), the echo signal power expressions of APD A and APD B are written as
1 2 R d 2 E T 2T Pr1 t t a o D r exp 2 t c 2 2 r 2 r . (4) 1 2 R d 2 Et Ta2ToD r Pr 2 t 2 2 exp 2 t c r 2 r Equation (3) is under the ideal condition with no effects of background power. In fact, the background power should be concerned in the system, especially in the long-range measurement. The background power is written as [1, 21] PB r hsunTo Ar sin / 2 , 2
(5)
where ρr is the reflectance of target, hsun is the background solar irradiance, Ar is the area of the receiver, α is the field of view, and λ is the optical bandwidth. According to Eq. (5), PB is constant and does not change with time. The echo signal power from APD A and APD B with background power are described as following.
1 2 R d 2 E T 2T PrB1 t t a o D r exp 2 t PB c 2 2 r 2 r , 1 2 R d 2 Et Ta2ToD r PrB 2 t 2 2 exp 2 t c PB r 2 r
(6)
The differential echo power is obtained by subtraction and is written as
Prd t PrB 2 t PrB1 t
Et Ta2ToD r 2 2 r
1 2 R d 2 1 2 R d 2 exp 2 t exp 2 t , c c 2 r 2 r
(7)
Equation (7) shows that the background power can be suppressed by using the structure of differential optical-path. Furthermore, at the zero crossing temporal point when Prd = 0, we can obtain Eq. (8), which demonstrates that the TOF of zero cross is the same as peak discriminator.
#201148 - $15.00 USD (C) 2014 OSA
Received 11 Nov 2013; revised 13 Dec 2013; accepted 16 Dec 2013; published 3 Jan 2014 13 January 2014 | Vol. 22, No. 1 | DOI:10.1364/OE.22.000563 | OPTICS EXPRESS 567
2R 2R d 2R d . t t t c c c 2
2
(8)
2.3 Sensitivity of zero cross Sensitivity of zero cross kd = dPrd(t)/dt is defined as the temporal change rate of echo power at zero cross, and it is written as
kd
u22 u1 u12 Et Ta2ToD r u2 exp exp 2 2 2 , 2 2 2 r r 2 r r 2 r
(9)
where kd is sensitivity of zero cross, u1 = t-[(2R-d)/c], u2 = t-[(2R + d)/c] and other symbols are described above. In order to obtain the crossing point of the trailing edge and the leading edge of echo signals, the differential distance should be less than 8log(2) c r [20], i.e. there is an overlap between two echoes. When t = 2R/c, the sensitivity of zero cross is
kd
t 2 R / c
1 d 2 Et Ta2ToD r d exp . 2 r2 c 2 r 2 r c
(10)
Denoting f = kd|t = 2R/c, we can obtain Eq. (11) for the derivative term d from Eq. (10).
1 d 2 d 1 d 2 d 1 Et Ta2ToD r 1 2 exp 2 2 exp 2 . (11) 2 2 r 2 r c r c 2 r c c r c r c The highest sensitivity of zero cross is deduced by f’d = 0, yielding f 'd
(12) d c r . The highest sensitivity of zero cross is acquired when d = cτr, and the differential distance should be changed with τr which results from tilt angle of target [22]. Therefore, stage is used to adjust the position of the receivers to meet Eq. (12) in different conditions. According to analysis above, the method based on differential optical-path has two notable advantages. (1) Background power is suppressed because of the subtraction of two echo signals. (2) The sensitivity of zero cross is much higher than that of the peak. The proposed method transforms discriminating time of peak into detecting zero cross. . 2.4 SNR analysis SNR is one of most important parameters since it affects the measurement range and accuracy. Under the same conditions of transmitting system and target, the range and accuracy of system increase with improvement of SNR. SNR of traditional method is written as [4]
SNR
D2 Pr n
D2 Pr
2
2
2eB D Pr D PB 2eB iDK 4kTB / RTH
D Pr B 2hf
2
Pr PB
2
, (13)
h f 4kT 2e iDK 2 e D RTH 2
2
where ρD is the detector current responsivity, ρD = ηDe/hf, is effective value, i.e. root mean square (RMS) of the echo power at the detector, is RMS of total noise, B is the receiver bandwidth, h is the Planck’s constant, f = c/λ is the frequency of the received signal, e is the electron charge, is RMS of the dark current of detector, k is the Boltzmann’s
#201148 - $15.00 USD (C) 2014 OSA
Received 11 Nov 2013; revised 13 Dec 2013; accepted 16 Dec 2013; published 3 Jan 2014 13 January 2014 | Vol. 22, No. 1 | DOI:10.1364/OE.22.000563 | OPTICS EXPRESS 568
constant, T is the temperature in Kelvin, and is RMS of the effective load resistance that creates the same thermal noise spectral density as the receiver electronics. The background power PB is constant and suppressed by subtracting the two echoes. Therefore, the total noise of system based on differential optical-path can be written as
nd 2eB D Prd 2eB iDK 1 iDK 2 4kTB
1 1 R R TH 2 TH 1
2
2 B e D Prd e iDK 1 iDK 2
1 1 2kT R R TH 2 TH 1
,
(14)
According to the definition of SNR, the method based on differential optical-path can be written as
SNRd
D Prd h2 f 2 2 B hf Prd 2 e D
e iDK 1 iDK 2
2
2kT R1 R1 TH 2 TH 1
. (15)
3. Simulations and results 3.1 System model verification According to echo analysis discussed above, in long-range finding system, echo of traditional method is mainly affected by background power. According to parameters of typical ranging finding and target, simulation parameters are set as following: Et = 0.4nJ, ρr = 0.5, To = 0.8, ηD = 0.6, τ = 2ps, d = 250mm, θ = 10°, 20°, 30°, 40°, d = 50mm, hsun = 500W/m2/μm (λ = 905nm) [23], α = 5°, λ = 10nm, R = 18km, 19km, 20km, 21km. Ta is difficult to determine because of the complex environment conditions. In order to simple the question, the approximate relation among γ(λ), visibility and λ is used in the simulation, shown in Eq. (16), where Rv is visibility, q is correction factor which is depended on different visibility, shown in Table 1. Rv = 10km is chosen in the simulation.
3.91 550 Rv
q
(16)
Table 1. Correction Factor under Different Visibility visibility (Rv)
correction factor (q)
Rv>50km
q = 1.6
Rv = 10km
q = 1.3
Rv
Abstract: A pulsed-laser range finding based on differential optical-path is proposed, and the mathematical models are developed and verified. Based on the method, some simulations are carried out and important conclusions are deduced. (1) Background power is suppressed effectively. (2) Compared with signal-to-noise ratio (SNR) of traditional method, SNR of the proposed method is more suitable than traditional method in long-range finding and large tilt angle of target. (3) No matter what the tilt angle of target is, it always has optimal sensitivity of zero cross as long as the differential distance is equal to the light speed multiplied by the received pulse length and there is an overlap between two echoes. ©2014 Optical Society of America OCIS codes: (280.3400) Laser range finder; (150.5670) Range finding; (140.3538) Lasers, pulsed; (040.1345) Avalanche photodiodes (APDs).
References and links 1. 2. 3. 4. 5. 6. 7.
8.
9. 10.
11. 12. 13. 14. 15. 16. 17.
R. D. Richmond and S. C. Cain, in Direct-detection LADAR Systems (SPIE, 2010). G. Berkovic and E. Shafir, “Optical methods for distance and displacement measurements,” Adv. Opt. Photonics 4(4), 441–471 (2012). B. Schwarz, “Mapping the world in 3D,” Nat. Photonics 4(7), 429–430 (2010). P. F. McManamon, “Errata: Review of ladar: a historic, yet emerging, sensor technology with rich phenomenology,” Opt. Eng. 51(6), 060901 (2012). M. Fridlund, “Future space missions to search for terrestrial planets,” Space Sci. Rev. 135(1-4), 355–369 (2008). B. Kaldvee, A. Ehn, J. Bood, and M. Aldén, “Development of a picosecond lidar system for large-scale combustion diagnostics,” Appl. Opt. 48(4), B65–B72 (2009). J. Yun, C. Gao, S. Zhu, C. Sun, H. He, L. Feng, L. Dong, and L. Niu, “High-peak-power, single-mode, nanosecond pulsed, all-fiber laser for high resolution 3D imaging LIDAR system,” Chin. Opt. Lett. 10(12), 121402 (2012). A. McCarthy, R. J. Collins, N. J. Krichel, V. Fernández, A. M. Wallace, and G. S. Buller, “Long-range time-offlight scanning sensor based on high-speed time-correlated single-photon counting,” Appl. Opt. 48(32), 6241– 6251 (2009). S. Pellegrini, G. S. Buller, J. M. Smith, A. M. Wallace, and S. Cova, “Laser-based distance measurement using picosecond resolution time-correlated single-photon counting,” Meas. Sci. Technol. 11(6), 712–716 (2000). S. Kurtti and J. Kostamovaara, “An integrated receiver channel for a laser scanner,” in Proceedings of IEEE Conference on Instrumentation and Measurement Technology (Congress Graz, Graz, Austria, 2012), pp. 1358– 1361. H. Lim, “Comparison of time corrections using charge amounts, peak values, slew rates, and signal widths in leading-edge discriminators,” Rev. Sci. Instrum. 74, 3115–3119 (2003). M. Lee and S. Baeg, “Advanced compact 3D lidar using a high speed fiber coupled pulsed laser diode and a high accuracy timing discrimination readout circuit,” Proc. SPIE 8379, 83790Z (2012). S. Mitchell, J. P. Thayer, and M. Hayman, “Polarization lidar for shallow water depth measurement,” Appl. Opt. 49(36), 6995–7000 (2010). T. R. Chevalier and O. K. Steinvall, “Laser radar modeling for simulation and performance evaluation,” Proc. SPIE 7482, 748206 (2009). H. J. Kong, T. H. Kim, S. E. Jo, and M. S. Oh, “Smart three-dimensional imaging LADAR using two Geigermode avalanche photodiodes,” Opt. Express 19(20), 19323–19329 (2011). Y. Qin, T. T. Vu, Y. Ban, and Z. Niu, “Range determination for generating point clouds from airborne small footprint LiDAR waveforms,” Opt. Express 20(23), 25935–25947 (2012). F. Wang, Y. Zhao, Y. Zhang, and X. Sun, “Range accuracy limitation of pulse ranging systems based on Geiger mode single-photon detectors,” Appl. Opt. 49(29), 5561–5566 (2010).
#201148 - $15.00 USD (C) 2014 OSA
Received 11 Nov 2013; revised 13 Dec 2013; accepted 16 Dec 2013; published 3 Jan 2014 13 January 2014 | Vol. 22, No. 1 | DOI:10.1364/OE.22.000563 | OPTICS EXPRESS 563
18. R. Agishev, B. Gross, F. Moshary, A. Gilerson, and S. Ahmed, “Simple approach to predict APD/PMT lidar detector performance under sky background using dimensionless parametrization,” Opt. Lasers Eng. 44(8), 779– 796 (2006). 19. Z. Zhang, Y. Zhao, Y. Zhang, L. Wu, and J. Su, “A real-time noise filtering strategy for photon counting 3D imaging lidar,” Opt. Express 21(8), 9247–9254 (2013). 20. J. Yang, L. Qiu, W. Zhao, and H. Wu, “Laser differential reflection-confocal focal-length measurement,” Opt. Express 20(23), 26027–26036 (2012). 21. S. Der, B. Redman, and R. Chellappa, “Simulation of error in optical radar range measurements,” Appl. Opt. 36(27), 6869–6874 (1997). 22. S. E. Johnson, “Effect of target surface orientation on the range precision of laser detection and ranging systems,” J. Appl. Remote Sens. 3(1), 033564 (2009). 23. T. Ishii, K. Otani, T. Takashima, and Y. Xue, “Solar spectral influence on the performance of photovoltaic (PV) modules under fine weather and cloudy weather conditions,” Prog. Photovolt. Res. Appl. 21, 481–489 (2011). 24. M. Jack, J. Wehner, J. Edwards, G. Chapman, D. N. Hall, and S. M. Jacobson, “HgCdTe APD-based linearmode photon counting components and Ladar receivers,” Proc. SPIE 8033, 80330M (2011).
1. Introduction Pulsed-laser range finding is an active remote sensing technique. The target is illuminated by short pulse emitted from a pulsed-laser source, and the distance is obtained by calculating time of flight (TOF) of echo from target. Supposing the light speed is c, and the round-trip time is t, the distance can be obtained with R = ct/2 [1, 2]. Since this method has advantages of simplicity, high accuracy and utility, it is widely used in the fields of both military and civilian [3–5]. Laser source with short pulse duration of nanosecond, picosecond or even femtosecond increase the range finding accuracy greatly [6–9]. The key of acquiring TOF is discriminating the exact arrival time of the echo pulse. Some methods have been used in acquiring TOF. 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 easy to carry out because of its simple electrical structure, but it produces large walk error of a few of nanosecond [10]. Hansang Lim et al used four kinds of amplitude parameters, including slew rates, peak values, signal widths, as well as charge amounts [11], to correct time error in the leading edge discriminator respectively. Constant fraction discriminator (CFD) is used to enhance timing accuracy, and it reduces the walk error to less than picosecond [12, 13]. Peak discriminator is an approach to decrease walk error, but the disadvantage of this method is that echo is easily affected by both background power and targets tilt angle, which results into poor performance in the condition of low SNR [14]. Recently, Hong Jin Kong et al proposed a method using two Geiger-mode avalanche photodiodes (GmAPD) to realize acquisition of TOF. The echo was divided into two beams by splitter and arrival time of the electrical signals from the GmAPDs were compared. Though intensity of echo is decreased by half, the false alarm was decreased and detection probability was increased because the noise was filtered out [15]. Actually, the sources of noise of range finding include speckle, thermal and background, etc. Among of them, background power is prime noise for long rang detecting and exists in most of optical system [16–18]. Meanwhile, it is constant and does not change with time. Other noises distribute randomly [19]. In general, the method of differential optical-path has the ability to suppress background power. The method uses two receiving channels, of which one is reference channel, and the other is signal channel. Background power is suppressed by subtracting them. For example, the structure of differential optical-path suppresses commonmode noise and improves measurement accuracy of the confocal microscopy [20]. In order to suppress background power and increase SNR of pulsed-laser range finding, a method based on differential optical-path is proposed. The principle and theoretical analysis are illustrated in Section 2. Simulations based on the method are carried out in section 3. Conclusions are listed in the last section, which suggest the proposed pulsed-laser range finding can suppress background power and gain high SNR at long range.
#201148 - $15.00 USD (C) 2014 OSA
Received 11 Nov 2013; revised 13 Dec 2013; accepted 16 Dec 2013; published 3 Jan 2014 13 January 2014 | Vol. 22, No. 1 | DOI:10.1364/OE.22.000563 | OPTICS EXPRESS 564
2. Methods and materials 2.1 Principle The system based on differential optical-path is shown as Fig. 1. A short pulse is triggered by field programmable gate array (FPGA) and collimated by TL. Then, the pulse is divided into two parts by beam splitter BS1. One is focused by CL and detected by PD, which generates the electrical start signal. The other is used to illuminate the target. The scattered or reflected light from the target is reflected by BS1 and divided into two beams by BS2. There are two same receivers consisting of an APD and the corresponding lens RL, respectively. APD A is illuminated by reflected light from BS2 and RL1, and generates echo signal Pr2. Similarly, APD B generates echo signal Pr1. The differential echo signal Pr2-Pr1 is obtained by subtraction in FPGA. The differential echo signal has a point of zero power, i.e. zero cross, and it is set as the stop signal. TOF is determined between the start and stop signal. The temporal change rate of the power at the zero cross in the differential echo signal is defined as the sensitivity of zero cross. It can be changed by adjusting differential distance between optical-path OA and OB. FPGA controls the stage using SC to change differential distance until the system acquire highest sensitivity of zero cross. Supposing the distance between BS1 and CL is l0, the distance between BS1 and BS2 is l1, the distance between BS2 and RLA is l2, the distance between BS2 and RLB is l3, differential distance between OA and OB is 2d. The positions of two receivers can be described as
l1 l2 l0 d . l1 l3 l0 d
(1) PD
CL
Air
Trigger
TL
Laser
BS1
Position B
FPGA
B
APD B
Target
O BS2
+
RL B
Pr1 Pr2
A RL A
SC1 Position A APD A SC2
Fig. 1. Pulsed-laser range finding system structure based on differential optical path. BS-beam splitter, TL-transmitting lens, RL-receiving lens, PD-photo detector, APD-avalanche photo diode, CL-convergent lens, SC- stage controller.
Figure 2 shows the difference of echo signal between proposed method based on differential optical path and peak discriminator. On the left side is the start signal from PD. The peak is easy to detect because of the high intensity and low background power, so it is set as the start timing moment. Traditional system includes only a single APD. In the long-range measurement, peak position of the echo is difficult to discriminate because of the background power and echo broadening. Meanwhile, the temporal change rate of echo power near the peak is very small, i.e. the sensitivity near peak is very low, which increases the difficulty of discriminating peak position. Different from peak discriminator, differential optical-path
#201148 - $15.00 USD (C) 2014 OSA
Received 11 Nov 2013; revised 13 Dec 2013; accepted 16 Dec 2013; published 3 Jan 2014 13 January 2014 | Vol. 22, No. 1 | DOI:10.1364/OE.22.000563 | OPTICS EXPRESS 565
method uses two APDs. Two receivers are moved by a distance of d symmetrically near or far from BS2. Compared with traditional method, although echo power is reduced by half in each detector, the background power can be suppressed by subtracting between two echo signals, Meanwhile, there is a zero cross in the differential echo signal and the sensitivity of zero cross is obviously higher than that of the peak in the original echo signal. t0=2R/c
I
traditional method proposed method
Start
Stop Pr
Pr2 (APD A)
Pr1 (APD B) 0
t Stop Prd=Pr2-Pr1
Fig. 2. Difference between differential echo and echo of peak discriminator.
2.2 Echo analysis Schematic diagram of laser range finding is shown in Fig. 3, left side is an system of transmitter and receiver, and right side is a target plane, which has a tilt angle of θ. R is the range between the system and the target. Laser pulse is with a temporal function of Gaussian model, which is written as [1]
Pt t
t 2 Et exp 2 , 2 2
(2)
where Et is the original pulse energy, τ is transmitting pulse width. Traditional receiver includes a single detector and echo signal power expression is written as [1, 20]
X
Transmitter /Receiver
O
Z R
Y Fig. 3. Schematic diagram of pulsed-laser range finding.
#201148 - $15.00 USD (C) 2014 OSA
Received 11 Nov 2013; revised 13 Dec 2013; accepted 16 Dec 2013; published 3 Jan 2014 13 January 2014 | Vol. 22, No. 1 | DOI:10.1364/OE.22.000563 | OPTICS EXPRESS 566
1 2 R 2 E T 2T Pr t t a o D r exp 2 t c 2 r 2 r tan 2 w2 z 2 2 , r c2 z 2 w z w0 1 2 w0
(3)
where Pr(t) is the received power on the detector, Ta is the one way atmospheric transmission, To is the receiver optics transmission efficiency, ηD is quantum efficiency, ρr is the reflectance of the target, τr is the received pulse width, w0 is the waist radius of the laser, w(z) is the beam radius, and λ is the wavelength. According to Fig. 1, Eqs. (1) and (3), the echo signal power expressions of APD A and APD B are written as
1 2 R d 2 E T 2T Pr1 t t a o D r exp 2 t c 2 2 r 2 r . (4) 1 2 R d 2 Et Ta2ToD r Pr 2 t 2 2 exp 2 t c r 2 r Equation (3) is under the ideal condition with no effects of background power. In fact, the background power should be concerned in the system, especially in the long-range measurement. The background power is written as [1, 21] PB r hsunTo Ar sin / 2 , 2
(5)
where ρr is the reflectance of target, hsun is the background solar irradiance, Ar is the area of the receiver, α is the field of view, and λ is the optical bandwidth. According to Eq. (5), PB is constant and does not change with time. The echo signal power from APD A and APD B with background power are described as following.
1 2 R d 2 E T 2T PrB1 t t a o D r exp 2 t PB c 2 2 r 2 r , 1 2 R d 2 Et Ta2ToD r PrB 2 t 2 2 exp 2 t c PB r 2 r
(6)
The differential echo power is obtained by subtraction and is written as
Prd t PrB 2 t PrB1 t
Et Ta2ToD r 2 2 r
1 2 R d 2 1 2 R d 2 exp 2 t exp 2 t , c c 2 r 2 r
(7)
Equation (7) shows that the background power can be suppressed by using the structure of differential optical-path. Furthermore, at the zero crossing temporal point when Prd = 0, we can obtain Eq. (8), which demonstrates that the TOF of zero cross is the same as peak discriminator.
#201148 - $15.00 USD (C) 2014 OSA
Received 11 Nov 2013; revised 13 Dec 2013; accepted 16 Dec 2013; published 3 Jan 2014 13 January 2014 | Vol. 22, No. 1 | DOI:10.1364/OE.22.000563 | OPTICS EXPRESS 567
2R 2R d 2R d . t t t c c c 2
2
(8)
2.3 Sensitivity of zero cross Sensitivity of zero cross kd = dPrd(t)/dt is defined as the temporal change rate of echo power at zero cross, and it is written as
kd
u22 u1 u12 Et Ta2ToD r u2 exp exp 2 2 2 , 2 2 2 r r 2 r r 2 r
(9)
where kd is sensitivity of zero cross, u1 = t-[(2R-d)/c], u2 = t-[(2R + d)/c] and other symbols are described above. In order to obtain the crossing point of the trailing edge and the leading edge of echo signals, the differential distance should be less than 8log(2) c r [20], i.e. there is an overlap between two echoes. When t = 2R/c, the sensitivity of zero cross is
kd
t 2 R / c
1 d 2 Et Ta2ToD r d exp . 2 r2 c 2 r 2 r c
(10)
Denoting f = kd|t = 2R/c, we can obtain Eq. (11) for the derivative term d from Eq. (10).
1 d 2 d 1 d 2 d 1 Et Ta2ToD r 1 2 exp 2 2 exp 2 . (11) 2 2 r 2 r c r c 2 r c c r c r c The highest sensitivity of zero cross is deduced by f’d = 0, yielding f 'd
(12) d c r . The highest sensitivity of zero cross is acquired when d = cτr, and the differential distance should be changed with τr which results from tilt angle of target [22]. Therefore, stage is used to adjust the position of the receivers to meet Eq. (12) in different conditions. According to analysis above, the method based on differential optical-path has two notable advantages. (1) Background power is suppressed because of the subtraction of two echo signals. (2) The sensitivity of zero cross is much higher than that of the peak. The proposed method transforms discriminating time of peak into detecting zero cross. . 2.4 SNR analysis SNR is one of most important parameters since it affects the measurement range and accuracy. Under the same conditions of transmitting system and target, the range and accuracy of system increase with improvement of SNR. SNR of traditional method is written as [4]
SNR
D2 Pr n
D2 Pr
2
2
2eB D Pr D PB 2eB iDK 4kTB / RTH
D Pr B 2hf
2
Pr PB
2
, (13)
h f 4kT 2e iDK 2 e D RTH 2
2
where ρD is the detector current responsivity, ρD = ηDe/hf, is effective value, i.e. root mean square (RMS) of the echo power at the detector, is RMS of total noise, B is the receiver bandwidth, h is the Planck’s constant, f = c/λ is the frequency of the received signal, e is the electron charge, is RMS of the dark current of detector, k is the Boltzmann’s
#201148 - $15.00 USD (C) 2014 OSA
Received 11 Nov 2013; revised 13 Dec 2013; accepted 16 Dec 2013; published 3 Jan 2014 13 January 2014 | Vol. 22, No. 1 | DOI:10.1364/OE.22.000563 | OPTICS EXPRESS 568
constant, T is the temperature in Kelvin, and is RMS of the effective load resistance that creates the same thermal noise spectral density as the receiver electronics. The background power PB is constant and suppressed by subtracting the two echoes. Therefore, the total noise of system based on differential optical-path can be written as
nd 2eB D Prd 2eB iDK 1 iDK 2 4kTB
1 1 R R TH 2 TH 1
2
2 B e D Prd e iDK 1 iDK 2
1 1 2kT R R TH 2 TH 1
,
(14)
According to the definition of SNR, the method based on differential optical-path can be written as
SNRd
D Prd h2 f 2 2 B hf Prd 2 e D
e iDK 1 iDK 2
2
2kT R1 R1 TH 2 TH 1
. (15)
3. Simulations and results 3.1 System model verification According to echo analysis discussed above, in long-range finding system, echo of traditional method is mainly affected by background power. According to parameters of typical ranging finding and target, simulation parameters are set as following: Et = 0.4nJ, ρr = 0.5, To = 0.8, ηD = 0.6, τ = 2ps, d = 250mm, θ = 10°, 20°, 30°, 40°, d = 50mm, hsun = 500W/m2/μm (λ = 905nm) [23], α = 5°, λ = 10nm, R = 18km, 19km, 20km, 21km. Ta is difficult to determine because of the complex environment conditions. In order to simple the question, the approximate relation among γ(λ), visibility and λ is used in the simulation, shown in Eq. (16), where Rv is visibility, q is correction factor which is depended on different visibility, shown in Table 1. Rv = 10km is chosen in the simulation.
3.91 550 Rv
q
(16)
Table 1. Correction Factor under Different Visibility visibility (Rv)
correction factor (q)
Rv>50km
q = 1.6
Rv = 10km
q = 1.3
Rv
