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Construction of backscattering echo caused by cloud in laser fuze
Optik - International Journal for Light and Electron Optics 171 (2018) 153–160
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.com/locate/ijleo
Original research article
Construction of backscattering echo caused by cloud in laser fuze ⁎
T
Fengjie Wang, Huimin Chen , Chao Ma, Lixin Xu Science and Technology on Electromechanical Dynamic Control Laboratory, Beijing Institute of Technology, Beijing, 100081, China
A R T IC LE I N F O
ABS TRA CT
Keywords: Laser fuze Cloud Backscattering echo Monte Carlo
Laser fuze is a weapon subsystem that uses laser to detect, identify and detonate in due time the target in short distance (generally not more than 10 m), and its working performance can be easily affected by the backscattering echo caused by cloud and other atmospheric particles. In this paper, we took the laser fuze and cloud of low visibility (less than 100 m) as the research subject, and established the laser detection model in cloud based on the Mie theory and Monte Carlo method. Using the laser detection model, we simulated the generation of cloud backscattering echo for the laser with 860 nm, and obtained the number of scattering events, penetration space and transmission time inside cloud of the echo, and analyzed the construction of echo on these aspects and the influence of cloud particle size parameter on the construction of echo. The data and results obtained in this paper can provide important support for the characterization of cloud backscattering laser echo, and the design of methods of laser anti-interference in cloud.
1. Introduction Fuze, an important part of weapon system, has the function of detecting, identifying and detonating in due time the target in short distance [1,2]. Laser fuze, which uses laser to detect and identify targets, has the advantages of strong anti-electromagnetic interference and high accuracy in positioning [3]. However, laser fuze can be easily affected by atmospheric particles. When laser fuze encounters the cloud of low visibility in air, the cloud will produce a strong backscattering echo of laser fuze, forming a false echo that would lead to the false alarm and premature explosion of the laser fuze. It is an effective way to improve the performance of the laser fuze in the cloud of low visibility by identifying the target echo and the backscattering echo caused by cloud through the beam characteristics. But it is necessary to conduct an in-depth analysis on the characteristics of the backscattering laser echo. D. M. Winker and D. Kim studied the proportion of multiple scattering echoes in the backscattering echo of cloud [4,5]. V. V. Belov studied the spatiotemporal structure of the backscattering echo of cloud [6], and R. Krawczyk studied the pulse broadening of cloud backscattering echo [7]. However, all of the above studies are conducted on the detection of laser radar within the range from several kilometers to several hundred kilometers, and the cloud with visibility greater than 100 m. Thus, the data and conclusions obtained may not be applicable to laser fuze whose detection range is short (generally not more than 10 m) and clouds of lower visibility. W. Zhang and H. M. Chen respectively studied the cloud echo characteristics of FMCW laser fuze and pulse laser fuze [8,9], but their studies only focused on the waveform of cloud echo. Therefore, based on the laser detection model set up by the method of Monte Carlo, this paper further studies the characteristics of cloud backscattering laser echo, including the number of scattering events, the penetration space and transmission time of echo with laser fuze and the cloud of low visibility (less than 100 m) as the research objects.
⁎
Corresponding author. E-mail address: [email protected] (H. Chen).
https://doi.org/10.1016/j.ijleo.2018.06.028 Received 16 April 2018; Accepted 6 June 2018 0030-4026/ © 2018 Elsevier GmbH. All rights reserved.
Optik - International Journal for Light and Electron Optics 171 (2018) 153–160
F. Wang et al.
2. Laser detection model A more perfect laser detection model in cloud is built by adding the optical shaping process on the basis of previous work [10]. According to the detection process of laser detection system in cloud, the laser detection model can be divided into two sub-models: the laser transceiver model and the laser transmission model. (1) Laser transceiver model The laser transceiver model is used to simulate the laser emission, optical shaping and receiving processes of laser detection system. The model disperses a beam of light into a large number of photons, and emits them sequentially in chronological order according to the emission time, position and direction of photons. The spatial positions of photons at the emission moment follow Gauss distribution, which can be expressed as:
⎧ x = ω0 ξ1 y = ω0 ξ2 ⎨ z ⎩ =0
(1)
where ω0 is the radius of laser beam waist, ξ1, ξ2 are the random numbers of standard normal distribution. The direction of photons at the emission moment can be obtained by the following equations:
⎧u x = sin θ0 cos φ0 u y = sin θ0 sin φ0 ⎨ ⎩uz = cos θ0
(2)
where θ0 = |(θ′/2)⋅ξ3| is the zenith angle of photon emission direction, θ′ is the divergence angle of laser beam, ξ3 is the standard normal distribution random number, φ0 = 2π⋅ξ 4 is the azimuth angle of photon emission direction, ξ 4 is the uniform random number in the interval [0,1]. The model will adjust the transmission path via the emission optical shaping system before emitted photons transmission in external environment. When photons pass through the emission optical shaping system, the refraction direction of photons at the optical lens incident end, the photon move trajectory inside the optical lens, and the refraction direction of photons at the optical lens exit end are calculated sequentially according to the structure size and refractive index of optical lens and the incident position and direction of photons at the optical lens incident end to obtain the position and direction of photons after passing through the optical shaping system. For the returned photons due to cloud particles backscattering, the laser transceiver model, in turn, determines whether they can enter the receiving optical shaping system; and whether they can enter the photodetector after the receiving optical shaping. The receiving optical shaping process is similar to the emission optical shaping process. If both conditions satisfy the requirements, the photons will be received successfully and generate the cloud backscattering echo. For the photons received by laser detection system, the laser transceiver model can obtain the information such as the number of scattering events, the propagation trajectory, and the transmission time. The number of scattering events can be obtained by counting the number of collision between photons and cloud particles. The transmission time can be obtained by the following equation: (3)
t=L c
where L is the move distance of photons during the detection process, and c is the light speed. (2) Laser transmission model The laser transmission model is used to simulate the transmission process of photons in cloud, which includes the collision between photons and cloud particles, and the move process of photons in cloud. The collision between photons and cloud particles will lead to the scattering and absorption of photons, thereby changing the photon propagation direction and energy. The photon propagation direction after collision is determined by the following expression [11]:
⎧u′ x = sin θ (u x uz cosφ − u y sinφ) 1 − uz2 + u x cos θ ⎪ u′ = sin θ (u y uz cosφ + u x sinφ) 1 − uz2 + u y cos θ ⎨ y ⎪u′ = −sin θ cos φ 1 − u 2 + u cos θ z z ⎩ z
(4)
if |uz | > 0.99999, the Eq. (4) is changed to:
⎧u′ x = sin θ cos φ u′ y = sin θ sin φ ⎨ ⎩u′z = uz /|uz|⋅cos θ
(5)
where u x , u y , uz are the propagation direction before collision, φ is the azimuth angle and uniform distributed between 0 and 2π , θ is the scattering angle, and can be obtained by sampling based on the weights of scattering angles 0° - 180°, which are expressed by the scattering phase function as follows [8]: 154
Optik - International Journal for Light and Electron Optics 171 (2018) 153–160
F. Wang et al.
Fig. 1. Mie phase function at complex refractive index of 1.656-0.595i and particle size parameters (a) πd λ = 0.2π and (b) πd λ = 20π .
P (θ) =
|S1 (θ)|2 + |S2 (θ)|2 (2n + 1)(|an |2 + |bn |2 )
∞ ∑n = 1
(6)
where an , bn are the Mie coefficients, S1 (θ) , S2 (θ) are the scattering amplitudes. The change of photon energy after collision is determined by the following expression [8]: (7)
ω = Qsca Qext
where Qsca is the particle scattering efficiency, Qext is the particle extinction efficiency. The photon propagation process in cloud is divided into several discrete propagation processes by collision. The direction of each propagation process is determined by the scattering direction of the previous collision. The propagation distance is characterized by the scattering free path length, whose expression is [12]:
Δs = −ln ξ μt
(8)
where ξ is the uniform random number in the interval [0,1], μt is the cloud extinction coefficient. The photon will repeat the process of collision-propagation-collision in cloud until the photon is either absorbed or exits the cloud. In this paper, the accuracy of laser detection model simulation is verified using the existing theory and research results. The simulation accuracy of laser detection model depends mainly on the accuracy of particle scattering and extinction efficiency algorithms in the model. The scattering efficiency is closely related to the scattering phase function, by which the accuracy of scattering efficiency algorithm can be verified. The scattering phase functions are calculated under complex refractive index of 1.656–0.595i and particle size parameters of 0.2π , 20π , respectively, with the laser detection model, and the results are shown in Fig. 1. The calculations in this paper are in complete agreement with those in paper [13]. The extinction efficiency of cloud is closely related to the laser transmittance, through which the accuracy of extinction efficiency factor algorithm can be verified. The transmittances of one billion photons in cloud (ratio of photons that pass through cloud without scattering) are simulated at various optical depths with the laser detection model. The simulation results are shown in Table 1, which are almost identical to the calculations by Lambert-Beer law. The above results demonstrate that the laser detection model is accurate in solving the particle scattering and extinction efficiency factors, thus proving the simulation accuracy of the most critical part in the model, i.e. laser scattering, absorption and move processes in cloud.
Table 1 Comparison of laser transmittance between calculations by Lambert-Beer law vs. simulation results with laser detection model. Parameters
Laser transmittance
Error
Optical depth
Calculations by Lambert-Beer Law
Simulation results with laser detection model
0.1 0.5 1 2 4 6
0.90484 0.60653 0.36788 0.13534 0.01832 0.00248
0.90485 0.60666 0.36686 0.13512 0.01832 0.00244
155
0.00001 0.00013 0.00102 0.00022 0.00000 0.00004
Optik - International Journal for Light and Electron Optics 171 (2018) 153–160
F. Wang et al.
Table 2 Main parameters in simulation. Simulation parameter
Value
Wavelength/nm Emission-receiving distance/mm Divergence angle/mrad Beam waist radius/mm Emission optical lens diameter/mm Emission optical lens focal length/mm Receiving photosensitive surface diameter/mm Receiving optical lens diameter/mm Receiving optical lens focal length/mm Cloud particle size parameters Cloud mass concentration/(g/m3) Complex refractive index Distance from laser detection system to cloud/m
860 35 5 0.11 12.7 50.8 5 25.4 75 6π , 8π , 10π , 14π 1 (corresponding visibility is 6 m) 1.329-2.93 × 10−7i 0
3. Simulation of the construction of cloud backscattering laser echo 3.1. Conditions and methods In the simulation, cloud is a monodisperse particle group which distributed uniformly in a cylindrical space with a radius of 50 m and a length of 100 m, and the mass concentration is 1 g/m3 (the corresponding visibility is 6 m). The laser detection system is located at the center of cloud circular surface, the distance from laser detection system to cloud is 0 m, and the distance between the laser emission axis and the receiving axis is 35 mm. The wavelength of the laser emitted by laser detection system is 860 nm, the divergence angle of the laser beam is 5 m rad, and the time domain modulation signal is Dirac. The diameter of the receiving photosensitive is 5 mm. The complex refractive index of cloud to 860 nm laser is 1.329–2.93 × 10−7i [14]. Four groups of cloud particle diameters are set, namely, 5.16 μm, 6.88 μm, 8.60 μm and 12.04 μm (when the laser wavelength is 860 nm, the corresponding particle size parameters are 6π , 8π , 10π and 14π ), to analyze the influence of particle diameter on the results. The main parameters in simulation are shown in Table 2. Using the laser detection model, the generation of cloud backscattering echo for incident laser emitted by laser detection system is simulated under various particle size parameters. The number of scattering events, the penetration depth (maximum distance between laser detection system and photon position in transmission route), the penetration azimuth angle (maximum angle between emission axis and the line between laser detection system and photon position) and the transmission time inside cloud of all backscattering photons are recorded. Statistical processing yields: (1) The construction of cloud backscattering laser echo on the number of scattering events; (2) the construction of cloud backscattering laser echo on the penetration depth and penetration azimuth angle; and (3) the construction of cloud backscattering laser echo on the transmission time inside cloud, in order to analyze the timedomain waveform spreading of the echo. For each simulation, the number of photons is 2 billion. The generation of cloud backscattering photons is shown in Fig. 2. 3.2. Results and discussion 3.2.1. Number of scattering events Fig. 3 displays the construction of cloud backscattering laser echo on the number of scattering events under particle size parameters of 6π , 8π , 10π and 14π , respectively. In the figure, S90 is the distribution parameter, which represents the number of scattering events when the echo energy is accumulated to 90%. When the particle size parameter is 6π , the proportions of the echo with 1–5 scattering events in all echo is 48.3%, 26.7%, 12.4%, 6.3% and 2.8%, respectively, showing an obvious declining trend. When the particle size parameters are 8π , 10π and 14π , the variation trend is the same, which indicates that the echo intensity is inversely proportional to the number of scattering events. Echo intensity corresponding to the same number of scattering events under different particle size parameters has little difference, and the parameter S90 corresponds to four times of scattering events in all conditions,
Fig. 2. Schematic of the generation of cloud backscattering photons. 156
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F. Wang et al.
Fig. 3. Construction of cloud backscattering laser echo on the number of scattering events.
which shows that the particle size parameter has little effect on the number of scattering events. The mean of echo construction on the number of scattering events in four particle size parameters are fitted, and the fitting function obtained is a Gaussian function, which is expressed as:
I (n) = 0.90 exp[−(n + 2.47)/4.08]2
(9)
where n is the number of scattering events, I (n) is the proportion of backscattering echo that the number of scattering events is n. 3.2.2. Penetration space Fig. 4 illustrates the construction of cloud backscattering laser echo on the penetration depth at particle size parameters of 6π , 8π , 10π and 14π , respectively. In the figure, D10, D50 and D90 are the distribution parameters, which represent the penetration depth when the echo energy is accumulated to 10%, 50% and 90%, respectively. Concerning the distribution parameters, the value of D90 is 400 cm at a particle size parameter of 6π , which increases to 500 cm, 730 cm and 940 cm, respectively, as the particle size
Fig. 4. Construction of cloud backscattering laser echo on the penetration depth in space at particle size parameters of (a) 6π , (b) 8π , (c) 10π , and (d) 14π . 157
Optik - International Journal for Light and Electron Optics 171 (2018) 153–160
F. Wang et al.
Fig. 5. Construction of cloud backscattering laser echo on the penetration azimuth angle in space.
parameter increases to 8π , 10π and 14π . The parameters D10 and D50 exhibit a same trend as D90. In terms of distribution pattern, the backscattering echo intensity first increases and then decreases with increasing penetration depth under all four particle size parameter conditions; moreover, the peak depths are all located at the leftward position of penetration depth interval. The above results indicate that when the cloud particle diameter is larger than the laser wavelength, the overall penetration depth of cloud backscattering laser echo is positively correlated with the cloud particle size parameter, and the backscattering echo intensity follows the positively skewed distribution on the penetration depth. The penetration depth of cloud backscattering laser echo is negatively correlated with the cloud extinction coefficient. Besides, the cloud extinction coefficient is negatively correlated with the cloud particle size parameter when the particle diameter is larger than the laser wavelength, so the penetration depth of backscattering photons is positively correlated with the particle size parameter. The distribution pattern of backscattering laser echo intensity on the penetration depth is related to the number of scattering events. The more the scattering events, the greater the overall penetration depth. The backscattering echo intensity obeys decline distribution on the number of scattering events, so the backscattering echo with less penetration depth account for a large proportion, which results in the positively skewed distribution of backscattering echo intensity on the penetration depth. Fig. 5 presents the construction of cloud backscattering laser echo on the penetration azimuth angle in space at particle size parameters of 6π , 8π , 10π and 14π , respectively. In the figure, A10, A50 and A90 are the distribution parameters, which represent the penetration azimuth angles when the echo energy is accumulated to 10%, 50% and 90%, respectively. Concerning the distribution parameters, A10 and A50 are 0°in all four parameter conditions. The value of A90 is 10°, 8°, 5°and 4°corresponding to 6π , 8π , 10π and 14π . In terms of distribution pattern, the backscattering echo intensity decreases gradually with the increasing penetration azimuth angle under all four conditions. The above results indicate that the overall penetration azimuth angle of cloud backscattering laser echo is negatively correlated with the cloud particle size parameter when the particle diameter is larger than the laser wavelength; and that the backscattering echo intensity follows decline distribution on the penetration azimuth angle. The overall penetration azimuth angle is closely related to the number of scattering events and scattering characteristics of cloud particles. The stronger the particle backscattering, the larger the penetration azimuth angle. Fig. 6 illustrates the normalized scattering phase functions at cloud particle size parameters of 6π and 14π , respectively. As can be seen, the cloud particles with a size parameter of 6π exhibit stronger backscattering ability than those with a size parameter of 14π , so its backscattering echo has larger overall penetration azimuth angle. The distribution pattern of backscattering echo intensity on the penetration azimuth angle is related to the number of scattering events, and the observance of
Fig. 6. Normalized scattering phase function at particle size parameters of (a) 6π , (b) 14π . 158
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Fig. 7. Construction of cloud backscattering laser echo on the transmission time inside cloud at particle size parameters of (a) 6π , (b) 8π , (c) 10π , and (d) 14π .
decline distribution is mainly due to the decline distribution of backscattering echo on the number of scattering events.
3.2.3. Transmission time inside cloud Fig. 7 displays the construction of cloud backscattering echo on the transmission time inside cloud under various particle size parameters. The arrow marks the duration (10% width) during which the echo energy exceeds 10% of peak energy. The 10% width is 11.5 ns at a 6π particle size parameter, which increases to 23.3 ns, 27.4 ns and 27.3 ns as the parameter increases to 8π , 10π and 14π , respectively. These results suggest the presence of time-domain waveform spreading for the cloud backscattering laser echo, as well as the positive correlation of spreading width with the particle size parameter. For the cloud backscattering laser echo, the timedomain spreading width is positively correlated with the optical path in cloud, while the optical path is positively correlated with the cloud particle size parameter. Hence, there is a positive correlation between the spreading width and the particle size.
4. Conclusions In this paper, the construction of laser fuze echo caused by cloud of low visibility on the number of scattering events, penetration space and transmission time inside cloud are studied with laser detection model under various cloud particle size parameter conditions. The following conclusions are reached under the specific conditions: (1) In terms of the number of scattering events, the cloud particle size parameter has little effect on the number of scattering events, and the echo construction on the number of scattering events can be expressed approximately as I (n) = 0.90 exp[−(n + 2.47)/4.08]2 . (2) In terms of penetration space, the penetration depth of most laser echo (more than 90%) is less than 10 m, the penetration azimuth angle is less than 10°. The echo intensity follows the positively skewed distribution on the penetration depth, and the decline distribution on the penetration azimuth angle. (3) In terms of transmission time, the temporal spreading of laser echo is larger than 10 ns, and the spreading width is positively correlated with the particle size parameter. These conclusions are only applicable to the case where the cloud particles size parameter satisfies π ≤ πd λ ≤ 14π , and the cloud mass concentration is 1 g/m3. The data and results obtained in this paper can provide important support for the characterization of cloud backscattering laser echo, and the design of methods of laser anti-interference in cloud. Future work will further focus on the construction of cloud backscattering laser echo in more conditions (various visibility of cloud and various distances from laser detection system to cloud), and the recognition method of cloud backscattering echo based on the echo construction.
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Acknowledgements This work was supported by NSAF (grant number U1630131); and SAST (grant number sast2017-074). References [1] T.J. Hu, Y.L. Zhao, Y. Zhao, W. Ren, Integration design of a MEMS based fuze, Sens. Actuators A 268 (2017) 193–200. [2] Y.J. Tang, Z. Yang, X.J. Wang, J. Wang, Research on the piezoelectric ultrasonic actuator applied to smart fuze safety system, Int. J. Appl. Electrom. 53 (2017) 303–313. [3] W. Zhang, Y.L. Li, Z.H. Huang, C. Ma, Cloud backscattering interference suppression algorithm for FMCW laser fuze based on normalized frequency spectrum threshold, Optik 131 (2017) 188–193. [4] D.M. Winker, L.R. Poole, Monte-Carlo calculations of cloud returns for ground-based and space-based LIDARS, Appl. Phys. B: Lasers Opt. 60 (1995) 341–344. [5] D. Kim, C.H. Du, Y. Kim, S. Volkov, J. Lee, Optical depth and multiple scattering depolarization in liquid clouds, Opt. Rev. 17 (2010) 507–512. [6] V.V. Belov, A.B. Serebrennikov, Spatiotemporal structure of multiply scattered components of lidar return signals, Proceedings of the SPIE - The International Society for Optical Engineering, Tomsk, Russian, 1999, pp. 271–278. [7] R. Krawczyk, O. Goretta, A. Kassighian, Temporal pulse spreading of a return lidar signal, Appl. Opt. 32 (1993) 6784–6788. [8] W. Zhang, Y.L. Li, Z.H. Huang, Research on the characteristics of cloud backscattering signals for frequency modulated continuous wave laser fuze, Optik 127 (2016) 9046–9055. [9] F.J. Wang, H.M. Chen, Simulation of characteristics of cloud and cloud echo for pulse laser fuze, Opt. Precis. Eng. 23 (2015) 1–7. [10] H.M. Chen, Y. Liu, X.W. Zhu, F.J. Wang, Simulation of the characteristics of backscattering signals for frequency modulated continuous wave laser fuze, Acta Armamentaria 36 (2015) 2247–2253. [11] J. Guo, H. Zhang, X.J. Zhang, Propagating characteristics of pulsed laser in rain, Int. J. Antenn. Propag. (2015) (2015) 292905. [12] E. Berrocal, D.L. Sedarsky, M.E. Paciaroni, I.V. Meglinski, M.A. Linne, Laser light scattering in turbid media I: experimental and simulated results for the spatial intensity distribution, Opt. Express 15 (2007) 10649–10665. [13] D. Toublanc, Henyey-Greenstein and Mie phase functions in Monte Carlo radiative transfer computations, Appl. Opt. 35 (1996) 3270–3274. [14] G.M. Hale, M.R. Querry, Optical constants of water in the 200-nm to 200-μm wavelength region, Appl. Opt. 12 (1973) 555–563.
160
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.com/locate/ijleo
Original research article
Construction of backscattering echo caused by cloud in laser fuze ⁎
T
Fengjie Wang, Huimin Chen , Chao Ma, Lixin Xu Science and Technology on Electromechanical Dynamic Control Laboratory, Beijing Institute of Technology, Beijing, 100081, China
A R T IC LE I N F O
ABS TRA CT
Keywords: Laser fuze Cloud Backscattering echo Monte Carlo
Laser fuze is a weapon subsystem that uses laser to detect, identify and detonate in due time the target in short distance (generally not more than 10 m), and its working performance can be easily affected by the backscattering echo caused by cloud and other atmospheric particles. In this paper, we took the laser fuze and cloud of low visibility (less than 100 m) as the research subject, and established the laser detection model in cloud based on the Mie theory and Monte Carlo method. Using the laser detection model, we simulated the generation of cloud backscattering echo for the laser with 860 nm, and obtained the number of scattering events, penetration space and transmission time inside cloud of the echo, and analyzed the construction of echo on these aspects and the influence of cloud particle size parameter on the construction of echo. The data and results obtained in this paper can provide important support for the characterization of cloud backscattering laser echo, and the design of methods of laser anti-interference in cloud.
1. Introduction Fuze, an important part of weapon system, has the function of detecting, identifying and detonating in due time the target in short distance [1,2]. Laser fuze, which uses laser to detect and identify targets, has the advantages of strong anti-electromagnetic interference and high accuracy in positioning [3]. However, laser fuze can be easily affected by atmospheric particles. When laser fuze encounters the cloud of low visibility in air, the cloud will produce a strong backscattering echo of laser fuze, forming a false echo that would lead to the false alarm and premature explosion of the laser fuze. It is an effective way to improve the performance of the laser fuze in the cloud of low visibility by identifying the target echo and the backscattering echo caused by cloud through the beam characteristics. But it is necessary to conduct an in-depth analysis on the characteristics of the backscattering laser echo. D. M. Winker and D. Kim studied the proportion of multiple scattering echoes in the backscattering echo of cloud [4,5]. V. V. Belov studied the spatiotemporal structure of the backscattering echo of cloud [6], and R. Krawczyk studied the pulse broadening of cloud backscattering echo [7]. However, all of the above studies are conducted on the detection of laser radar within the range from several kilometers to several hundred kilometers, and the cloud with visibility greater than 100 m. Thus, the data and conclusions obtained may not be applicable to laser fuze whose detection range is short (generally not more than 10 m) and clouds of lower visibility. W. Zhang and H. M. Chen respectively studied the cloud echo characteristics of FMCW laser fuze and pulse laser fuze [8,9], but their studies only focused on the waveform of cloud echo. Therefore, based on the laser detection model set up by the method of Monte Carlo, this paper further studies the characteristics of cloud backscattering laser echo, including the number of scattering events, the penetration space and transmission time of echo with laser fuze and the cloud of low visibility (less than 100 m) as the research objects.
⁎
Corresponding author. E-mail address: [email protected] (H. Chen).
https://doi.org/10.1016/j.ijleo.2018.06.028 Received 16 April 2018; Accepted 6 June 2018 0030-4026/ © 2018 Elsevier GmbH. All rights reserved.
Optik - International Journal for Light and Electron Optics 171 (2018) 153–160
F. Wang et al.
2. Laser detection model A more perfect laser detection model in cloud is built by adding the optical shaping process on the basis of previous work [10]. According to the detection process of laser detection system in cloud, the laser detection model can be divided into two sub-models: the laser transceiver model and the laser transmission model. (1) Laser transceiver model The laser transceiver model is used to simulate the laser emission, optical shaping and receiving processes of laser detection system. The model disperses a beam of light into a large number of photons, and emits them sequentially in chronological order according to the emission time, position and direction of photons. The spatial positions of photons at the emission moment follow Gauss distribution, which can be expressed as:
⎧ x = ω0 ξ1 y = ω0 ξ2 ⎨ z ⎩ =0
(1)
where ω0 is the radius of laser beam waist, ξ1, ξ2 are the random numbers of standard normal distribution. The direction of photons at the emission moment can be obtained by the following equations:
⎧u x = sin θ0 cos φ0 u y = sin θ0 sin φ0 ⎨ ⎩uz = cos θ0
(2)
where θ0 = |(θ′/2)⋅ξ3| is the zenith angle of photon emission direction, θ′ is the divergence angle of laser beam, ξ3 is the standard normal distribution random number, φ0 = 2π⋅ξ 4 is the azimuth angle of photon emission direction, ξ 4 is the uniform random number in the interval [0,1]. The model will adjust the transmission path via the emission optical shaping system before emitted photons transmission in external environment. When photons pass through the emission optical shaping system, the refraction direction of photons at the optical lens incident end, the photon move trajectory inside the optical lens, and the refraction direction of photons at the optical lens exit end are calculated sequentially according to the structure size and refractive index of optical lens and the incident position and direction of photons at the optical lens incident end to obtain the position and direction of photons after passing through the optical shaping system. For the returned photons due to cloud particles backscattering, the laser transceiver model, in turn, determines whether they can enter the receiving optical shaping system; and whether they can enter the photodetector after the receiving optical shaping. The receiving optical shaping process is similar to the emission optical shaping process. If both conditions satisfy the requirements, the photons will be received successfully and generate the cloud backscattering echo. For the photons received by laser detection system, the laser transceiver model can obtain the information such as the number of scattering events, the propagation trajectory, and the transmission time. The number of scattering events can be obtained by counting the number of collision between photons and cloud particles. The transmission time can be obtained by the following equation: (3)
t=L c
where L is the move distance of photons during the detection process, and c is the light speed. (2) Laser transmission model The laser transmission model is used to simulate the transmission process of photons in cloud, which includes the collision between photons and cloud particles, and the move process of photons in cloud. The collision between photons and cloud particles will lead to the scattering and absorption of photons, thereby changing the photon propagation direction and energy. The photon propagation direction after collision is determined by the following expression [11]:
⎧u′ x = sin θ (u x uz cosφ − u y sinφ) 1 − uz2 + u x cos θ ⎪ u′ = sin θ (u y uz cosφ + u x sinφ) 1 − uz2 + u y cos θ ⎨ y ⎪u′ = −sin θ cos φ 1 − u 2 + u cos θ z z ⎩ z
(4)
if |uz | > 0.99999, the Eq. (4) is changed to:
⎧u′ x = sin θ cos φ u′ y = sin θ sin φ ⎨ ⎩u′z = uz /|uz|⋅cos θ
(5)
where u x , u y , uz are the propagation direction before collision, φ is the azimuth angle and uniform distributed between 0 and 2π , θ is the scattering angle, and can be obtained by sampling based on the weights of scattering angles 0° - 180°, which are expressed by the scattering phase function as follows [8]: 154
Optik - International Journal for Light and Electron Optics 171 (2018) 153–160
F. Wang et al.
Fig. 1. Mie phase function at complex refractive index of 1.656-0.595i and particle size parameters (a) πd λ = 0.2π and (b) πd λ = 20π .
P (θ) =
|S1 (θ)|2 + |S2 (θ)|2 (2n + 1)(|an |2 + |bn |2 )
∞ ∑n = 1
(6)
where an , bn are the Mie coefficients, S1 (θ) , S2 (θ) are the scattering amplitudes. The change of photon energy after collision is determined by the following expression [8]: (7)
ω = Qsca Qext
where Qsca is the particle scattering efficiency, Qext is the particle extinction efficiency. The photon propagation process in cloud is divided into several discrete propagation processes by collision. The direction of each propagation process is determined by the scattering direction of the previous collision. The propagation distance is characterized by the scattering free path length, whose expression is [12]:
Δs = −ln ξ μt
(8)
where ξ is the uniform random number in the interval [0,1], μt is the cloud extinction coefficient. The photon will repeat the process of collision-propagation-collision in cloud until the photon is either absorbed or exits the cloud. In this paper, the accuracy of laser detection model simulation is verified using the existing theory and research results. The simulation accuracy of laser detection model depends mainly on the accuracy of particle scattering and extinction efficiency algorithms in the model. The scattering efficiency is closely related to the scattering phase function, by which the accuracy of scattering efficiency algorithm can be verified. The scattering phase functions are calculated under complex refractive index of 1.656–0.595i and particle size parameters of 0.2π , 20π , respectively, with the laser detection model, and the results are shown in Fig. 1. The calculations in this paper are in complete agreement with those in paper [13]. The extinction efficiency of cloud is closely related to the laser transmittance, through which the accuracy of extinction efficiency factor algorithm can be verified. The transmittances of one billion photons in cloud (ratio of photons that pass through cloud without scattering) are simulated at various optical depths with the laser detection model. The simulation results are shown in Table 1, which are almost identical to the calculations by Lambert-Beer law. The above results demonstrate that the laser detection model is accurate in solving the particle scattering and extinction efficiency factors, thus proving the simulation accuracy of the most critical part in the model, i.e. laser scattering, absorption and move processes in cloud.
Table 1 Comparison of laser transmittance between calculations by Lambert-Beer law vs. simulation results with laser detection model. Parameters
Laser transmittance
Error
Optical depth
Calculations by Lambert-Beer Law
Simulation results with laser detection model
0.1 0.5 1 2 4 6
0.90484 0.60653 0.36788 0.13534 0.01832 0.00248
0.90485 0.60666 0.36686 0.13512 0.01832 0.00244
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0.00001 0.00013 0.00102 0.00022 0.00000 0.00004
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Table 2 Main parameters in simulation. Simulation parameter
Value
Wavelength/nm Emission-receiving distance/mm Divergence angle/mrad Beam waist radius/mm Emission optical lens diameter/mm Emission optical lens focal length/mm Receiving photosensitive surface diameter/mm Receiving optical lens diameter/mm Receiving optical lens focal length/mm Cloud particle size parameters Cloud mass concentration/(g/m3) Complex refractive index Distance from laser detection system to cloud/m
860 35 5 0.11 12.7 50.8 5 25.4 75 6π , 8π , 10π , 14π 1 (corresponding visibility is 6 m) 1.329-2.93 × 10−7i 0
3. Simulation of the construction of cloud backscattering laser echo 3.1. Conditions and methods In the simulation, cloud is a monodisperse particle group which distributed uniformly in a cylindrical space with a radius of 50 m and a length of 100 m, and the mass concentration is 1 g/m3 (the corresponding visibility is 6 m). The laser detection system is located at the center of cloud circular surface, the distance from laser detection system to cloud is 0 m, and the distance between the laser emission axis and the receiving axis is 35 mm. The wavelength of the laser emitted by laser detection system is 860 nm, the divergence angle of the laser beam is 5 m rad, and the time domain modulation signal is Dirac. The diameter of the receiving photosensitive is 5 mm. The complex refractive index of cloud to 860 nm laser is 1.329–2.93 × 10−7i [14]. Four groups of cloud particle diameters are set, namely, 5.16 μm, 6.88 μm, 8.60 μm and 12.04 μm (when the laser wavelength is 860 nm, the corresponding particle size parameters are 6π , 8π , 10π and 14π ), to analyze the influence of particle diameter on the results. The main parameters in simulation are shown in Table 2. Using the laser detection model, the generation of cloud backscattering echo for incident laser emitted by laser detection system is simulated under various particle size parameters. The number of scattering events, the penetration depth (maximum distance between laser detection system and photon position in transmission route), the penetration azimuth angle (maximum angle between emission axis and the line between laser detection system and photon position) and the transmission time inside cloud of all backscattering photons are recorded. Statistical processing yields: (1) The construction of cloud backscattering laser echo on the number of scattering events; (2) the construction of cloud backscattering laser echo on the penetration depth and penetration azimuth angle; and (3) the construction of cloud backscattering laser echo on the transmission time inside cloud, in order to analyze the timedomain waveform spreading of the echo. For each simulation, the number of photons is 2 billion. The generation of cloud backscattering photons is shown in Fig. 2. 3.2. Results and discussion 3.2.1. Number of scattering events Fig. 3 displays the construction of cloud backscattering laser echo on the number of scattering events under particle size parameters of 6π , 8π , 10π and 14π , respectively. In the figure, S90 is the distribution parameter, which represents the number of scattering events when the echo energy is accumulated to 90%. When the particle size parameter is 6π , the proportions of the echo with 1–5 scattering events in all echo is 48.3%, 26.7%, 12.4%, 6.3% and 2.8%, respectively, showing an obvious declining trend. When the particle size parameters are 8π , 10π and 14π , the variation trend is the same, which indicates that the echo intensity is inversely proportional to the number of scattering events. Echo intensity corresponding to the same number of scattering events under different particle size parameters has little difference, and the parameter S90 corresponds to four times of scattering events in all conditions,
Fig. 2. Schematic of the generation of cloud backscattering photons. 156
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Fig. 3. Construction of cloud backscattering laser echo on the number of scattering events.
which shows that the particle size parameter has little effect on the number of scattering events. The mean of echo construction on the number of scattering events in four particle size parameters are fitted, and the fitting function obtained is a Gaussian function, which is expressed as:
I (n) = 0.90 exp[−(n + 2.47)/4.08]2
(9)
where n is the number of scattering events, I (n) is the proportion of backscattering echo that the number of scattering events is n. 3.2.2. Penetration space Fig. 4 illustrates the construction of cloud backscattering laser echo on the penetration depth at particle size parameters of 6π , 8π , 10π and 14π , respectively. In the figure, D10, D50 and D90 are the distribution parameters, which represent the penetration depth when the echo energy is accumulated to 10%, 50% and 90%, respectively. Concerning the distribution parameters, the value of D90 is 400 cm at a particle size parameter of 6π , which increases to 500 cm, 730 cm and 940 cm, respectively, as the particle size
Fig. 4. Construction of cloud backscattering laser echo on the penetration depth in space at particle size parameters of (a) 6π , (b) 8π , (c) 10π , and (d) 14π . 157
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Fig. 5. Construction of cloud backscattering laser echo on the penetration azimuth angle in space.
parameter increases to 8π , 10π and 14π . The parameters D10 and D50 exhibit a same trend as D90. In terms of distribution pattern, the backscattering echo intensity first increases and then decreases with increasing penetration depth under all four particle size parameter conditions; moreover, the peak depths are all located at the leftward position of penetration depth interval. The above results indicate that when the cloud particle diameter is larger than the laser wavelength, the overall penetration depth of cloud backscattering laser echo is positively correlated with the cloud particle size parameter, and the backscattering echo intensity follows the positively skewed distribution on the penetration depth. The penetration depth of cloud backscattering laser echo is negatively correlated with the cloud extinction coefficient. Besides, the cloud extinction coefficient is negatively correlated with the cloud particle size parameter when the particle diameter is larger than the laser wavelength, so the penetration depth of backscattering photons is positively correlated with the particle size parameter. The distribution pattern of backscattering laser echo intensity on the penetration depth is related to the number of scattering events. The more the scattering events, the greater the overall penetration depth. The backscattering echo intensity obeys decline distribution on the number of scattering events, so the backscattering echo with less penetration depth account for a large proportion, which results in the positively skewed distribution of backscattering echo intensity on the penetration depth. Fig. 5 presents the construction of cloud backscattering laser echo on the penetration azimuth angle in space at particle size parameters of 6π , 8π , 10π and 14π , respectively. In the figure, A10, A50 and A90 are the distribution parameters, which represent the penetration azimuth angles when the echo energy is accumulated to 10%, 50% and 90%, respectively. Concerning the distribution parameters, A10 and A50 are 0°in all four parameter conditions. The value of A90 is 10°, 8°, 5°and 4°corresponding to 6π , 8π , 10π and 14π . In terms of distribution pattern, the backscattering echo intensity decreases gradually with the increasing penetration azimuth angle under all four conditions. The above results indicate that the overall penetration azimuth angle of cloud backscattering laser echo is negatively correlated with the cloud particle size parameter when the particle diameter is larger than the laser wavelength; and that the backscattering echo intensity follows decline distribution on the penetration azimuth angle. The overall penetration azimuth angle is closely related to the number of scattering events and scattering characteristics of cloud particles. The stronger the particle backscattering, the larger the penetration azimuth angle. Fig. 6 illustrates the normalized scattering phase functions at cloud particle size parameters of 6π and 14π , respectively. As can be seen, the cloud particles with a size parameter of 6π exhibit stronger backscattering ability than those with a size parameter of 14π , so its backscattering echo has larger overall penetration azimuth angle. The distribution pattern of backscattering echo intensity on the penetration azimuth angle is related to the number of scattering events, and the observance of
Fig. 6. Normalized scattering phase function at particle size parameters of (a) 6π , (b) 14π . 158
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Fig. 7. Construction of cloud backscattering laser echo on the transmission time inside cloud at particle size parameters of (a) 6π , (b) 8π , (c) 10π , and (d) 14π .
decline distribution is mainly due to the decline distribution of backscattering echo on the number of scattering events.
3.2.3. Transmission time inside cloud Fig. 7 displays the construction of cloud backscattering echo on the transmission time inside cloud under various particle size parameters. The arrow marks the duration (10% width) during which the echo energy exceeds 10% of peak energy. The 10% width is 11.5 ns at a 6π particle size parameter, which increases to 23.3 ns, 27.4 ns and 27.3 ns as the parameter increases to 8π , 10π and 14π , respectively. These results suggest the presence of time-domain waveform spreading for the cloud backscattering laser echo, as well as the positive correlation of spreading width with the particle size parameter. For the cloud backscattering laser echo, the timedomain spreading width is positively correlated with the optical path in cloud, while the optical path is positively correlated with the cloud particle size parameter. Hence, there is a positive correlation between the spreading width and the particle size.
4. Conclusions In this paper, the construction of laser fuze echo caused by cloud of low visibility on the number of scattering events, penetration space and transmission time inside cloud are studied with laser detection model under various cloud particle size parameter conditions. The following conclusions are reached under the specific conditions: (1) In terms of the number of scattering events, the cloud particle size parameter has little effect on the number of scattering events, and the echo construction on the number of scattering events can be expressed approximately as I (n) = 0.90 exp[−(n + 2.47)/4.08]2 . (2) In terms of penetration space, the penetration depth of most laser echo (more than 90%) is less than 10 m, the penetration azimuth angle is less than 10°. The echo intensity follows the positively skewed distribution on the penetration depth, and the decline distribution on the penetration azimuth angle. (3) In terms of transmission time, the temporal spreading of laser echo is larger than 10 ns, and the spreading width is positively correlated with the particle size parameter. These conclusions are only applicable to the case where the cloud particles size parameter satisfies π ≤ πd λ ≤ 14π , and the cloud mass concentration is 1 g/m3. The data and results obtained in this paper can provide important support for the characterization of cloud backscattering laser echo, and the design of methods of laser anti-interference in cloud. Future work will further focus on the construction of cloud backscattering laser echo in more conditions (various visibility of cloud and various distances from laser detection system to cloud), and the recognition method of cloud backscattering echo based on the echo construction.
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