• Infrared and Laser Engineering
  • Vol. 50, Issue 5, 20200319 (2021)
Jiaqian Bao, Bingting Zha*, He Zhang, and Chenyoushi Xu
Author Affiliations
  • Ministerial Key Laboratory of ZNDY, Nanjing University of Science and Technology, Nanjing 210094, China
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    DOI: 10.3788/IRLA20200319 Cite this Article
    Jiaqian Bao, Bingting Zha, He Zhang, Chenyoushi Xu. Simulation method of pulse laser fuze echo in dust environment[J]. Infrared and Laser Engineering, 2021, 50(5): 20200319 Copy Citation Text show less

    Abstract

    Since the most widely used single-scattering phase function—Henyey-Greenstein scattering phase function (H-G scattering phase function) cannot reproduce the forward scattering and backscattering behavior well, a method based on the T-matrix scattering phase function was proposed to analyze and simulate the multiple scattering and echo signal of the pulse laser in the dust environments. The single-scattering properties of dust particles were calculated by the T-matrix method and a sample method was proposed to apply T-matrix scattering phase function to the Monte Carlo simulation with a random number. Furthermore, the theoretical model of the transmission and reception of a laser fuze in dust environments was built with the above sample method and semianalytic sensing geometric method of a photon. To verify the precision of the theoretical model, a dust environment laboratory was designed and built to evaluate the performance of laser fuzes in different dust environments. Therefore some experiments were completed to derive the echo amplitudes of a laser fuze in the dust environments with different dust concentrations and the results were compared with corresponding simulation results of H-G scattering phase function and T-matrix method. The simulation results show that echo powers are increased with the increase of dust concentrations and relative humidity. And the method based on T-matrix scattering phase function has a better consistency with the experiment and is more stable, especially in denser dust environments.
    ${P_{{\rm{HG}}}}{\rm{(}}\theta ,g{\rm{) = }}\frac{{1 - {g^2}}}{{{{\left( {1 + {g^2} - 2g\cos \theta } \right)}^{1.5}}}}$(1)

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    $\left[ {\begin{array}{*{20}{c}} {{p}} \\ {{q}} \end{array}} \right]{ = { T}}\left[ {\begin{array}{*{20}{c}} {{a}} \\ {{b}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {{{{T}}^{{\rm{11}}}}}&{{{{T}}^{{\rm{12}}}}} \\ {{{{T}}^{{\rm{21}}}}}&{{{{T}}^{{\rm{22}}}}} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{a}} \\ {{b}} \end{array}} \right]$(2)

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    $\begin{split} {C_{{\rm{ext}}}} = & - \frac{1}{{{k^2}{{\left| {{{E}}_0^{{\rm{inc}}}} \right|}^2}}}{\rm{Re}} \sum\limits_{n = 1}^\infty {\sum\limits_{m = - n}^n {\left[ {{a_{mn}}{{({p_{mn}})}^ * } + {b_{mn}}{{({q_{mn}})}^ * }} \right]} } =\\ & - \frac{{2\pi }}{{{k^2}}}{\rm{Re}} \sum\limits_{n = 1}^\infty {\sum\limits_{m = - n}^n {\left[ {T_{mnmn}^{11} + T_{mnmn}^{22}} \right]} } \end{split} $(3)

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    $\begin{split} {C_{{\rm{sca}}}} = &\frac{1}{{{k^2}{{\left| {{{E}}_0^{{\rm{inc}}}} \right|}^2}}}\sum\limits_{n = 1}^\infty {\sum\limits_{m = - n}^n {\left[ {{{\left| {{p_{mn}}} \right|}^2} + {{\left| {{q_{mn}}} \right|}^2}} \right]} } = \\ &\frac{{2\pi }}{{{k^2}}}\sum\limits_{n = 1}^\infty {\sum\limits_{n' = 1}^\infty {\sum\limits_{m = - n}^n {\sum\limits_{m' = - n'}^{n'} {\sum\limits_{i = 1}^2 {\sum\limits_{j = 1}^2 {{{\left| {T_{mnm'n'}^{ij}} \right|}^2}} } } } } } \\ \end{split}$(4)

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    $\begin{split} {\mu _t} = N{C_{\rm ext}},\;\;\;\;&{{\mu _s} = N{C_{\rm sca}}} \end{split} $(5)

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    $g = 2\pi \frac{{{C_{{\rm{ext}}}}}}{{{C_{{\rm{sca}}}}}}\int_0^\pi {{a_1}(\theta )\cos\theta \sin\theta {\rm{d}}\theta } $(6)

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    ${a_1}(\theta ) = \sum\limits_{s = 0}^\infty {a_1^s} P_{00}^s(\cos\theta )\begin{array}{*{20}{c}} ,&{a_1^s = g_{00}^s + g_{0 - 0}^s} \end{array}$(7)

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    $\frac{1}{2}\int_0^\pi {{a_1}(\theta )\sin \theta } {\rm{d}}\theta = 1$(8)

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    $\cos (\theta ) = \left\{ {\begin{array}{*{20}{l}} {\dfrac{1}{{2g}}\left[ {1{\rm{ + }}{g^2} - {{(\dfrac{{1 - {g^2}}}{{1 - g + 2g\xi }})}^2}} \right],\;g \ne 0} \\ {2\xi - 1,\;g = 0} \end{array}} \right.$(9)

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    ${P_i}(\theta ) = \sum\limits_1^i {{a_1}({\theta _i})\sin } ({\theta _i})\Bigg/\sum\limits_1^{1\;801} {{a_1}({\theta _i})\sin } ({\theta _i})$(10)

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    $\left\{ {\begin{array}{*{20}{c}} {u' = \dfrac{{\sin {\theta _m}}}{{\sqrt {1 - {w^2}} }}(uw\cos\phi - v\sin\phi ) + u\cos {\theta _m}} \\ {v' = \dfrac{{\sin {\theta _m}}}{{\sqrt {1 - {w^2}} }}(vw\cos\phi + u\sin\phi ) + v\cos {\theta _m}} \\ {w' = - \sin {\theta _m}\cos \phi \sqrt {1 - {w^2}} + w\cos {\theta _m}} \end{array}} \right.$(11)

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    $\left\{ {\begin{array}{*{20}{c}} {u' = \sin {\theta _m}\cos \varphi } \\ {v' = \sin {\theta _m}\sin \varphi } \\ {w' = w\cos {\theta _m}/\left| w \right|} \end{array}} \right.$(12)

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    ${E_m} = \frac{1}{{4\pi }}{a_1}(\theta ')\Delta \Omega {{\rm e}^{( - {\mu _t}{R_m})}}{\omega _m}$(13)

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    ${\omega '_m} = \left(1 - \frac{1}{{4\pi }}{a_1}(\theta ')\Delta \Omega {{\rm e}^{( - {\mu _t}{R_m})}}\right){\omega _m}$(14)

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    $C = {C_0}{{\rm e}^{ - \alpha t}}$(15)

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    $\left(\frac{1}{N} + \frac{{{k_0}}}{\beta }\right) = \left(\frac{1}{{{N_0}}} + \frac{{{k_0}}}{\beta }\right){{\rm e}^{\beta t}}$(16)

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    $\left\{ \begin{array}{l} {m_{re}} = {m_{rw}} + ({m_r} - {m_{rw}})fr{h^{ - 3}} \\ \dfrac{{{m_{ie}}}}{{m_{re}^2 + 2}} = \dfrac{{{m_{iw}}}}{{m_{rw}^2 + 2}} + \left(\dfrac{{{m_i}}}{{m_r^2 + 2}} - \dfrac{{{m_{iw}}}}{{m_{rw}^2 + 2}}\right)fr{h^{ - 3}} \\ fr{h^{ - 3}} = \dfrac{{{r_e}}}{r} = {(1 - {\rm{RH}})^{ - \frac{1}{\upsilon }}} \end{array} \right.$(17)

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    Jiaqian Bao, Bingting Zha, He Zhang, Chenyoushi Xu. Simulation method of pulse laser fuze echo in dust environment[J]. Infrared and Laser Engineering, 2021, 50(5): 20200319
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