• 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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    $\left[ {pq} \right]{ = { T}}\left[ {ab} \right] = \left[ {T11T12T21T22} \right]\left[ {ab} \right]$(2)

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    $Cext=1k2|E0inc|2Ren=1m=nn[amn(pmn)+bmn(qmn)]=2πk2Ren=1m=nn[Tmnmn11+Tmnmn22] $(3)

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    $Csca=1k2|E0inc|2n=1m=nn[|pmn|2+|qmn|2]=2πk2n=1n=1m=nnm=nni=12j=12|Tmnmnij|2$(4)

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    $μt=NCext,μs=NCsca $(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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    ${a_1}(\theta ) = \sum\limits_{s = 0}^\infty {a_1^s} P_{00}^s(\cos\theta ),a1s=g00s+g00s$(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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    $\cos (\theta ) = \left\{ {12g[1+g2(1g21g+2gξ)2],g02ξ1,g=0} \right.$(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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    $\left\{ {u=sinθm1w2(uwcosϕvsinϕ)+ucosθmv=sinθm1w2(vwcosϕ+usinϕ)+vcosθmw=sinθmcosϕ1w2+wcosθm} \right.$(11)

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    $\left\{ {u=sinθmcosφv=sinθmsinφw=wcosθm/|w|} \right.$(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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    $\left\{ mre=mrw+(mrmrw)frh3miemre2+2=miwmrw2+2+(mimr2+2miwmrw2+2)frh3frh3=rer=(1RH)1υ \right.$(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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