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    Journals >Infrared and Laser Engineering >Volume 49 >Issue 7 >Page 20190453 > Article
    • Infrared and Laser Engineering
    • Vol. 49, Issue 7, 20190453 (2020)
    Modeling research on angle measurement accuracy of four-quadrant detector of laser seeker
    Xiong Qiu, Shicheng Wang, Zhiguo Liu, and Weibo Xu
    Author Affiliations
  • 火箭军工程大学，陕西 西安 710025
    • show less
    DOI: 10.3788/IRLA20190453 Cite this Article
    Xiong Qiu, Shicheng Wang, Zhiguo Liu, Weibo Xu. Modeling research on angle measurement accuracy of four-quadrant detector of laser seeker[J]. Infrared and Laser Engineering, 2020, 49(7): 20190453 Copy Citation Text show less

    Abstract

    The accuracy of the four-quadrant detector on the target directly affects the guidance precision of the laser guided weapon. Therefore, it is very important to study the accuracy of the four-quadrant detector. In this paper, the method of computation and simulation analysis was adopted, based on the uniform distribution of the pulse peak power density at the entrance of the seeker, and the noise interference current obeyed the Gaussian distribution, and the beam deflection angle error model of the laser seeker was established; however, the beam deflection angle error had random probability due to noise interference, so the mean and standard deviation of the beam deflection angle error were used as the measurement of the four-quadrant detector angle measurement accuracy. The relationship was established between the mean and standard deviation of the beam deflection angle error and the optical parameters of the seeker, the spot radius, the incident angle of the diffuse reflection laser, the noise interference current, and the pulse peak power density at the entrance of the seeker. Taking the standard deviation of the deflection angle of the seeker beam as an example, the simulation analysis was carried out in combination with the application background.

    Keywords

    ${I_i} = {R_{\rm{P}}} \cdot {\rho _s} \cdot {S_i}\begin{array}{*{20}{c}} {}&{i = A,B,C,D} \end{array}$(1)

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    ${U_i} = {K_1} \cdot {R_{A \to V}} \cdot {I_i}$(2)

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    $\left\{ {\begin{aligned} & {\Delta x = \frac{{({U_A} + {U_D}) - ({U_B} + {U_C})}}{{{U_A} + {U_B} + {U_C} + {U_D}}}} \\ & {\Delta y = \frac{{({U_A} + {U_B}) - ({U_C} + {U_D})}}{{{U_A} + {U_B} + {U_C} + {U_D}}}} \end{aligned}} \right.$(3)

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    $\left\{ {\begin{aligned} & {\Delta x = \frac{{({S_A} + {S_D}) - ({S_B} + {S_C})}}{{{S_A} + {S_B} + {S_C} + {S_D}}}} \\ & {\Delta y = \frac{{({S_A} + {S_B}) - ({S_C} + {S_D})}}{{{S_A} + {S_B} + {S_C} + {S_D}}}} \end{aligned}} \right.$(4)

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    $\left\{ \begin{aligned} & {S_{s(aobc)}} = \frac{1}{2}{r^2} \cdot {\theta _1} \\ & {S_{s(aobd)}} = {\text{π}} \cdot {r^2} - \frac{1}{2}{r^2} \cdot {\theta _1} \\ & {S_{\Delta (aob)}} = {x_0} \cdot \sqrt {{r^2} - {x_0}^2} \\ & {\theta _1} = {\text{π}} + 2\arcsin \left(\dfrac{{{x_0}}}{r}\right) \end{aligned} \right.$(5)

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    $\left\{ \begin{aligned} & {S_A} + {S_D} = {r^2}\left(\frac{{\text{π}} }{2} + \arcsin \left(\frac{{{x_0}}}{r}\right)\right) + {x_0} \cdot \sqrt {{r^2} - x_0^2} \\ & {S_B} + {S_C} = {r^2}\left(\frac{{\text{π}} }{2} - \arcsin \left(\frac{{{x_0}}}{r}\right)\right) - {x_0} \cdot \sqrt {{r^2} - x_0^2} \end{aligned} \right.$(6)

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    $\left\{ \begin{aligned} & \Delta x = \frac{2}{{\text{π}} }\left[ {\arcsin \left(\frac{{{x_0}}}{r}\right) + \frac{{{x_0}}}{r}\sqrt {1 - {{\left(\frac{{{x_0}}}{r}\right)}^2}} } \right]\begin{array}{*{20}{c}} {}&{\left| {\dfrac{{{x_0}}}{r}} \right| \leqslant 1} \end{array} \\ & \Delta y = \frac{2}{{\text{π}} }\left[ {\arcsin \left(\frac{{{y_0}}}{r}\right) + \frac{{{y_0}}}{r}\sqrt {1 - {{\left(\frac{{{y_0}}}{r}\right)}^2}} } \right]\begin{array}{*{20}{c}} {}&{\left| {\dfrac{{{y_0}}}{r}} \right| \leqslant 1} \end{array} \end{aligned} \right.$(7)

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    $\left\{ \begin{aligned} & {x_0} \approx \frac{{{\text{π}} \cdot r}}{4}\Delta x \\ & {y_0} \approx \frac{{{\text{π}} \cdot r}}{4}\Delta y \end{aligned} \right.$(8)

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    $\left\{ \begin{aligned} & \tan \psi = \frac{{{x_0}}}{{{f_{\rm{x}}}}} \\ & \tan \theta = \frac{{{y_0}}}{{\sqrt {f_{\rm{x}}^2 + x_0^2} }} \end{aligned} \right.$(9)

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    $\left\{ \begin{aligned} & \psi \approx \frac{{{x_0}}}{{{f_{\rm{x}}}}} \approx \frac{{{\text{π}} r}}{{4{f_{\rm{x}}}}}\frac{{({I_A} + {I_D}) - ({I_B} + {I_C})}}{{{I_A} + {I_B} + {I_C} + {I_D}}} \\ &\theta \approx \frac{{{y_0}}}{{{f_{\rm{x}}}}} \approx \frac{{{\text{π}} r}}{{4{f_{\rm{x}}}}}\frac{{({I_A} + {I_B}) - ({I_C} + {I_D})}}{{{I_A} + {I_B} + {I_C} + {I_D}}} \end{aligned} \right.$(10)

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    $\left\{ \begin{aligned} & {\psi _N} = \frac{{{\text{π}} r}}{{4{f_{\rm{x}}}}}\frac{{({I_A} + {i_A} + {I_D} + {i_D}) - ({I_B} + {i_B} + {I_C} + {i_C})}}{{{I_A} + {I_B} + {I_C} + {I_D} + {i_A} + {i_B} + {i_C} + {i_D}}} \\ &{\theta _N} = \frac{{{\text{π}} r}}{{4{f_{\rm{x}}}}}\frac{{({I_A} + {i_A} + {I_B} + {i_B}) - ({I_C} + {i_C} + {I_D} + {i_D})}}{{{I_A} + {I_B} + {I_C} + {I_D} + {i_A} + {i_B} + {i_C} + {i_D}}} \end{aligned} \right.$(11)

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    $\left\{ \begin{aligned} & \Delta \psi = {\psi _N} - \psi \\ & \Delta \theta = {\theta _N} - \theta \end{aligned} \right.$(12)

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    $\left\{ \begin{aligned} &\Delta {{\psi }} \approx \frac{{{\text{π}} r}}{{4{f_{\rm{x}}}}}\left[ {\frac{{({I_{AD}} + {i_{AD}}) - ({I_{BC}} + {i_{BC}})}}{{{I_{AD}} + {i_{AD}} + {I_{BC}} + {i_{BC}}}} - \frac{{{I_{AD}} - {I_{BC}}}}{{{I_{AD}} + {I_{BC}}}}} \right] \\ &\Delta \theta \approx \frac{{{\text{π}} r}}{{4{f_{\rm{x}}}}}\left[ {\frac{{({I_{AB}} + {i_{AB}}) - ({I_{CD}} + {i_{CD}})}}{{{I_{AB}} + {i_{AB}} + {I_{CD}} + {i_{CD}}}} - \frac{{{I_{AB}} - {I_{CD}}}}{{{I_{AB}} + {I_{CD}}}}} \right] \end{aligned} \right.$(13)

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    $\left\{ \begin{aligned} & {E_\psi } = \frac{{{\text{π}} \cdot r}}{{4{f_{\rm{x}}}}}\left[ {2\frac{{{I_{BC}} \cdot {i_{AD}} - {I_{AD}} \cdot {i_{BC}}}}{{{{({I_{AD}} + {I_{BC}})}^2}}}} \right] \\ & {E_\theta } = \frac{{{\text{π}} \cdot r}}{{4{f_{\rm{x}}}}}\left[ {2\frac{{{I_{CD}} \cdot {i_{AB}} - {I_{AB}} \cdot {i_{CD}}}}{{{{({I_{AB}} + {I_{CD}})}^2}}}} \right] \end{aligned} \right.$(14)

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    $\left\{ \begin{aligned} & E({E_\psi }) = \frac{{{\text{π}} \cdot r \cdot \mu }}{{4{f_{\rm{x}}}}} \cdot \frac{{({I_B} + {I_C}) - ({I_A} + {I_D})}}{{{{({I_A} + {I_B} + {I_C} + {I_D})}^2}}} \\ & E({E_\theta }) = \frac{{{\text{π}} \cdot r \cdot \mu }}{{4{f_{\rm{x}}}}} \cdot \frac{{({I_C} + {I_D}) - ({I_A} + {I_B})}}{{{{({I_A} + {I_B} + {I_C} + {I_D})}^2}}} \\ &\sigma ({E_\psi }) = \frac{{\sqrt 2 {\text{π}} \cdot r \cdot \sigma }}{{4{f_{\rm{x}}}}}\frac{{\sqrt {{{({I_A} + {I_D})}^2} + {{({I_B} + {I_C})}^2}} }}{{{{({I_A} + {I_B} + {I_C} + {I_D})}^2}}} \\ &\sigma ({E_\theta }) = \frac{{\sqrt 2 {\text{π}} \cdot r \cdot \sigma }}{{4{f_{\rm{x}}}}}\frac{{\sqrt {{{({I_A} + {I_B})}^2} + {{({I_C} + {I_D})}^2}} }}{{{{({I_A} + {I_B} + {I_C} + {I_D})}^2}}} \end{aligned} \right.$(15)

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    $\left\{ {\begin{aligned} & {{I_A} + {I_B} + {I_C} + {I_D} = {P_s} \cdot {S_s} \cdot T \cdot {R_{\rm{P}}}} \\ & {{I_i} = \frac{{{S_i}}}{{{\text{π}} \cdot {r^2}}} \cdot ({I_A} + {I_B} + {I_C} + {I_D})} \end{aligned}} \right.$(16)

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    $\left\{ \begin{aligned} & {\psi _f} = {{{x_0}}}/{{{f_{{x}}}}} \;\;\;\;\;\;\;\; {\theta _f} = {{{y_0}}}/{{{f_{{x}}}}} \\ & {{\Delta f}}/{f} = {r}/{{{R_t}}} \;\;\;\; {f_x} = f - \Delta f \end{aligned} \right.$(17)

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    $\left\{ \begin{aligned} & E\left({E_\psi }\right) = - \dfrac{\mu }{{2\left(1 - \dfrac{r}{{{R_t}}}\right) \cdot f \cdot r \cdot {P_s} \cdot {\text{π}} \cdot {R_t}^2 \cdot T \cdot {R_{\rm{P}}}}} \cdot \left[ {{r^2}\arcsin \left(\dfrac{{{\psi _f}\left(1 - \dfrac{r}{{{R_t}}}\right)f}}{r}\right) + {\psi _f}\left(1 - \dfrac{r}{{{R_t}}}\right)f \cdot \sqrt {{r^2} - {{\left({\psi _f}\left(1 - \dfrac{r}{{{R_t}}}\right)f\right)}^2}} } \right] \\ & E\left({E_\theta }\right) = - \dfrac{\mu }{{2\left(1 - \dfrac{r}{{{R_t}}}\right) \cdot f \cdot r \cdot {P_s} \cdot {\text{π}} \cdot {R_t}^2 \cdot T \cdot {R_{\rm{P}}}}} \cdot \left[ {{r^2}\arcsin \left(\dfrac{{{\theta _f}\left(1 - \dfrac{r}{{{R_t}}}\right)f}}{r}\right) + {\theta _f}\left(1 - \dfrac{r}{{{R_t}}}\right)f \cdot \sqrt {{r^2} - {{\left({\theta _f}\left(1 - \dfrac{r}{{{R_t}}}\right)f\right)}^2}} } \right] \\ & \sigma \left({E_\psi }\right) = \dfrac{1}{{2\left(1 - \dfrac{r}{{{R_t}}}\right) \cdot f \cdot r \cdot SNR}} \cdot \sqrt {\dfrac{{{{\text{π}} ^2} \cdot {r^4}}}{4} + {{\left[ {{r^2}\arcsin \left(\dfrac{{{\psi _f}\left(1 - \dfrac{r}{{{R_t}}}\right)f}}{r}\right) + {\psi _f}\left(1 - \dfrac{r}{{{R_t}}}\right)f \cdot \sqrt {{r^2} - {{\left({\psi _f}\left(1 - \dfrac{r}{{{R_t}}}\right)f\right)}^2}} } \right]}^2}} \\ & \sigma \left({E_\theta }\right) = \dfrac{1}{{2\left(1 - \dfrac{r}{{{R_t}}}\right) \cdot f \cdot r \cdot SNR}} \cdot \sqrt {\dfrac{{{{\text{π}} ^2} \cdot {r^4}}}{4} + {{\left[ {{r^2}\arcsin \left(\dfrac{{{\theta _f}\left(1 - \dfrac{r}{{{R_t}}}\right)f}}{r}\right) + {\theta _f}\left(1 - \dfrac{r}{{{R_t}}}\right)f \cdot \sqrt {{r^2} - {{\left({\theta _f}\left(1 - \dfrac{r}{{{R_t}}}\right)f\right)}^2}} } \right]}^2}} \end{aligned} \right.$(18)

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    Xiong Qiu, Shicheng Wang, Zhiguo Liu, Weibo Xu. Modeling research on angle measurement accuracy of four-quadrant detector of laser seeker[J]. Infrared and Laser Engineering, 2020, 49(7): 20190453
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