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从图 3可以看出,入射激光经探测器反射之后不能全部返回,一部分激光因传播方向的原因不能经透镜射出[15]。为探究“猫眼”回波通过率与激光入射角之间的关系,假设“猫眼”光学系统为理想光学系统,利用几何光学的方法,将“猫眼”光学系统等效为如图 3所示的4f等效模型[11-12]。其中, 通光孔径为D, 汇聚透镜焦距为f,探测器直径为Φ,激光入射角(入射激光光轴与光学系统光轴的夹角)为ω,出射激光与光轴的夹角为ω′。当入射角超过导引头的视角时(即ω>arctan(Φ/2f), arctan(Φ/2f)为导引头的视角)汇聚点会落在焦平面探测器之外,无法在探测器平面形成反射,可能不会产生原路返回的“猫眼”回波。
由于激光在探测器平面的反射包括镜面反射和漫反射,假设探测器平面的反射率为ρ,反射光束中80%为镜面反射,20%为漫反射,且光束能量分布均匀。则出射激光占反射激光的比例η(本文中将“猫眼”效应过程中的比值η简称为回波通过率)为[16] :
$ \begin{array}{*{20}{c}} {\eta = \left\{ {1 - \cos \left[ {\arctan \left( {\frac{D}{{2f}} - \tan \omega } \right)} \right]} \right\}/}\\ {\left\{ {1 - \cos \left[ {0.5\arctan \left( {\frac{D}{{2f}} + \tan \omega } \right) + 0.5\arctan \left( {\frac{D}{{2f}} - \tan \omega } \right)} \right]} \right\} \times }\\ {80\% + \left( {1 - D/\sqrt {4{f^2} + {D^2}} } \right) \times 20\% } \end{array} $
(1) 图 4为激光入射角与回波通过率之间的关系图。
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“猫眼”回波探测设备一般与干扰光源处于同一位置,干扰激光照射导引头成像设备,产生并返回“猫眼”光斑,再由回波探测设备接收,激光主动探测过程如图 5所示[9]。如果干扰光源与回波接收设备相距较远,导致探测设备接收返回激光束的入射角增大,对“猫眼”光斑探测造成影响。
从图 3的光路图可以发现,光束入射角ω与出射角ω′始终相同,“猫眼”回波具有原路返回的特点。设接收回波探测设备到干扰光源的距离为Δl,导引头到接收探测组件的距离为l,其中$,则探测接收到的“猫眼”回波入射角为φ=Δl/l。若回波探测组件靠近照射源组件的位置,则回波入射角可以忽略不计。
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假设发射激光的平均功率为P,波长为λ,发散角为θ,发射系统的激光透过率为τs,大气对该波长激光的透过率为τ,成像导引头光学系统的透过率为τt,通光孔径为Dt,探测器平面激光反射率为ρ,返回光的发散角为θ′,接收“猫眼”光斑的探测光学系统透过率为τr,通光孔径为Dr,激光入射角为ω, 回波入射角为φ。
大气透过率τ与衰减系数μ(λ)以及干扰距离L有关,关系如下[17]:
$ \tau = \exp [ - \mu (\lambda )L] $
(2) 由高斯激光的衍射积分法,可得发射激光经大气传输到达成像导引头标探测器平面的干扰功率为[7, 18] :
$ {P_s} = \frac{{0.865P{\tau _s}\tau {\tau _1}D_1^2}}{{4{L^2}{\theta ^2}}}\cos \omega $
(3) 经导引头返回的光束也近似满足高斯激光的特点,因此接收探测器平面的回波功率为:
$ {P_{\rm{r}}} = \frac{{0.865{P_{\rm{s}}}\rho \eta {\tau _{\rm{t}}}\tau {\tau _{\rm{r}}}D_{\rm{r}}^2}}{{4{L^2}{\theta ^2}}}\cos \varphi $
(4) 若定义导引头探测器平面的功率Ps为干扰功率,回波接收探测器平面的功率Pr为回波功率。从数学表达式可以看出,回波功率与干扰功率具有很强的相关性,其比值δ为:
$ \delta = \frac{{{P_s}}}{{{P_r}}} = \frac{{0.865\rho \eta {\tau _1}\tau {\tau _r}D_r^2}}{{4{L^2}{\theta ^2}}}\cos \varphi $
(5) 式中, 除变量ω和L外, 其它量可视为常量,因此掌握ω, L的变化情况即可掌握Ps, Pr之间的关系。
“猫眼”效应在激光干扰效果实时评估中的应用
The application of "cat-eye" effect in real-time evaluation of laser directional jamming effect
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摘要: 为了对非合作条件下激光干扰效果进行实时评估,根据“猫眼”效应形成原理,提出一种利用猫眼回波强度来评估激光干扰效果的新方法。分析了激光入射角、激光发射功率与距离对“猫眼”回波功率的影响,研究并实验验证了“猫眼”回波功率与光电成像系统被激光干扰效果之间的关系。结果表明,“猫眼”回波功率受激光干扰距离和干扰激光入射角影响最大, 当对抗反坦克导弹时,回波探测器离激光源的距离超过50m, 回波功率和干扰持续时间显著下降,可见“猫眼”效应原理用于激光定向干扰效果实时评估是可行的。这一结论对激光定向干扰设备技术研究具有一定的参考意义。Abstract: In order to evaluate the effect of laser interference under non-cooperative conditions, a new method was proposed to evaluate the effect of laser interference by using "cat-eye" echo intensity by the forming principle of "cat-eye effect". The influence of laser incidence angle, laser jamming power, and distance on the echo power of "cat-eye" was analyzed. The relationship between the power of "cat-eye" echo and the laser jamming effect of the photoelectric imaging system was obtained. The results show that the echo power of the "cat-eye" was mostly affected by the laser interference distance and the interference laser incidence angle, and the echo power and interference duration decreased significantly when the distance of the echo detector from the laser source exceeded 50m while jamming anti-tank missiles. It was feasible to apply the principle of "cat-eye" effect to evaluate the effect of laser directional jamming in real time. The conclusion had certain reference significance for laser directional jamming equipment.
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Key words:
- laser technique /
- effectiveness evaluation /
- "cat-eye" effect /
- geometrical optics /
- echo power
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