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系统组成图见图1,终端发射采用1550 nm的激光器,激光通信终端采用OOK调制,直接探测的通信体制,望远镜口径为60 mm,中心30 mm作为发射用,其外围口径用于接收,采用收发空间分离的方式实现双工通信,通信和跟踪共用同一个通信光源,并共用同一个通信探测器,捕获跟踪采用双棱镜调节的方案,可以满足±30°的建链角度范围要求,并减少了两轴跟踪架等结构,降低了资源消耗。在其焦平面处放置QAPD 作为接收探测器,QAPD的四象限信号相减后作为位置跟踪信号,相加后作为通信信号。激光链路的捕获跟踪采用旋转棱镜的方案,根据QAPD位置信号,旋转棱镜,调节望远镜的光束指向,实现通信光链路的稳定。
图2为旋转双棱镜光束指向系统的结构示意图。两直角折射棱镜Π1和Π2的X、Y轴平行于棱镜直角垂直面,双棱镜XOY面相互平行且垂直于Z轴。双棱镜的XOY平面可绕共同中心轴Z独立旋转。
设棱镜Π1入射光束为单位矢量
${{s}_i}$ ,棱镜Π1左侧斜界面法线矢量可表示为${{{{n}}_1}}$ ,α1为棱镜Π1的顶角,θ1为棱镜Π1尖端指向与X轴正向间的夹角,应用矢量形式的斯涅尔定律可得棱镜Π1左侧斜界面折射光线矢量为${{s}_1^{{r}}}$ [12-16]:$$ {{{{n}}_1}} =({\rm{sin}}{\alpha _1}{\rm{cos}}{\theta _1},\;{\rm{sin}}{\alpha _1}\sin {\theta _1},\;{\rm{cos}}{\alpha _1})$$ (1) $$ {{{s}}_1^{{r}}} =\dfrac{1}{{{n}}}\left[{{s_i}} - \left({{s_i}} . {{ n_1}} \right) {{ n_1}} \right] - {{ n_1}} \sqrt {1 - \dfrac{1}{{{n^2}}} + \dfrac{1}{{{n^2}}}{{\left({{s_i}} . {{ n_1}} \right)}^2}} $$ (2) 棱镜Π1右侧垂直界面和棱镜Π2左侧垂直界面相互平行,相当于平行光板,不改变光束的传播方向,Π2右侧斜界面的入射光线与Π1左侧斜界面的出射折射光线矢量一致,因此入射到棱镜Π2右侧斜界面的入射光线矢量为
${{{s}}_1^{{r}}}$ 。棱镜Π2右界面的法线矢量为${{{{n}}_2}}$ ,α2为棱镜Π2的顶角,θ2为棱镜Π2尖端指向与X轴正向间的夹角,则出射光线矢量为$ {s_2^{{r}}}$ :$$ {{{{n}}_2}} =({\rm{ - sin}}{\alpha _2}{\rm{cos}}{\theta _2},\;{\rm{ - sin}}{\alpha _2}\sin {\theta _2},\;{\rm{cos}}{\alpha _2})$$ (3) $$ { s_2^{{r}}} {{ = n}}\left[ { s_1^{{r}}} - \left( { s_1^{{r}}} . {{ n_2}} \right){{ n_2}} \right] - {{ n_2}} \sqrt {1 - {n^2} + {n^2}{{\left({ s_1^{{r}}} . {{ n_2}} \right)}^2}} $$ (4) 由公式(1)~(4)可计算出入射光线、出射光线和棱镜旋转角度之间的关系,从而实现光束的指向和调控。
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设本星的位置矢量为
${ A}_{01}$ ,对方星的位置矢量为${ B}_{02}$ 。根据星上GNSS设备可得卫星的轨道6根数,${\Omega _A}$ 为本星轨道的升交点赤经,${i_A}$ 为轨道倾角,${\omega _A}$ 为近地点角,先绕Z轴旋转${\Omega _A}$ ,再绕X轴旋转${i_A}$ ,最后绕Z轴旋转${\omega _A}$ ,则有地心轨道焦点坐标系下粗指向矢量${\Delta { \rho _E}}$ 为:$$ {\Delta { \rho }_{E}}={ R}_{ {\textit{z}}}({\omega }_{A}){ R}_{x}({i}_{A}){ R}_{ {\textit{z}}}({\Omega }_{A})({B_{02}}-{A_{01}}) $$ (5) 其中:
$$ \begin{array}{*{20}{l}} {{ R_x}(\alpha ) = \left[ {\begin{array}{*{20}{c}} 1&0&0\\ 0&{c\alpha }&{s\alpha }\\ 0&{ - s\alpha }&{c\alpha } \end{array}} \right]{ R_y}(\alpha ) = \left[ {\begin{array}{*{20}{c}} {c\alpha }&0&{ - s\alpha }\\ 0&1&0\\ {s\alpha }&0&{c\alpha } \end{array}} \right]}\\ {{ R_z}(\alpha ) = \left[ {\begin{array}{*{20}{c}} {c\alpha }&{s\alpha }&0\\ { - s\alpha }&{c\alpha }&0\\ 0&0&1 \end{array}} \right]} \end{array} $$ 式中:cα,sα分别代表了角度的余弦、正弦值;
${ R_*}(\cdot)$ 代表了绕*轴转动的旋转矩阵。以面向旋转轴看,逆时针旋转为正,顺时针为负。设ε为真近点角,卫星轨道坐标系矢量为
${\Delta { \rho _O}}$ ,卫星本体坐标系矢量为${\Delta { \rho _{BEN}}}$ ,姿态角分别为滚动角φA,俯仰角θA和偏航角ψA,先绕X轴顺时针旋转90°,再绕Y轴旋转(270°-ε),得到卫星轨道系下坐标,然后按照ZXY的顺序旋转,则有卫星本体坐标系指向为:$$ {\Delta { \rho }_{BEN}}={ R}_{{y}}({\theta }_{A}){ R}_{{x}}({\phi }_{A}){ R}_{{ {\textit{z}}}}({\psi }_{A}){ R}_{{y}}\left(\dfrac{3\pi }{2}-\varepsilon \right){ R}_{{x}}\left(-\dfrac{\pi }{2}\right){\Delta { \rho }_{E}}$$ (6) 光通信终端坐标系矢量为
${\Delta { \rho _{SOLVE}}}$ ,η1、ζ1、γ1 为卫星本体坐标系到光学终端安装棱镜的安装矩阵对应角度,光学终端安装棱镜坐标系到光学终端坐标系的安装矩阵对应角度为 η2、ζ2 、γ2,均按照ZXY的顺序旋转,则有: $$ {\Delta { \rho _{SOLVE}}} ={{{ R}}_y}{\rm{(}}{\zeta _2}{\rm{)}}{{{R}}_x}{\rm{(}}{\gamma _2}{\rm{)}}{{{R}}_{{ {\textit{z}}}}}{\rm{(}}{\eta _2}{\rm{)}}{{\rm{R}}_y}{\rm{(}}\zeta _1 {\rm{)}}{{{ R}}_x}{\rm{(}}\gamma _1 {\rm{)}}{{{ R}}_{{ {\textit{z}}}}}{\rm{(}}\eta _1 {\rm{)}}{\Delta { \rho _{{\rm{BEN}}}}} $$ (7) 在公式(2)和(4)的基础上,已知光的输入为沿Z向的单位矢量和输出为
${\Delta { \rho _{SOLVE}}}$ ,求出双棱镜转动的角度,从而实现指向。 -
扫描方式采取螺旋曲线方式,如图3所示,小圆圈为单激光光束束散角覆盖范围,大圆圈为激光通信载荷指向不确定区域范围,正方形及序号表示由内至外的扫描顺序。
根据双棱镜指向输出计算偏转角和方位角,坐标系定义如图2所示,偏转角
$\varphi $ 为出射光矢量与Z轴负方向的夹角,方位角$\theta $ 为出射光矢量在XOY平面的投影与X轴之间的夹角,计算出偏转角φ、方位角θ,设计算的出射矢量为${{{{ r}}_0}} =(k,l,m)$ ,$$\varphi {\rm{ = acos}}({\rm{ - m}})$$ (8) $$\theta =\left\{ {\begin{array}{*{20}{c}} \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! {{{\arctan }}({{l}}/k);k > 0,l \geqslant 0} \\ {{{\arctan }}(l/k) + 2\pi ;k > 0,l < 0} \\ \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! \!\!\!\!\!\! {{{\arctan }}(l/k) + \pi ;k < 0} \end{array}} \right.$$ (9) $xscan$ 为X方向扫描步进索引,$stepval$ 为步进量,${{DxScan}}$ 为X方向扫描偏置点,$yscan$ 为Y方向扫描步进,${{DyScan}}$ 为Y方向扫描偏置点,则出射矢量为${{ T_0}} = $ $ ({{x}},{{y}},{\rm{ - 1}})$ ,其中$$ \left\{ \begin{array}{l} x = \tan \varphi \cos \theta + xscan \times stepval{{ + DxScan}}\\ y = \tan \varphi \sin \theta + yscan \times stepval{{ + DyScan}}\\ {{{\textit{z}} = - 1}} \end{array} \right. $$ (10) 在公式(2)和(4)的基础上,已知光的输入为沿着Z轴方向的单位矢量,采用公式(9)~(11)输出为单位化的出射矢量,求出双棱镜转动的角度,从而实现矩形螺旋扫描。
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四象限探测器光敏面通过两条相互垂直的死区线分割为A、B、C、D四部分。由于收发环形空间分离的特性,QAPD上的入射光斑为圆环形且能量分布均匀,照射在光敏面上的光斑被四个象限分成四个部分。由于光电效应,对应的四个象限的感光面电极将光能转换成电能,产生大小为IA、IB、IC、ID的光生电流。当光斑中心在QAPD光敏面的位置改变时,QAPD各象限上的光斑面积也会改变,导致各象限光生电流的变化,通过一定的建模方法计算出环形光斑的圆心位置[17-18]。
用σx、σy表示QAPD光敏面X、Y轴上建立模型后的相对偏移量,EA、EB、EC、ED表示激光光斑入射到QAPD各个象限上的光能量,由于空间激光通信距离遥远,且无大气干扰,因此光强均匀分布,可以用激光入射到该象限中的光斑面积表示光能量,SA、SB、SC、SD分别表示入射到各个象限上光斑的面积,所以:
$$ \begin{split} {\sigma _{{x}}}=&\dfrac{{\left( {{{{I}}_{\rm{A}}}+{{{I}}_{\rm{D}}}} \right){\rm{ - }}\left( {{{{I}}_{\rm{B}}}+{{{I}}_{\rm{C}}}} \right)}}{{{{{I}}_{\rm{A}}}+{{{I}}_{\rm{B}}}+{{{I}}_{\rm{C}}}+{{{I}}_{\rm{D}}}}}=\dfrac{{\left( {{{{E}}_{\rm{A}}}+{{{E}}_{\rm{D}}}} \right){\rm{ - }}\left( {{{{E}}_{\rm{B}}}+{{{E}}_{\rm{C}}}} \right)}}{{{{{E}}_{\rm{A}}}+{{{E}}_{\rm{B}}}+{{{E}}_{\rm{C}}}+{{{E}}_{\rm{D}}}}}=\\ &\dfrac{{\left( {{{{S}}_{\rm{A}}}+{{{S}}_{\rm{D}}}} \right){\rm{ - }}\left( {{{{S}}_{\rm{B}}}+{{{S}}_{\rm{C}}}} \right)}}{{{{{S}}_{\rm{A}}}+{{{S}}_{\rm{B}}}+{{{S}}_{\rm{C}}}+{{{S}}_{\rm{D}}}}} \end{split} $$ (11) $$ \begin{split} {\sigma _y} = &\dfrac{{\left( {{I_{{\rm A}}} + {I_{{\rm B}}} } \right) - \left( {{I_{{{\rm C}}}} + {I_{{{\rm D}}}} } \right)}}{{{I_{{\rm A}}} + {I_{{\rm B}}} + {I_{{{\rm C}}}} + {I_{{{\rm D}}}} }} = \dfrac{{\left( {{E_{\rm A}} + {E_{\rm B}}} \right) - \left( {{E_{{\rm C}}} + {E_{{\rm D}}}} \right)}}{{{E_{\rm A}} + {E_{\rm B}} + {E_{{\rm C}}} + {E_{{\rm D}}}}} =\\ & \dfrac{{\left( {{S_{{\rm A}}}+{S_{\rm B}}} \right){\rm{ - }}\left( {{S_{{\rm C}}}+{S_{{\rm D}}}} \right)}}{{{S_{\rm A}}+{S_{\rm B}}+{S_{{\rm C}}}+{S_{{\rm D}}}}} \end{split} $$ (12) 由此可以看出,相对偏移量
$ {\sigma }_{x} $ 、$ {\sigma }_{y} $ 能够反映光斑位置的变化,假设光斑外径为R,内径为r,光斑中心坐标为(x0,y0),利用几何知识求出每个象限中光斑的面积,代入公式(12),(13)可得:$$ \begin{split} {\sigma _x} = &\dfrac{1}{{\pi ({R^2} - {r^2})}}\Bigg(2{R^2}{\arcsin }\dfrac{{{x_0}}}{R} + 2{x_0}\sqrt {{R^2} - {x_0}^2} -\\ & 2{r^2}{\arcsin}\frac{{{x_0}}}{r} - 2{x_0}\sqrt {{r^2} - {x_0}^2} \Bigg) \\ \end{split} $$ (13) $$ \begin{split} {\sigma _y} = &\dfrac{1}{{\pi ({R^2} - {r^2})}}\Bigg(2{R^2}{\arcsin }\dfrac{{{y_0}}}{R} + 2{y_0}\sqrt {{R^2} - {y_0}^2} - \\ & 2{r^2}{\arcsin }\frac{{{y_0}}}{r} - 2{x_0}\sqrt {{r^2} - {y_0}^2} \Bigg) \\ \end{split} $$ (14) 由公式(14)、(15)可以看出,通常情况下,由于受到光斑大小、光斑实际位置的影响,由偏移量解算公式计算所得的光斑位置与光斑实际位置并不呈线性关系。在光斑大小保持不变的情况下,仅当光斑离开坐标原点很小时,即
$ \left|{x}_{0}\right| $ 、$ \left|{y}_{0}\right| $ 均远小于光斑半径r时,有:$${x_0}=\frac{{\pi (R+r)}}{4}{\sigma _x}$$ (15) $${{{y}}_0}=\frac{{\pi (R+r)}}{4}{\sigma _y}$$ (16) 由公式(16)、(17)解算出QAPD的入射光线,即双棱镜的出射光线,根据双棱镜公式和编码器的角度值计算出双棱镜的入射光线,当出射光线为沿Z轴方向的单位矢量时,计算出此时双棱镜需要旋转的角度,实现系统的双向互锁,系统进入跟踪状态。
XY-2 satellite laser communication equipment PAT test in orbit
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摘要: 针对低轨小卫星星座的通信需求,设计了基于双棱镜和四象限雪崩光电二极管(QAPD)结构收发同轴的激光通信载荷,该方案是无信标光体制,具有体积小、轻量化和大视场的特点。文中针对双棱镜结构,给出了双棱镜输入输出光线的计算模型,在此基础上,提出了星间指向、捕获和跟踪的实现方式,并在XY-2号卫星上进行了在轨测试和验证,进行指向测试时,更新了指向偏移量,标定了QAPD跟踪点,并进行了双向建链测试。进行了15次双向建链测试表明,该激光通信载荷捕获时间小于20 s,捕获成功率达到100%,捕获后双星建链时间优于2 s,建链测试成功率达到了93%,建链后跟踪精度RMS值小于30 μrad。Abstract: According to the communication requirements of Leo satellite constellation, a laser communication equipment structure based on double Risley prisms and quadrant avalanche photodiode (QAPD) was designed. The scheme was beaconless optical system. It had the characteritics of small size, low weight and large field of view. In this paper, the calculation model of input and output light of double Risley prisms structure was given. On this basis, the interstellar of pointing, capturing and tracking was proposed, then in orbit test and verification were carried out on XY-2 satellite. The pointing offset was updated, based on pointing test, the QAPD tracking point was calibrated, and the two-way link up with the XY-2 satellite test was carried out. The bidirectional chain building test which was repeated 15 times showed that the acquisition time of the laser communication equipment was less than 20 s, and the acquisition success ratio was 100%. After the acquisition, the chain building time of the two satellites was better than 2 s and the linking success ratio reached 93%, and the RMS value of tracking accuracy was less than 30 μrad.
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Key words:
- laser communication /
- double Risley prisms /
- pointing /
- capturing /
- tracking
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