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现代光纤陀螺仪的设计和原理(3)
tvb2058 | 2007-10-10 15:04:37    阅读:50659   发布文章
 

根据公式1.10,可以获得这种仪器的灵敏度的表达式为:

<!--[if !vml]--><!--[endif]-->    <!--[if !vml]--><!--[endif]-->

(1.14)

从这个表达式也同样说明这种陀螺仪在90度的相位偏置时可以使仪器达到最大的灵敏度。根据这个公式,经过相位偏置以后,在接收器上的光强的表达式为:

<!--[if !vml]--><!--[endif]-->    <!--[if !vml]--><!--[endif]-->

(1.15)

另外一种调制方法所使用的波形不是方波,而是一个余弦波,这个调制量的表达式为:

<!--[if !vml]--><!--[endif]-->    <!--[if !vml]--><!--[endif]-->

(1.16)

这时陀螺仪所接收到的信号应该为:

<!--[if !vml]--><!--[endif]-->    <!--[if !vml]--><!--[endif]-->

(1.17)

这个信号可以分解为:

<!--[if !vml]--><!--[endif]-->    <!--[if !vml]--><!--[endif]-->

(1.18)

进一步利用贝塞尔函数的级数展开可得:

<!--[if !vml]--><!--[endif]-->    <!--[if !vml]--><!--[endif]-->

(1.19)

在这个表达式中所有偶数阶的项均正比于转角的余弦值,而所有的奇数阶的项均正比于转角的正弦值。如果在仪器中引进同步的反调制,就会产生下列的偏制调制后的光强的变化:

<!--[if !vml]--><!--[endif]-->    <!--[if !vml]--><!--[endif]-->

(1.20)

这时为了取得仪器的最大的灵敏度,相位的最大偏置值应该为 <!--[if !vml]--><!--[endif]-->,而不是利用方形波调制时的90度,即1。5弧度。这是因为 <!--[if !vml]--><!--[endif]-->。当仪器是静止的时候,光强信号主要是二阶的高频谐振,而当仪器存在转角时,则光强信号主要是在光纤的特征频率上的一阶的调制振动,这个调制振动的频率是系统的基本频率,而二阶的频率是这个基频的两倍。

开环控制的干涉式的光纤陀螺仪在测量时具有相当稳定性,在较小的转动速度的范围内,它的响应基本上是线性的。但是它的动态范围相当小,如果超出这个范围它的响应就变成非线性的了。同时它所能测量的范围应该限制于 <!--[if !vml]--><!--[endif]-->的范围内。对于具有1000圈面积为 <!--[if !vml]--><!--[endif]-->的陀螺仪,当光的波长为 <!--[if !vml]--><!--[endif]-->时,这个可以测量的最大转动速度为 <!--[if !vml]--><!--[endif]-->。 

为了提高陀螺仪的测量性能,必须采用闭环控制的干涉式的陀螺仪。闭环控制的最后目的是使得接收器所收到的信号正好为零,这样这个仪器将始终运行在线性的范围之内。采用闭环控制的好处有下面几点:1)可以大大提高仪器的灵敏度;2)可以极大地减小仪器的动态响应时间,大大提高仪器的动态响应;3)可以避免仪器的任何非线性响应,特别是当转动速度较高的时候。闭环控制的干涉陀螺仪也有多种途径,有的是通过光电调频的方法,有的是通过相位等斜率锯齿形变化的方法,有的是通过相位平衡元件的控制方法,也有是通过陀螺仪反向转动的方法。前面已经讲过在光纤陀螺仪的设计中光的极化方向的变化是一个很大的问题外,这中间温度和声音的振动对光纤的稳定性都有很大的影响。据测定当光纤承受87分贝的声压时,这相当于4毫巴的气压的变化,在25微米的裸露单模光纤上会引起 <!--[if !vml]--><!--[endif]-->的相位误差。对于有保护层的光纤,保护层的直径为 <!--[if !vml]--><!--[endif]-->,当声音的分贝数为100时,这相当于20毫巴的气压变化,这时所引起的相位误差也是 <!--[if !vml]--><!--[endif]-->。光纤对温度的变化也十分敏感。为了消除温度差别的影响,现代光纤陀螺仪的光纤圈有着很多不同的绕制方法。最常用的是从线圈的中部向两个方向同时绕制,这样温度差对仪器的影响将减少到最小。

和光纤干涉陀螺仪不同,光纤谐振陀螺仪是应用谐振原理而设计的。从广义上讲光纤谐振式陀螺仪和光学中的法布里-佩奴 <!--[if !vml]--><!--[endif]-->干涉仪具有相同的设计原理和结构。法布里-佩奴干涉仪是由两个相互平行的表面形成一个谐振腔,由于两个表面的反射率很高,所以光线会在谐振腔内不断地反射。当两个反射表面之间的光程和光的波长整数倍相同时,就会在两个表面上分别产生出频率非常单一的反射和透射光波。光纤谐振陀螺仪的光纤环路同样是一个光学谐振腔,当光纤环路转动的时候,由于塞格尼克效应,光纤环这一谐振腔的光程会发生变化,而光线在谐振腔中不断在同一个方向运动的作用则是不断地加强这种效应。这样当谐振腔的光程正好是光的波长的整数倍时,光纤谐振陀螺仪就会在它的反射出口和透射出口上输出一定的谐振信号。从理论上讲谐振式的光纤陀螺仪要比干涉式的光纤陀螺仪有更好的灵敏度,但是在实际的研制中,谐振式的陀螺仪的研制有一定的难度,它对光源的相干度方面的要求要比较干涉式的光纤陀螺仪高得多,它要求的光源要具有很窄的频宽,从而有很长的相干距离。

这种光纤谐振陀螺仪一般共包括三个光纤回路或部分回路。从频宽很小的激光二极管向一根光纤的一端发出一束光,同时这一光纤的末端通过第一个光纤耦合器藕合,在这个光纤耦合器上的反射出口连接到一个接收器上,形成谐振陀螺仪的第一个回路。在第一个光纤耦合器中,另一个入口以及它的透射入口和第二个光纤耦合器的一个入口和它相应的反射出口分别相连,形成一个完整的环路。这个环路是陀螺仪的最主要的部分,也是它的谐振腔。这个谐振腔的反射出口在第一个回路上,它连接着一个接收器。同时在这第二个光纤耦合器上,另外一个入口和它的透射出口形成陀螺仪的第三个回路。这个回路上的透射出口就是光纤谐振腔的透射出口。这个陀螺仪中的两个光纤耦合器都不是等量的耦合器。它们有着非常不平衡的能量分配,从而使90至99%的光能能够进入并保留在第二个回路,即仪器的光纤谐振腔之中。第三光纤回路也是一个开环回路,它的透射出口和一个探测器相连接。在这种系统中如果谐振腔回路的长度是固定的,当系统是静止的时候,它就会对一个特定的波长的光产生谐振。而当仪器有一个很小的转角时,谐振回路中沿着光线传播方向上的光程会变化,因此这个系统会在一个不同的光的频率上产生谐振。通过测量谐振频率的变化就可以来了解仪器转动角速度的变化,以达到角度测量的目的。现代谐振式的光纤陀螺仪在透射通道上的响应可以用下式表示:

<!--[if !vml]--><!--[endif]-->    <!--[if !vml]--><!--[endif]-->

(1.21)

式中 <!--[if !vml]--><!--[endif]-->是光的空间频率,它是光的波长的倒数, <!--[if !vml]--><!--[endif]-->是光纤陀螺仪中的总光程, <!--[if !vml]--><!--[endif]--> <!--[if !vml]--><!--[endif]-->是光纤耦合器分配在光纤环中的能量的比例, <!--[if !vml]--><!--[endif]-->是光在真空中的传播速度。从这个公式出发,光纤陀螺仪的响应的频率周期,用时间频率表示为 <!--[if !vml]--><!--[endif]-->,如果用园频率来表示这个周期,就要在这个频率上乘上一个 <!--[if !vml]--><!--[endif]-->的数值。

假如光源的频率和谐振腔的谐振响应的最高点正好相同,那么当光纤环具有一定的转动角速度时,透射的能量和转动角速度 <!--[if !vml]--><!--[endif]-->之间的关系为:

<!--[if !vml]--><!--[endif]-->    <!--[if !vml]--><!--[endif]-->

(1.22)

式中 <!--[if !vml]--><!--[endif]-->是光纤环由于转动在一个方向上所形成的光程的变化。

谐振式的陀螺仪和相对应的干涉式的陀螺仪在条纹响应上十分相似,在干涉式光纤陀螺仪中,光强和转动角速度的关系图中,每一个响应瓣的半极值的瓣宽 <!--[if !vml]--><!--[endif]-->为:

<!--[if !vml]--><!--[endif]-->    <!--[if !vml]--><!--[endif]-->

(1.23)

而对于谐振式的光纤陀螺仪,响应的瓣的半极值宽度为:

<!--[if !vml]--><!--[endif]-->    <!--[if !vml]--><!--[endif]-->

(1.24)

式中是谐振腔的一个参量 <!--[if !vml]--><!--[endif]--> <!--[if !vml]--><!--[endif]-->

谐振式的陀螺仪的信号处理方法和干涉式的陀螺仪基本相同,第一步可以采用开环式的相位偏置和调制和反调制的方法。第二步再采用误差的信号进行闭环控制。和干涉式的陀螺仪不同,当陀螺仪处于静止状态时,谐振式的陀螺仪并不能自动地得到最大的响应。这时光源的频率和谐振腔的光程首先要在转动的一个方向上匹配,这样才会在相反的方向上有最好的响应。

和光纤陀螺仪十分相似的是激光谐振陀螺仪。它是通过激光在一个三角形的通道中构成一个谐振腔所制成的,它的详细结构和特点将在另外的文章中介绍。

 

 

参考文献:

Vali, V. and Shorthill, R. W., 1976, Fiber ring interferometer, Appl. Opt., Vol 15,

Ruffin, P. B., 2002, Fiber Gyroscope Sensors, in Fiber Optic Sensors, Edited by Yu, F. T. S. and Yin S., Marcel Dekker, Inc., New York.

Lefevre, H., 1993, The Fiber-optic Gyroscoe, Artech House, Boston.

Moorre, E. L. and Paula, R. P., 1989, Optical fibers and integrated optics, in Sensors, edited By Gopel, W. et al, VCH Verlagsgesellschaft mbH, D-6940 Weinheim, Germany.
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