中文摘要：

利用菲涅尔双棱镜反射测量三维小角度的方法是一种利用成一定夹角的两面反射镜代替单块平面反射镜的改进型自准直测量方法,通过建立反射光斑位移与反射镜旋转角度的数学关系,求解获得空间三维角度变化。但是在传统菲涅尔双棱镜测角方法的建模中,物体的空间角偏转状态由一个固定顺序的动态转角过程给定,其建模方式求解结果不唯一,且转角表达不直接。针对用于在轨三维小角度测量的菲涅尔双棱镜测角法,提出了一种新的建模方式,构建了初始状态与最终状态的空间角度变化的数学关系,该模型不受转角顺序的影响,其求解结果具有唯一性,且对于三维角度偏转表达更为直接、客观,同时使得菲涅尔双棱镜三维测角法适用于更大的测角范围。最后,通过仿真计算验证了这种建模方式的正确性。

英文摘要：

The three-dimensional small angle measurement system based on Fresnel biprism was an improved autocollimation method which replaced the single mirror by two mirrors with a certain angle. It measured the space angle change through solving the mathematical relationship between the reflected spot displacement and the mirror rotation angle. The traditional modeling method always predetermined a rotation order to indirectly establish the mathematical relationship between the state of the object space angle change and the rotation angle, which had not one result for the predetermined rotation order was random. A new modeling method was proposed which directly established the mathematical relationship between the initial object state and the final state after rotation, which didn ′ t need to predetermine a rotation order making one rotation state having only one mathematical relationship. This method was objective, direct and could be used to measure bigger range of three-dimensional angle. Finally, the correctness of this modeling method by using simulation calculation was verified.