A method of assembly error calculation is proposed in this paper. First, the posture of the mirrors and the direction of the laser beam are represented by using unit normal vector and unit direction vector. Then, using the coordinate transformation and the transfer matrix, the unit normal vector of the mirrors is obtained in the global coordinate system. The beam direction vector after twice specular reflection by the vector symmetry is calculated. Finally, taking the theoretical value and the actual value of the parameters of the assembly into the algorithm, the theoretical and actual direction vector of the laser beam reflected twice from the mirror are obtained. The intersection angle between two vectors is the pointing error of the assembly. After getting the relationship of the global pointing error and the part error, the average part error can be obtained by the pointing error back calculation. The testing pointing error of the prototype is 0.005 7°, and the value of assembly pointing error which is obtained by taking the part testing error into the algorithm is 0.006 1°. With this value, the average parts error is 0.002 25° by back calculation. The calculation data is closed to the result of testing, and it can provide a reference for the accuracy design of the periscope pointing assembly.
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