Alignment off-axis optical system using Nodal Aberration Theory

We present the Fringe Zernike coefficients of the parent system pupil can be converted into coefficients of off-axis system, it is show that the coefficients of the Fringe Zernike polynomials in the off-axis pupil only contain orders equal to or lower than the Fringe Zernike polynomials originally placed on the parent pupil, and for the 3 rd aberration the pupil transformation matrix has been finding. Using nodal aberration, we get the misaligned matrix of rotational symmetry parent optical system. Then with the pupil transformation matrix, the misaligned matrix of off-axis two-mirror system was found, the amounts of the misalignments are calculated by the off-axis misaligned matrix.