三阶彗差是同轴三反消像散(TMA)光学系统镜面失调产生的主要像差之一。使用矢量像差理论分析了同轴TMA光学系统失调后彗差变化特性，给出了次镜和三镜像差偏移矢量的求解方法及公式，并推导了系统次镜和三镜失调导致的彗差增量系数公式，证明了三镜在X-Y 平面内偏心产生的彗差可以通过一个固定比例的次镜偏心量完全补偿，提出了次镜对偏心三镜的消彗差补偿条件、次镜和三镜各自的X-Y 平面偏心无彗差条件。计算了同轴TMA光学系统中三镜失调的两个例子，在消彗差补偿条件下，经过次镜主动偏心补偿，全视场均值彗差增量仅为未失调前的0.6%和1.9%，证明了消彗差补偿条件的正确性。

Three-order coma is one of the main aberration types to produce mirror disorders of coaxial threemirror astigmatism (TMA) optical system. The variation characteristics of coma in perturbed coaxial TMA optical system is analyzed using vector aberration theory. The solving method and formula of aberration displacement vectors of secondary mirror and three mirror is proposed, and the coma increment coefficient formula caused by secondary mirror and three mirror of system is deduced. It is proved that the three-order coma produced by decenter of tertiary mirror in X-Y plane can be totally compensated by constant ratio of decenter amount of secondary mirror. The coma-free compensation condition of secondary is proposed, and the coma-free decenter conditions of secondary mirror and tertiary mirror are proposed respectively. Two examples of disordered three mirror in coaxial TMA optical system are used to calculate the coma-free compensation condition. Under the condition of coma-free compensate, the all field of view mean coma increment is only 0.6% and 1.9% before disorder, which shows the validity of the proposed coma-free compensation condition.