Abstract: Formulae of the third order geometric aberrations caused by the pirallcl planar deflection systems consisting of two planar deflectors disposed sequentially and orthogonally have been derived. These formulae can be used as an analytic solution for quickly estimating the geometric aberrations of a known deflection system and checking the related computer program. In view of attaining minimum and equal deflection aberration on the horizontal and vertical sides of a square scanning area, a method of optimum design is proposed. When the total length of the deflection region and the distance between the two deflectors are given, the optimum length of each of the two deflectors can be calculated by this method.