In the manufacture of electron optical system, the dimension and alignments of the electrodes may have some small perturbations. The performance of the electron optical system is affected by these tolerances. It is important to analyse the in#uence of the tolerance. Usually, the perturbations of the potential and the trajectory are obtained by the difference of parameters at various positions of the movable electrode. Because the value of the tolerance is usually very small, it is diffcult to estimate the acceptable tolerance. Serious numerical error may also be introduced in this method. This paper proposes another method to determine the acceptable tolerance in the manufacture. In this method, the derivative of the potential versus the displacement vector is obtained from the unperturbed field. Then the derivative of trajectory is calculated with the RK method from the normal result. According to the first-order approximation, the acceptable tolerance can be determined. This paper analyses some typical perturbations in the main lens of CRT. (1999 Elsevier Science B.V. All rights reserved.