为了避免连续变焦光学系统中，各组元像差自动设计对设计者经验要求高、计算复杂且计算量大的难点，提出了一种利用差值线性方程组进行像差自动设计的方法，并用此方法设计了一套可见光波段连续变焦光学系统。利用高斯光学计算理想近轴系统的结构参数；利用差值线性方程组进行系统像差自动设计，使系统的初级像差系数SI 、SII 与SIII 在各焦距位置处近似相等；基于像差自动设计结果计算光学系统的初始结构参数；利用Zemax自动设计软件进行像差校正平衡。优化结果表明：系统可实现20~300 mm 的连续变焦，且在截止频率50 lp/mm 处，各焦距位置各视场的传递函数(MTF)均大于0.4。因此，应用差值线性方程组法进行像差自动设计，可以简化计算，减少对设计者经验的依赖，并且能够取得良好的像质。

In the process of continuous zoom optical system design, the aberration automatic design demands prior experience , complicated algorithm and massive calculation. In order to overcome these difficulties, the method of using subtractive linear equations to carry out the aberration automatic design is proposed. With this method, a continuous zoom optical system of visible spectrum is designed. Using Gaussian optics to calculate the paraxial structural parameters of the system; the application of subtractive linear equations in the aberration automatic design make the value of primary aberration coefficients SI , SII and SIII approximately equal at different focal lengths positions; based on the results of the aberration automatic design, the initial structural parameters of system are calculated; the aberrations are corrected by Zemax optical design software. The design result indicates that the focal length could vary from 20 mm to 300 mm continuously for this system and the modulation transfer function is always bigger than 0.4 at the spatial frequency of 50 lp/mm and every focal length position. In conclusion, the method of subtractive linear equations in the aberration automatic design can simplify the calculation, reduce the degree of relying on the prior experience and achieve high quality of image.