在传统怀特池的基本原理上, 采用高斯光学分析方法推导出了多次反射怀特池的总光程和光斑分布的数学公式。分析表明: 连续奇数号光斑间距与连续偶数号光斑间距相等, 为两次镜曲率中心间距的2倍, 且交替排布; 当主镜上有N个光斑时, 怀特池总光程OP≈2(N+1)L, 其中L为怀特池的基长。根据分析所得结论, 对传统怀特池进行了改进, 使其能够在减小主镜口径的同时充分利用其有效口径和中间光程。结合设计实例, 将结构数据在CODE V上进行模拟和优化计算, 通过实际装调验证了所推得的数学公式和结论对指导设计多次反射池的正确性。

Based on the basic theory of classical White-Cell, the formulas of the total optical path(OP) and the distribution of the beam spots of the Multi-Pass White Cell are deduced. The two basic conclusions are obtained after the formulas are analyzed, that: the distance between successive odd images equals to that between successive even images, and equals to twice that between the centers of curvatures of the secondary mirrors; the OP approximates 2(N+1)L when the number of the beam spots on the primary mirror is N. The classical White-Cell is improved to take advantage of the intermediate optical path while reducing the diameter of the primary mirror according to the result of analysis. The new configuration is simulated and optimized with CODE V. Through the practical alignment, the formulas and the conclusions are proved right and proper for guiding the Multi-Pass Cell design.