Buchdahl模型的无焦系统消色差方法

基于Buchdahl模型的色散向量分析法可以用于指导光学设计中的材料选择与替换，得到消色差效果良好的材料组合，但是目前该理论由于数学形式的限制，只应用于有焦系统设计中，并没有用于指导无焦系统设计的先例。针对此问题进一步探究该理论在无焦系统下的应用，提出适用于无焦系统的色散向量比例因子的变形表达，以该方法对一个七倍望远无焦系统进行材料的选取，优化后的系统在0.707孔径处最大色差值仅为2.705×10^-5 D (屈光度)，632.8 nm和1 064 nm两波长的焦移差为0.000 21 D，波段范围内最大焦移也仅为0.004 7 D，系统色差得到有效校正，各视场MTF完全达到衍射极限。研究成果使基于Buchdahl模型的色散向量分析法可以同样应用于无焦系统设计中，为无焦系统消色差材料组合的选择提供了一种新思路。

Buchdahl model of achromatic method for unfocused systems

The dispersion vector analysis method based on Buchdahl model can be used to guide material selection and replacement in optical design to obtain material combinations with good achromatic effect, but at present the theory is only applied to the design of focused systems due to the limitation of mathematical form, and there is no precedent for guiding the design of unfocused systems. To further investigate the application of this theory to the unfocused system, a deformed expression of the dispersion vector scale factor applicable to the unfocused system is proposed, and the material selection of a seven-fold telescopic unfocused system is carried out by this method. The optimized system has a maximum chromatic aberration of only 2.705×10?5 D (Diopter) at 0.707 aperture. The focal shift difference between 632.8 nm and 1 064 nm wavelengths is 0.000 21 D, and the maximum focal shift in the wavelength range is only 0.004 7 D. The chromatic aberration of the system is effectively corrected, and the MTF of each field of view completely reaches the diffraction limit. The research results enable the dispersion vector analysis method based on Buchdahl model to be applied to the design of unfocused systems as well, providing a new idea for the selection of achromatic material combinations for unfocused systems.