Werner W
Institute of Applied Physics TNO-TH,Postbus 155, Delft, The Netherlands.
Appl Opt. 1967 Oct 1;6(10):1691-9. doi: 10.1364/AO.6.001691.
The theory of the formation of a spectrum by means of an equally spaced grating has been studied in considerable detail by methods of geometrical optics. The difference of approach, compared with other papers on this subject, is mainly in the choice of the pupil coordinates. It appeared to be essential to take the orientation of these coordinates around the normal to the grating surface as a variable. Consequently, the variations from known results may be considerable. Another difference of this paper is the way the deviations from perfect imaging are considered. Furthermore, the shape of the grating surface is given in the form of a general series expansion in order to cover all kinds of surfaces, and the location of the object is not limited to small distances from the Rowland plane; grazing incidence in an extreme offplane mounting is therefore included. The results give the position of the spectral image, generally lineshaped by astigmatism, with the coordinates of the center of this line and two slant angles. Expressions are also derived for length and radius of curvature of the astigmatic line and the width of this line caused by coma and spherical aberration. Finally, conditions are derived for the optimum slant angle of a slit and the shape of the grating surface for minimum aberrations. Extensive checks with ray tracing completely covered the results in this paper.
利用等间距光栅形成光谱的理论已经通过几何光学方法进行了相当详细的研究。与关于该主题的其他论文相比，方法上的差异主要在于光瞳坐标的选择。将这些坐标围绕光栅表面法线的取向作为一个变量似乎至关重要。因此，与已知结果的差异可能相当大。本文的另一个不同之处在于考虑偏离完美成像的方式。此外，光栅表面的形状以一般级数展开的形式给出，以便涵盖各种表面，并且物体的位置不限于离罗兰平面很近的距离；因此包括了在极端离平面安装中的掠入射情况。结果给出了光谱图像的位置，通常因像散而呈线状，以及这条线的中心坐标和两个倾斜角。还推导了像散线的长度和曲率半径以及由彗差和球差引起的这条线的宽度的表达式。最后，推导了狭缝最佳倾斜角和光栅表面形状以使像差最小的条件。用光线追迹进行的广泛检验完全证实了本文的结果。
