Astigmatism and White cells: theoretical considerations on the construction of an anastigmatic White cell

The subject of this study is the theoretical background of astigmatism at spheres and its compensation. As a result of this study, it is shown that it is possible to construct White cells free of astigmatism for one light pass or more by separating the two rows of foci on the field mirror by a distance h. This row distance h depends on the number of passes of the light beam, the common radius of curvature R, the distance between entrance and exit focus, and the distance between the two central points on the objective mirrors. The theoretically derived mathematical equations describing this relationship are compared with results of computer simulations, and excellent agreement is observed.