Higher order aplanatism

Abstract

The usual aplanatic imaging (axial stigmatism and fulfilment of the sine condition) means an ideal aberrationfree imaging in an approximation being linear in regard to the dependence on the off-axis distance of an object point [1,2]. The degree of this approximation can be improved by aplanatism of higher order [3]. mth order aplanatism means that the wave aberration is, over the total pupil, equal to zero in case only the powers r 0, r 1,… r m of the off-axis distance r of an object point are taken into account ( m = 1 meaning the known usual aplanatism mentioned above). Concerning the case m = 2, an algorithm is developed by which it should be possible to design an optical system of 4 refracting aspherics that is 2nd order aplanatic. Furthermore, we give the number of aspheric surfaces required to attain aplanatism of mth order.