Considering the pupil coordinate of aberration theory from the view point of the sine condition in the presence of spherical aberration

Abstract

Considering the sine condition or the physical meaning of imaging, pupil coordinate should be defined by direction cosine of ray. Using the pupil coordinate defined by the direction cosine of ray, Marx and the author had derived the sine condition in the presence of spherical aberration independently. Also we had confirmed its validity by practical lens designing. On the other hand, in order to deal with the object imaging and pupil imaging equivalently, conventional aberration theory (theory of image error) uses the pupil coordinate defined by the cross point between the ray and the tangential pupil plane. However, by using this pupil coordinate, Focke had deduced the wrong result that there exists no spherical aberration when the isoplanatic condition is fulfilled (when coma aberration does not exist). Therefore one might think that the conventional aberration theory has less meaning. However, in this paper, we find that there can exist 3rd order spherical aberration with no 3rd order coma aberration even when we use the conventional aberration theory. Namely the conventional aberration theory is effective at least for 3-rd order aberration from the viewpoint of the sine condition.