On the Image Sharpness in the Central Field of a System Presenting Third- and Fifth-Order Spherical Aberration*

Abstract

It is customary in photographic lenses to leave some third-order spherical aberration to partially compensate the higher order terms. However, so far no satisfactory answer has been given to the question of the amount of third-order aberration which gives the best balance. The problem has been attacked with the assumption that all the higher order terms can be approximately included in the fifth-order term, a situation that in most practical cases holds with great accuracy. It has also been assumed that useful indications regarding the image sharpness resulting from a given correction can be arrived at by pure geometrical optics. The illumination in the image of a sharp edge has been calculated for a constant fifth-order aberration and for different values of the third-order aberration and of the distance of the image plane from the paraxial focus. The numerical integration needed has been carried out with the aid of an IBM computing machine. The best results are obtained for a condition approaching that of the smallest circle of confusion.