Aberration-free Imaging of Large Fields with Thin Pencils

Aspheric surfaces make aberration-free imaging of large fields possible if the imaging pencils are so thin that higher powers of the aperture angle can be neglected. The order of this freedom from aberrations is defined. Powers of the field angle are not neglected. For example, for large fields, a thin-pencil aberration-free system of second order is entirely free from distortion, field curvature and astigmatism. Such a system can be designed with three aspherics, and the principles of this design are described. The aspheric surfaces can be determined, step by step, by means of a succession of rays, the aberrations of which are made equal to zero by suitable surface elements. For a thin-pencil aberration-free system of nth order, the number of necessary aspherics is given.