Many books on modern optics confine the treatment of lens theory to the paraxial approximation. Aberrations are treated casually as an afterthought, and it usually remains unexplained whether they are due to the laws of physics or due to the limited art of the lens designer. The reader is often left with the notion that lenses must be designed to obey the laws of Gaussian optics as closely as possible. This is regrettable, because it has been known since the eighteenth century that paraxial optics used with finite heights and angles leads to projective geometry, a valuable branch of mathematics which is, however, a poor representation of the behavior of actual lenses.

The development of Fourier optics over the last forty years has brought lens theory and physics much closer together, but again many insights are lost because most authors, in spite of the ubiquity of high aperture lenses in the laboratory, are content with the small angle approximation when dealing with the theory of image formation. Either a clear and convincing demonstration should be given that the small angle approximation can be used with impunity for very large angles, or the theory should be developed honestly, without the small angle approximation. This honest theory exists, but is buried in books and papers providing so much detail that beginners are apt to get lost in the mathematical intricacies.