Aspheric surfaces of revolution in optical design

Part I. After a brief introduction to aspheric surface, the early work in the seventeenth century is described and the emergence of the optical path equality principle. The Abbe sine theorem in the nineteenth century is shown to lead to a number of aspheric aplanatic objectives in which this theorem is fulfilled. The Schmidt telescope, an astigmatic system of high performance is considered briefly in conjunction with some variations of it. Part II. The Schmidt camera is considered in more detail, including descriptions of a number of author's' methods for deriving the equation of the corrector plate, and the possibilities in balancing the aberrations over the whole field. A number of the Schmidt variations are described including field flattened and folded types. Part III. The de signs of two mirror and more complicated mirror pate systems are analysed by first order and other methods, and the use of aspheric surfaces to provide field correctors for large paraboloid mirrors described. Part IV. The general first order design of aspherics with the see-saw diagram and the application of differential methods of correction, are followed by methods for obtaining axial stigmatise and aplanatism. Lastly a number of ray tracing method are examined, most of which involve the due of an electronic computer