Geometrical properties of the normals of second-order nonspherical surfaces of revolution

This paper determines how the scatter of the points where the normals to a second-order nonspherical surface of revolution intersect the optical axis depends on the angle between the normal and the axis. It is shown that the scatter of the points where the normals to the surfaces of an ellipsoid and a paraboloid of revolution intersect has a fairly monotonic character, whereas it is determined by an alternating series in a hyperboloid of revolution, and this determines the requirements on the correction possibilities of the optical system of a compensator when the compensation method is used to monitor the shape of nonspherical surfaces.