An assessment of approximating aspheres with more easily manufactured surfaces

In designing optical systems for synchrotron radiation, one is often led to conclude that optimal performance can be obtained from optical surfaces described by conic sections of revolution, usually paraboloids and ellipsoids. The resulting design can lead to prescriptions for three-dimensional optical surfaces that are difficult to fabricate accurately. Under some circumstances satisfactory system performance can be achieved through the use of more easily manufactured surfaces such as cylinders, cones, bent cones, toroids and elliptical cylinders. These surfaces often have the additional benefits of scalability to large aperture, lower surface roughness and improved surface figure accuracy. In this paper we explore some of the conditions under which these more easily manufactured surfaces can be utilized without sacrificing performance.