An assessment of approximating aspheres with more easily manufactured surfaces

Abstract

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 dif®cult 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 bene®ts of scalability to large aperture, lower surface roughness and improved surface ®gure accuracy. In this paper we explore some of the conditions under which these more easily manufactured surfaces can be utilized without sacri®cing performance.

Theory and practice of elliptically bent x-ray mirrors

“…To investigate the range of validity of these approximations, we made a calculation 31 in which the length of the circular or cubic mirror is allowed to extend in each direction until the slope error relative to the corresponding ellipse reaches a prescribed value ⌬. This means 2⌬ is roughly the peak-to-valley slope error.…”