Methods to define circular off-axis aspheric mirrors

We investigated the definition for circular off-axis aspheric mirrors (COAMs). The clear opening of the COAM obtained by projecting a circular aperture on the aspheric surface does not form a plane but a curved surface. To avoid ambiguity due to the non-planar opening, we propose to use a plane to cut the aspheric surface to obtain a COAM. The COAM has three characteristics: 1) an elliptical opening; 2) the major axis of the opening lies on the meridional plane containing the original optical axis of the aspheric surface, and the minor axis lies on the sagittal plane perpendicular to the meridian plane; and 3) it is not deepest at the center of the ellipse. The third characteristic suggests two methods for defining the COAM using a plane: 1) with the center of the elliptical opening as a reference and 2) with the deepest point of the mirror as a reference. All the formulas required to obtain the desired COAM using the two methods are presented.