Abstract
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 solve this problem, we propose to use a plane to cut the aspheric surface to obtain a COAM. The COAM has three characteristics: (i) an elliptical opening; (ii) 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 (iii) it is not deepest at the center of the ellipse. The third characteristic suggests two methods for defining the COAM using a plane: (i) with the center of the elliptical opening as a reference and (ii) 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.
Highlights
An off-axis aspheric mirror is a well-established form for largescale telescope mirrors, and many of the recently developed telescopes employ a large number of segmented off-axis aspheric mirrors
The reference optical axis (ROA) is the normal line at the vertex of the aspheric surface that passes through the center of the surface or opening
Because the tangent plane at the deepest point is parallel to the xu-plane ð∵dduv jðuÃ;vÃÞ 1⁄4 0Þ, the plane cutting the aspheric surface must be parallel to the tangential plane, indicating that the angle for the plane can be obtained by the angle of the tangent plane at the offaxis distance (OAD)
Summary
An off-axis aspheric mirror is a well-established form for largescale telescope mirrors, and many of the recently developed telescopes employ a large number of segmented off-axis aspheric mirrors. For most lenses or mirrors of aspheric surfaces in rotational symmetry, various terms such as the center of the opening, vertex, center of curvature, deepest point, or the optical axis all refer to the same element. The ROA is the normal line at the vertex of the aspheric surface that passes through the center of the surface or opening It is the deepest point at the center of the opening. This result has caused considerable difficulty in establishing shapes and related terms for the COAM, and the necessity of developing methods to define the COAM has been raised.
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