Geometry for off-axis parabolic mirrors

We investigated the geometrical characteristics of off-axis parabolic mirrors (OPMs). We found that the clear aperture of an OPM is an ellipse with a set of major/minor diameters, and the center of the elliptical aperture does not correspond to the deepest depth of the mirror. Despite this property, the distance from the reference optical axis (ROA) of the parent parabolic mirror to the deepest point of the OPM is equal to the distance from the ROA to the center of the elliptical aperture of the OPM. This enables one to define an OPM by projecting a aperture perpendicular to the ROA on a parabolic surface.