Geometric analysis of the null screens used for testing convex optical surfaces

A geometric analysis of the screens used for testing convex optical surfaces is presented. Some properties of the transformation between the image plane and the screen plane, such as symmetry and magnification, are presented for the case when the reflecting surface is a sphere. Due to the intrinsic variations in the magnification, the geometric relationship between the image and the object shows some unexpected behavior. Two cases are analyzed in detail: i) a set of concentric circles centered on the origin of coordinates of the image plane with a set of radial straight lines; and ii) a square grid and a square array of circles of the same size