rays in mathematics, optical rays extend to infinity in both directions. Rays are real when they are in the part of the optical system to which they apply, and are virtual elsewhere. For example, object rays are real on the object side of the optical system. In stigmatic imaging an object ray intersecting any specific point in object space must be conjugate to an image ray intersecting the conjugate point in image space. A consequence is that every point on an object ray is conjugate to some point on the conjugate image ray. Geometrical similarity implies the image is a scale model of the object. There is no restriction on the image's orientation. The image may be inverted or otherwise rotated with respect to the object. Focal and afocal systems, focal points In afocal systems an object ray parallel to the optical axis is conjugate to an image ray parallel to the optical axis. Such systems have no focal points (hence afocal) and also lack principal and nodal points. The system is focal if an object ray parallel to the axis is conjugate to an image ray that intersects the optical axis. The intersection of the image ray with the optical axis is the focal point F' in image space. Focal systems also have an axial object point F such that any ray through F is conjugate to an image ray parallel to the optical axis. F is the object space focal point of the system. Transformation The transformation between object space and image space is completely defined by the cardinal points of the system, and these points can be used to map any point on the object to its conjugate image point. See also Film plane Pinhole camera model Radius of curvature (optics) Vergence (optics) Notes and references Pages 74–76 define the cardinal points. External links Learn to use TEM Geometrical optics Geometric centers Science of photography de:Brennebene