Aspherical mirror to form parabolic wave front

An exact mathematical description of the form of aspherical mirror converting a flat wave front to a parabolic one, is derived. The description may be used as an aspherical single-component null corrector for checking the parabolic surfaces or as a simulator to analyse and optimise the compensation checking circuits. A possibility is shown to replace exact equation by the approximate one describing the aspherical mirror in conventional form.