Direct measurement of phase in a spherical-wave Fizeau interferometer

When measuring the contours of spherical surfaces by direct phase measurement the Twyman-Green interferometer is usually chosen in preference to the Fizeau interferometer. In the Twyman-Green interferometer the phase reference is provided by moving a plane mirror in a direction normal to its surface. In the spherical-wave Fizeau interferometer the reflecting surfaces are spherical and, at the same instant at least, cannot be moved in a direction normal to the surfaces at all points over the optical aperture. It can be shown analytically, however, that for a spherical test surfaces having an N.A. less, similar0.8, the error introduced by moving the test surface axially, rather than radially, can be made