Focal length measurement based on Fresnel diffraction from a phase plate

Abstract

A method based on the Fresnel diffraction of light from the phase step is introduced for measuring effective focal length (EFL) and back focal length (BFL) of optical imaging systems. It is shown that, as a transparent plane-parallel plate is illuminated at a boundary region by a monochromatic beam of light, Fresnel diffraction occurs because of the abrupt change in phase imposed by the finite change in refractive index at the plate boundary. Variation of the incident angle in a convergent (or divergent) beam of light causes the periodic intensity along the central fringe of the diffraction pattern. The measurement of the extrema position of the intensity distribution accurately provides the EFL and BFL. The technique is easy to apply and can measure a wide range of both positive and negative focal lengths. The measuring setup can be very compact with low mechanical and optical noises. As examples of this technique, the EFLs of five different lenses are experimentally obtained. The results are quite consistent with the values indicated by the lens manufacturer.