Application of Newton’s method to determine the focal length of lenses using a lateral shearing interferometer and cyclic path optical configuration setup

Abstract

We present a technique for the focal length measurement of lenses applying Newton's method, using a cyclic path optical configuration (CPOC) and a wedge shear plate (WSP). Two point sources of orthogonal linearly polarized light waves that have a known longitudinal separation between them are generated using CPOC. Selecting a particular state of polarization (s or p), the corresponding point source is made to coincide with the back focal point of the test lens (TL). The collimation of the output beam from TL is tested using the WSP. With a change in the state of polarization, a spherical wavefront would emerge from TL because the corresponding point source is situated slightly away from the focal plane of TL. The radius of curvature of the emerging spherical wavefront from TL approximated as image distance is evaluated by analyzing the shear fringes produced by WSP. Appropriate formulae for the determination of the focal length of TL, from the image distance and known longitudinal separation between the sources, are derived using Newton's method. Results obtained for a positive doublet lens of nominal focal length of 500.0 mm is presented.