A new approach to high accuracy measurement of the focal lengths of lenses using a digital Fourier transform

Abstract A new approach is proposed for measuring the focal length of a lens. The lens is illuminated by an interference pattern with a regular pitch produced by an interferometer that uses a reflective grating. The focal length is determined by measuring the number of fringes falling inside a fixed aperture both with and without the test lens inserted in the set-up. To measure the number of fringes, three images of the interference pattern are digitized by a CCD camera. A one-dimensional FFT algorithm is applied to the digitized image to reconstruct the phase modulo 2π along each row. The phase is unwrapped along each row and averaged to calculate the number of fringes that fall inside the aperture of 512 pixels. This technique is alternative to methods based on the moire effect and a higher accuracy is obtainable. The focal lengths of both positive and negative lenses have been measured.