Focal length measurement by the analysis of moiré fringes using the wavelet transformation

A novel method, where moiré patterns, produced by the images of reference gratings, and a CCD pixel array are used to measure the focal length of a lens is presented. The tested lens could magnify the images of straight-line gratings onto the CCD camera. The positions of the lens being tested were moved so as to arrange that the pitch values between the reference grating images and the lattices of the CCD camera were similar. This generates moiré fringe images. Due to the structure of the lens system, it is always hard to identify the pitch value of the CCD lattice gratings accurately or what would be the distance between the gratings and the CCD arrays where moiré fringe images formed. Our method, in which micro-stages were used to precisely measure the displacement of the tested lens, and a one dimensional wavelet transform algorithm was applied to estimate the pitch values of the moiré patterns, could avoid these obstacles. Compared to those systems also based on moiré effects but using coherent light sources, our optical setup is less expensive, easier to implement and has an acceptable accuracy.