Talbot Interferometry for Measuring the Focal Length of a Lens without Moiré Fringes

(Received January 19, 2015 : revised February 10, 2015 : accepted February 10, 2015)A simple method to determine the focal length of a lens using the Talbot image is presented. This method uses only one grating, requiring neither Moire fringe analysis nor the angle between the gratings. The original Fourier transform was used to access the spectrum beyond the limitation set of the usual fast Fourier transform to determine the (de)magnification accurately enough to be used for the focal length. A set of Talbot images simulated numerically with the Fresnel diffraction integral was used to demonstrate the method. For focal lengths between 5550 mm and 5650 mm, the mean difference between the focal lengths determined from the Talbot images and the true values was 3.3 mm with the standard deviation of the difference being 3.8 mm. The true focal lengths can be recovered with an accuracy of 0.06%.