A simple method for determining focal distances using Talbot self-images

We present a simple method to determine the focal distances of lenses with the Talbot self-images. This method uses only one grating, and a priori knowledge of the period of the grating is replaced with a linear relation between the (de)magnified periods of the Talbot images and the lens-to-grating distance. A thick lens whose effective focal length is 500 mm was used to validate the method, and the focal distance of the converging beam was determined with the difference of 0.15% for the nominal focal distance of 521.9 mm. The determined period of the grating with the difference of 0.2% also supports the validation.