Limit precision analysis of focal length measurement of lens based on Talbot-Moiré

Talbot-Moir based methods utilizes Talbot self-image effect and amplification of Moir fringe for long focal length measurement. Because of the phase transformation of lens, the measurement based on Talbot effect and Moir fringes of Ronchi gratings is suitable to long focal length. The focal length of measured lens is calculated according to its relation to the slope coefficient of Moir fringes taken with CCD camera. Since the focal length of measured lens is much greater than its thickness,the phase transformation of lens to Gauss light beams is approximately expressed by the phase transformation of thin lens to spherical wave.Therefore, the measurement of long focal length is applicable for both Gauss and non-Gasussian lights. Finally, the concept, error and precision limit are analyzed, and the pitch error of the grating is the major contributor.