Focal length measurement of a thin lens based on defocused imaging speckle

This paper presents a method for measuring the focal length of a thin lens using defocused imaging speckle. The relationship between the focal length and the in-plane displacement magnification coefficient of a defocused imaging system is derived based on Abbe's principle of image formation. Then, a subjective speckle imaging system is set up. By adjusting a micrometer, the in-plane displacements of the scattering object are obtained, and after imaging, those of the defocused imaging speckle are measured using digital image correlation. A linear relationship between them is fitted to calculate the magnification coefficient, which is then used to determine the focal length of the imaging lens. The results demonstrate that this method can be applied to measure the focal lengths of both positive and negative lenses, with a simple structure, convenient operation, and good consistency with nominal values.