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Application of adaptive photodetectors and the Talbot effect to measure the focal length of a lens

Focal length is a fundamental lens parameter. The main methods to measure the focal length in the optical shop include nodal bench and image magnification. On the other hand, high accuracy methods involve diffraction and interferometric setups. We propose in this work the use of adaptive photodetectors based on the non-steady state photo-electromotive force effect and the Talbot effect to determine the focal length of a lens; in the range of few meters. As the adaptive photodetectors produce an electrical current proportional to the square of visibility of the light pattern which impinges on them, there is no image processing involved in the detection process. Adaptive photodetectors has been used to determine with high accuracy the positions of maximum and minimum visibility of the light patterns diffracted by a vibrating grating (Talbot effect or self-imaging phenomenon). Therefore, if we place the lens under test close to the diffraction grating, the positions of maximum and minimum visibility will be shifted. By measuring the value of this shift the focal length of the lens under test can be readily determined. Preliminary experiments demonstrate that is possible to determine focal lengths up to 3 meters with an uncertainty about 0.1 %.