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In this work, we propose and demonstrate experimentally a compact technique for the generation of cylindrical vector beams, based on a Michelson interferometer and a $\pi$-astigmatic mode converter, capable of inverting the topological charge of higher-order Laguerre-Gauss beams. Compared to previously demonstrated methods, this is relatively easy to align, and very compact. In addition, it generalises the concept of astigmatic mode conversion, commonly associated with scalar beams, to vector beams with non-homogeneous polarisation distribution. We anticipate that many of the applications based on Michelson interferometers will benefit from the unique properties of vector beams., Comment: 5 pages, 4 figures

In ground-based extensive air shower experiments, the direction and energy are reconstructed by measuring the relative arrival time of secondary particles, and the energy they deposit. The measurement precision of the arrival time is crucial for determination of the angular resolution. For this purpose, we need to obtain a precise relative time offset for each detector, and to apply the calibration process. The time offset is associated with the photomultiplier tube, cable, relevant electronic circuits, etc. In view of the transit time through long cables being heavily dependent on the ambient temperature, a real-time calibration method for the cable transit time is investigated in this paper. Even with a poor-resolution time-to-digital converter, this method can achieve high precision. This has been successfully demonstrated with the Front-End-Electronic board used in the Daya Bay neutrino experiment.