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The method of second order moments applied to laser on d beam propagation is reviewed. on; Beam propaga~on; Second order moments: @ti& vstems.

An apparatus was developed to obtain, for the first time, 2D maps of the surface resistance of the inner surface of an operating superconducting radio-frequency niobium cavity by a low-temperature laser scanning microscopy technique. This allows identifying non-uniformities of the surface resistance with a spatial resolution of about one order of magnitude better than with earlier methods and surface resistance resolution of ~ 1  at 3.3 GHz. A signal-to-noise ratio of about 10 dB was obtained with 240 mW laser power and 1 Hz modulation frequency. The various components of the apparatus, the experimental procedure and results are discussed in detail in this contribution.

A complete spatial characterization (in second-order moments) of a doughnut-type beam from a pulsed transversely excited atmospheric CO2 laser is described. It includes the measurement of the orbital angular momentum carried by the beam. The key element in the characterization is the use of a cylindrical lens in addition to the usual spherical optics. Internal features of the beam that would have remained hidden if only spherical optics were employed were revealed by use of the cylindrical lens. The experimental results are compared and agree with a theoretical Laguerre-Gauss mode beam.

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