In the application of cavity ring-down (CRD) high reflectivity measurement, precise adjustment of ring-down cavity (RDC) is of great importance. The transmission spot shape monitoring, which contains the judgment of the mode order and nodal direction of intracavity transverse mode, is an important method for cavity adjustment. In this paper, several criterions of circumscribed spot shape are compared. After spot binarization, the circumscribed circle, circumscribed rectangle, and circumscribed ellipse of transmission spot is analyzed, respectively. The theoretical comparison shows that the circumscribed ellipse criterion can effectively distinguish the mode order and nodal direction simultaneously. The spot can be recognized as the fundamental transverse mode when the area ratio of the spot to its circumscribed ellipse is in the range of 0.9 to 1.0. This method is tested by an experimental setup. It is found to be an efficient cavity adjustment method for the CRD technique.
For the accurate fitting of cavity decay rate in cavity ring-down technique, the theoretical fitting bias of the weighted least square algorithm for decay signal modulated by definite systemic response time is analyzed and tested. After proper data-point truncation, the finely precise and highly accurate fitting of cavity decay rate can be achieved simultaneously. This method is tested by experimental decay signals, results in better fitting performance than the nonlinear least square fitting (the Levenberg-Marquardt) algorithm.
Shack-Hartmann wavefront sensors calculate the position of focal spot in each sub-aperture from intensity distributions, the noises of the detector itself would have a certain impact on the detecting accuracy and would lead to inaccurate wavefront detections using conventional centroiding method. It has been demonstrated that the correlation algorithms with template matching is able to improve the accuracy. In this paper, several correlation algorithms such as absolute difference function, absolute difference function-squared, square difference function, cross-correlation function and normalized cross-correlation are compared at different signal-to-noise ratios. To further improve the accuracy, interpolation algorithms including equiangular line fitting, parabola interpolation, gauss interpolation and least square method are brought in, which turns out that least square method could minimize the detecting error. Besides, simulations within single aperture and full aperture both illustrate that cross-correlation function is most robust but needs more calculations, so is least square method. Moreover, although absolute difference function would be inaccurate at low signal-to-noise ratios, it still can obtain high detecting accuracy at high signal-to-noise ratios and it minimizes the calculations.
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