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The first aim of this paper is to give emphasis to the importance of assessing phase information when reconstructing and mapping a sound field. In fact, in acoustic analysis phase distribution is frequently simply either not considered or ignored, even though it can supply very useful information for the understanding of the mapping itself or for further analyses. In this paper a procedure to carry out phase mapping of acoustic sources in beamforming measurement is illustrated. The second aim of this paper is to propose a straightforward iterative optimization algorithm based on the monopole substitution starting from beamforming results. It allows for the reconstruction of sound field without the use of any matrix inversion. Both numerical and experimental validations of the method are presented. Results shown hereafter prove the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

As a three-dimensional measuring instrument, the laser tracker is widely used in industrial measurement. To avoid the influence of angle measurement error on the overall measurement accuracy, the multi-station and time-sharing measurement with a laser tracker is introduced on the basis of the global positioning system (GPS) principle in this paper. For the proposed method, how to accurately determine the coordinates of each measuring point by using a large amount of measured data is a critical issue. Taking detecting motion error of a numerical control machine tool, for example, the corresponding measurement algorithms are investigated thoroughly. By establishing the mathematical model of detecting motion error of a machine tool with this method, the analytical algorithm concerning on base station calibration and measuring point determination is deduced without selecting the initial iterative value in calculation. However, when the motion area of the machine tool is in a 2D plane, the coefficient matrix of base station calibration is singular, which generates a distortion result. In order to overcome the limitation of the original algorithm, an improved analytical algorithm is also derived. Meanwhile, the calibration accuracy of the base station with the improved algorithm is compared with that with the original analytical algorithm and some iterative algorithms, such as the Gauss-Newton algorithm and Levenberg-Marquardt algorithm. The experiment further verifies the feasibility and effectiveness of the improved algorithm. In addition, the different motion areas of the machine tool have certain influence on the calibration accuracy of the base station, and the corresponding influence of measurement error on the calibration result of the base station depending on the condition number of coefficient matrix are analyzed. [ABSTRACT FROM AUTHOR]