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A Study on the Uncertainty of a Laser Triangulator Considering System Covariances
摘要： A laser triangulation system, which is composed of a camera and a laser, calculates distances between objects intersected by the laser plane. Even though there are commercial triangulation systems, developing a new system allows the design to be adapted to the needs, in addition to allowing dimensions or processing times to be optimized; however the disadvantage is that the real accuracy is not known. The aim of the research is to identify and discuss the relevance of the most significant error sources in laser triangulator systems, predicting their error contribution to the final joint measurement accuracy. Two main phases are considered in this study, namely the calibration and measurement processes. The main error sources are identified and characterized throughout both phases, and a synthetic error propagation methodology is proposed to study the measurement accuracy. As a novelty in uncertainty analysis, the present approach encompasses the covariances of correlated system variables, characterizing both phases for a laser triangulator. An experimental methodology is adopted to evaluate the measurement accuracy in a laser triangulator, comparing it with the values obtained with the synthetic error propagation methodology. The relevance of each error source is discussed, as well as the accuracy of the error propagation. A linearity value of 40 μm and maximum error of 0.6 mm are observed for a 100 mm measuring range, with the camera calibration phase being the main error contributor.
关键词： accuracy,camera calibration,laser triangulation,laser calibration,uncertainty,covariances
更新于2025-09-23 15:19:57
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Means and covariances of photon numbers in multimode Gaussian states
摘要： In the field of continuous variables and particularly of Gaussian states an important role is played by the statistics of photon numbers. This issue has been considered in pioneering works for the one- and two-mode cases, but a systematic approach seems not to be available. In this paper, the most general multimode mixed Gaussian state, which is generated starting from a multimode thermal state and processed by the most general Gaussian unitary, is considered. In the N-mode the photon numbers are represented by N random variables, one for each mode, and the target is the evaluation of the means and of the covariances. The means describe statistically the amount of photon numbers in each mode, while the covariances give the correlations between the photon numbers in the different modes. For both means and covariances a closed-form result is obtained, expressed in simple and compact formulas. The main tools are provided by the representation of Gaussian unitaries (given by a cascade of an N-mode squeeze operator, an N-mode rotation operator, and a parallel set of N single-mode displacement operators) and by the corresponding Bogoliubov transformations.
关键词： means,photon numbers,multimode,covariances,Bogoliubov transformations,Gaussian states
更新于2025-09-19 17:15:36