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• The hand-eye calibration is reconsidered as minimizing two kinematic loops' errors. • The alternative linear programming is introduced to solve the calibration. • The semi-convex constraint is also proposed for the construction of cost function. • Two formulations of calibration are presented: homogeneous matrix, dual quaternion. A typical hand-eye robot system has two related kinematic loops, which proper functioning requires the accurate determination of robot-world (RW) and hand-eye (HY) transformations in them. Insofar as HY calibration can resolve only the issues related to HY transformation, this study is focused on the joint treatment of the RW&HY transformations, which process is referred to as simultaneous RW&HY calibration. An alternative linear programming is adopted for the construction of semi-convex objective functions via two algorithms. These involve the homogeneous matrix and dual quaternion parameterizations, respectively. Their feasibility was further tested using simulated and real experimental datasets and compared to the results obtained via two available methods (NL and LMI). The results obtained strongly suggest that the homogeneous matrix parametrization (ALP1) had better performance than the dual quaternion one (ALP2). Meanwhile, both of them yielded the good optimal calibration solutions instead of local minima ones. Therefore, both formulations provide new insights into the behavior and complexity of the simultaneous RW&HY calibration. [ABSTRACT FROM AUTHOR]

Conics-based calibration has been widely inves- tigated in the past several years. The primary method is to utilize the generalized eigenvalue decomposition (GED) of conics. In this paper, we extend the GED method to deal with a general case: two enclosing ellipses. We construct a link between enclosing ellipses and confocal conics. The homography is, thus, decomposed to three components, each of which corresponds to a clear geometrical meaning. Other general conics cases including separate case, intersecting case and hyperbolas case are also discussed. Experiments with simulated and real data demonstrate the good performance of our camera calibration algorithms. [ABSTRACT FROM AUTHOR]

The Follow-up X-ray telescope (FXT) is one of the instruments on board the Einstein Probe (EP) satellite of the Chinese Academy of Sciences (CAS) which was launched in January 2024. The EP mission is dedicated to the study of time-domain high-energy astrophysics, utilising a lobster-eye-based wide-field telescope, complemented by an eROSITA-like optics for follow-up observations. Max Planck Institute for Extraterrestrial Physics (MPE) has provided hardware and conducted measurement campaigns at its test facilities as part of a European contribution to Einstein Probe by ESA, and in addition the eROSITA flight spare mirror assembly as the second FXT module. Three FXT mirror assemblies – structural-thermal, qualification and flight models – have been manufactured. All components underwent acceptance testing using X-rays, followed by the installation of X-ray baffles for stray-light rejection. Subsequently, they underwent environmental tests and X-ray performance evaluations. The final tests of the qualification model, serving as a flight spare, and the flight model included an X-ray calibration at various photon energies ranging from about 0.3 keV to 8 keV. All tests were performed at MPE's test facilities: the laboratory for vibration and thermal-vacuum testing, and the PANTER X-ray facility. Reported are the setups and the results of the respective test sequences, focusing on the qualification and flight mirror assemblies. After delivery to China, all mirror assemblies were subjected to complementary measurements in the X-ray test facility of the Institute for High Energy Physics (IHEP) of CAS. • Design of the Follow-up X-ray telescope (FXT) on Einstein Probe. • FXT model philosophy and test matrix. • FXT X-ray test and calibration results. [ABSTRACT FROM AUTHOR]