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This corrects the article DOI: 10.1103/PhysRevLett.116.163901.

Calculations of the photonic band structure, transmission coefficients, and quality factors of various twodimensional, periodic and aperiodic, dielectric photonic crystals by using the finite element method (FEM) are reported. The fundamental equations governing the propagation of electromagnetic waves in inhomogeneous media are revisited together with the boundary conditions required for each of the performed calculations. A detailed account of the eigenvalue and harmonic propagation analysis of the electromagnetic problem is reported for several periodic and finite-length structures. It is found that this method reproduces quite well previous results for these lattices obtained with the standard plane wave method with regards to the eigenvalue analysis (photonic band structure calculations). However, in contrast with frequency methods, the finite element method easily allows one to study the time-harmonic propagation of electromagnetic fields and, thus, to calculate the transmission coefficient of finite clusters in a natural way. Moreover, the advantages of using this real space method for structures of arbitrary complexity are also discussed. In addition, point defect cluster quality factor calculations are reported by means of FEM and they are compared to the ones obtained with the FDTD and Harminv methods. As a result, FEM comes out as an effective, stable, robust, and rigorous tool to study light propagation and confinement in both periodic and aperiodic dielectric photonic crystals.

This manuscript focuses on methodological and technological advances in the field of health assessment and predictive maintenance for industrial robots. We propose a non-intrusive methodology for industrial robot joint health assessment. Torque sensor data is used to create a digital signature given a defined trajectory and load combination. The signature of each individual robot is later used to diagnose mechanical deterioration. We prove the robustness and reliability of the methodology in a real industrial use case scenario. Then, an in depth mechanical inspection is carried out in order to identify the root cause of the failure diagnosed in this article. The proposed methodology is useful for medium and long term health assessment for industrial robots working in assembly lines, where years of almost uninterrupted work can cause irreversible damage.

Flatness sensors are required for quality control of metal sheets obtained from steel coils by roller leveling and cutting systems. This article presents an innovative system for real-time robust surface estimation of flattened metal sheets composed of two line lasers and a conventional 2D camera. Laser plane triangulation is used for surface height retrieval along virtual surface fibers. The dual laser allows instantaneous robust and quick estimation of the fiber height derivatives. Hermite cubic interpolation along the fibers allows real-time surface estimation and high frequency noise removal. Noise sources are the vibrations induced in the sheet by its movements during the process and some mechanical events, such as cutting into separate pieces. The system is validated on synthetic surfaces that simulate the most critical noise sources and on real data obtained from the installation of the sensor in an actual steel mill. In the comparison with conventional filtering methods, we achieve at least a 41% of improvement in the accuracy of the surface reconstruction.

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