Sectorial perturbation of vortex beams: Shannon entropy, orbital angular momentum and topological charge

Transformations of the vortex beams structure subjected to sectorial perturbation were theoretically and experimentally studied. The analysis was based on computing (measuring) the vortex spectrum that enables us to find the orbital angular momentum (OAM) and Shannon entropy (informational entropy). We have revealed that, in the general case, the number of vortices caused by an external perturbation is not related to the topological charge. For arbitrary perturbation, the topological charge remains equal to the initial topological charge of the unperturbed vortex beam. Growth of the vortex number induced by perturbations is associated with the optical uncertainty principle between the sectorial angle and the OAM. The computer simulation has shown that OAM does not depend on the number of vortices induced by perturbations. Moreover, two maxima are formed both in the positive and negative regions of the vortex spectrum. As a result, the OAM does not practically change in a wide range of perturbation angles from 0 to 90 °. However, at large perturbation angles, when the energy is almost equally redistributed between the vortex modes with opposite signs of the topological charge, the OAM rapidly decreases. At the same time, the Shannon entropy monotonically increases with growing perturbation angle. This is due to the fact that the entropy depends only on the number of vortex states caused by external perturbations.

Advanced Nanomeasuring Techniques for Surface Characterization

Advanced precise and accurate nanomeasurement techniques play an important role to improve the function and quality of surface characterization. There are two basic approaches, the hard measuring techniques and the soft computing measuring techniques. The advanced soft measuring techniques include coordinate measuring machines, roundness testing facilities, surface roughness, interferometric methods, confocal optical microscopy, scanning probe microscopy, and computed tomography at the level of nanometer scale. On the other hand, a new technical committee in ISO is established to address characterization issues posed by the areal surface texture and measurement methods. This paper reviews the major advanced soft metrology techniques obtained by optical, tactile, and other means using instruments, classification schemes of them, and their applications in the engineering surfaces. Furthermore, future trends under development in this area are presented and discussed to display proposed solutions for the important issues that need to be addressed scientifically.