On the design of spherical gradient index lenses

Classical spherical gradient index (GRIN) lenses (such as Maxwell Fish Eye lens, Eaton lens, Luneburg lens, etc.) design procedure using the Abel integral equation is reviewed and reorganized. Each lens is fully defined by a function called the angle of flight which describes the ray deflection through the lens. The radial refractive index distribution is obtained by applying a linear integral transformation to the angle of flight. The interest of this formulation is in the linearity of the integral transformation which allows us to derive new solutions from linear combinations of known lenses. Beside the review of the classical GRIN designs, we present a numerical method for GRIN lenses defined by the Abel integral equation with fixed limits, which is an ill-posed problem.

Evaluating the quality of riparian forest vegetation: The Riparian Forest Evaluation (RFV) index

Aim of study: This paper presents a novel index, the Riparian Forest Evaluation (RFV) index, for assessing the ecological condition of riparian forests. The status of riparian ecosystems has global importance due to the ecological and social benefits and services they provide. The initiation of the European Water Framework Directive (2000/60/CE) requires the assessment of the hydromorphological quality of natural channels. The Directive describes riparian forests as one of the fundamental components that determine the structure of riverine areas. The RFV index was developed to meet the aim of the Directive and to complement the existing methodologies for the evaluation of riparian forests. Area of study: The RFV index was applied to a wide range of streams and rivers (170 water bodies) inSpain. Materials and methods: The calculation of the RFV index is based on the assessment of both the spatial continuity of the forest (in its three core dimensions: longitudinal, transversal and vertical) and the regeneration capacity of the forest, in a sampling area related to the river hydromorphological pattern. This index enables an evaluation of the quality and degree of alteration of riparian forests. In addition, it helps to determine the scenarios that are necessary to improve the status of riparian forests and to develop processes for restoring their structure and composition. Main results: The results were compared with some previous tools for the assessment of riparian vegetation. The RFV index got the highest average scores in the basins of northernSpain, which suffer lower human influence. The forests in central and southern rivers got worse scores. The bigger differences with other tools were found in complex and partially altered streams and rivers. Research highlights: The study showed the index’s applicability under diverse hydromorphological and ecological conditions and the main advantages of its application. The utilization of the index allows a better understanding of the status of riparian forests, and enhances improvements in the conservation and management of riparian areas.