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The approximation of smooth functions with a spectral basis typically leads to rapidly decaying coefficients where the rate of decay depends on the smoothness of the function and vice-versa. The optimal number of degrees of freedom in the…
Differential equations are used to model and predict the behaviour of complex systems in a wide range of fields, and the ability to solve them is an important asset for understanding and predicting the behaviour of these systems.…
The propagation and transmission of Bessel beams through nano-layered structures has been discussed recently. Within this framework we recognize the formation of unguided diffraction-free waves with the spot size approaching and…
The derivation of suitable analytical models is an important step for the design and analysis of molecular communication systems. However, many existing models have limited applicability in practical scenarios due to various simplifications…
Diffraction gratings with large angular dispersion rates are central to obtaining high spectral resolution in grating spectrometers operating over a broad spectral range from infrared to soft-x-ray domains. The greatest challenge is of…
Numerous applications require the simultaneous redistribution of the irradiance and phase of a laser beam. The beam shape is thereby determined by the respective application. An elegant way to control the irradiance and phase at the same…
An increasing number of research topics and applications ask for a precise measurement of the size distribution of small bubbles in a liquid - and hence for reliable and automated image analysis. However, due to the strong mismatch between…
The evaluation of vector wave fields can be accurately performed by means of diffraction integrals, differential equations and also series expansions. In this paper, a Bessel series expansion which basis relies on the exact solution of the…
The diameter of a graph is among its most basic parameters. Since a few years, it moreover became a key issue to compute it for massive graphs in the context of complex network analysis. However, known algorithms, including the ones…
To overcome the limit of diffraction while achieving the superresolution technique, solid immersion lenses are the key optical elements for data storage and nanophotonics applications. Recent demonstrations have shown how different…
We utilize the localization analysis method to precisely determine the light beam positions with the spatial separation beyond the optical diffraction limit. By such a direct spatial measurement, the associated optical setup is built to…
Approximating functions by a linear span of truncated basis sets is a standard procedure for the numerical solution of differential and integral equations. Commonly used concepts of approximation methods are well-posed and convergent, by…
We report on a versatile method to compensate the linear attenuation in a medium, independently of its microscopic origin. The method exploits diffraction-limited Bessel beams and tailored on-axis intensity profiles which are generated…
This paper introduces a novel approach to the fine alignment of images in a burst captured by a handheld camera. In contrast to traditional techniques that estimate two-dimensional transformations between frame pairs or rely on discrete…
This work describes a novel image analysis approach to characterize the uniformity of objects in agglomerates by using the propagation of normal wavefronts. The problem of width uniformity is discussed and its importance for the…
We propose a method for designing refractive optical elements for collimated beam shaping. In this method, the problem of finding a ray mapping is formulated as a linear assignment problem, which is a discrete version of the corresponding…
The imaging problem of a specular reflector is revisited. Retaining terms through second order in the reflector surface expansion, we derive the form of the aberration-limiting aperture for arbitrary magnification assuming no bandwidth…
We consider estimating a small transverse displacement of an optical beam over a line-of-sight propagation path: a problem that has numerous important applications ranging from establishing a lasercom link, single-molecule tracking, guided…
We propose a method for approximating the large deviation rate function of time-integrated observables of diffusion processes, used in statistical physics to characterize the fluctuations of nonequilibrium systems. The method is based on…
Consider scene understanding problems such as predicting where a person is probably reaching, or inferring the pose of 3D objects from depth images, or inferring the probable street crossings of pedestrians at a busy intersection. This…