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Optical fields propagating through quadratic-phase systems (QPSs) can be modeled as magnified fractional Fourier transforms (FRTs) of the input field, provided we observe them on suitably defined spherical reference surfaces. Non-redundant representation of the fields with the minimum number of samples becomes possible by appropriate choice of sample points on these surfaces. Longitudinally, these surfaces should not be spaced equally with the distance of propagation, but with respect to the FRT order. The non-uniform sampling grid that emerges mirrors the fundamental structure of propagation through QPSs. By providing a means to effectively handle the sampling of chirp functions, it allows for accurate and efficient computation of optical fields propagating in QPSs. © 2015 Elsevier B.V. All rights reserved.

Diplomsko delo obravnava problematiko tesnjenja temeljnih konstrukcij proti podzemni vodi. Izbrani sta dve možnosti tesnjenja — belo in črno tesnjenje, t.i. bela in črna kad. Obe sta namenjeni tesnitvi temeljnih konstrukcij, vendar se med seboj razlikujeta po tehnološki izvedbi. Ker pa so stroški pomemben razlog pri odločitvi investitorja, katero možnost bo izbral, bo diplomsko delo obravnavalo problem izbire ugodnejše variante izmed izbranima možnostma na konkretnem primeru. Diplomsko delo se sestoji iz dveh delov. V prvem delu diplomskega dela je podan splošni opis problematike vode v zemljini in njen vpliv na temeljne konstrukcije z opisom dveh izbranih možnosti varovanja tesnjenja (bele in črne kadi) proti vdoru talne vode. V drugem delu diplomskega dela je prikazana ekonomska primerjava med belo in črno kadjo na primeru objekta »Hotel City III« v Mariboru. This undergraduate thesis deals with the issue of sealing fundamental structures against groundwater. There are two options selected - white and black tub. Both of them are used for sealing fundamental structures but differ in the technological implementation. Since the cost is an important reason for the investor’s decisions which option to choose, the study will examine the problem of choosing the most advantageous variant of selected options applied to the certain case. The thesis consists of two parts. The first part of the thesis provides a general description of the problem of water in the soil and its impact on the fundamental structure. A description is given of two possibilities of sealing against the penetration of ground water (white and black tub). The second part of the thesis shows the economic comparison between white and black tub on the example of the “Hotel City III” in Maribor.

Fresnel integrals corresponding to different distances can be interpreted as scaled fractional Fourier transformations observed on spherical reference surfaces. Transverse samples can be taken on these surfaces with separation that increases with propagation distance. Here, we are concerned with the separation of the spherical reference surfaces along the longitudinal direction. We show that these surfaces should be equally spaced with respect to the fractional Fourier transform order, rather than being equally spaced with respect to the distance of propagation along the optical axis. The spacing should be of the order of the reciprocal of the space-bandwidth product of the signals. The space-dependent longitudinal and transverse spacings define a grid that reflects the structure of Fresnel diffraction.