Diffraction Fields of Fractally Bounded Apertures

Sakurada, Yasushi; Uozumi, Jun; Asakura, Toshimitsu

doi:10.1007/s10043-994-0003-9

Cited by 15 publications

(9 citation statements)

References 14 publications

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“…Fourier images, obtained by digitized pictures of domain structures, correspond both the results of the theoretical calculation and the experimentally observed diffraction patterns [7]. In addition, similar numerical methods have been used for a number of other fractal objects [8], for which the phenomenon of diffraction have been well studied by other authors [9][10][11]. The agreement obtained Fourier images (diffraction patterns) with the results of these experimental and theoretical studies was quite good.…”

Section: Declaration Of Procedures For Koch Fractals Fourier Images Obsupporting

confidence: 60%

“…Then the average resulting intensity of the diffracted radiation inside of each ring is calculated (3) after that the dependence Ī(r k ) in double logarithmic scale is built, and module of the slope of the linear section of which determines the fractal dimension D f .. For self-similar fractals, to discussed in this work fractals belong, the value of coincides with the scaling factor of the elements in the transition between adjacent hierarchical levels of the fractal, and the value of r 0 must be chosen so that each of the annular zones contained only congruent fragments of the dif-fraction patterns [9][10][11][12][13].…”

Section: Methods Of Koch Fractals Dimension Determinationmentioning

confidence: 99%

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Family of Generalized Triadic Koch Fractals: Dimentions and Fourier Images

Arzamastseva¹,

Evtikhov²,

Lisovsky³

et al. 2016

RENSIT

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Abstract. Fourier images of generalized triadic Koch fractals (curves and snowflakes) with variable vertex angle of generator were obtained by digital methods. The comparison of different methods of fractal dimensions determination using Fraunhofer diffraction patterns was made. Analysis of the size ratio dependence of central (fractal) and peripheral (lattice) parts of diffraction pattern both upon vertex angle at a fixed value of prefractal generation number and upon prefractal generation number at a fixed value of vertex angle was made. The features of Koch curves and Koch snowflakes Fourier images are discussed.

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Section: Declaration Of Procedures For Koch Fractals Fourier Images Obsupporting

confidence: 60%

Section: Methods Of Koch Fractals Dimension Determinationmentioning

confidence: 99%

Family of Generalized Triadic Koch Fractals: Dimentions and Fourier Images

Arzamastseva¹,

Evtikhov²,

Lisovsky³

et al. 2016

RENSIT

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“…and the creation of its artificial implants by using new biocomposit materials are described most completely by using Mueller matrix, 1000 {F} = 0 f22 f23 124 (1) Here: p -orientation angle of biocrystal optical axis in relation incidence plane, ö-phase shift magnitude introduced by fractal domain.…”

Section: Theory Studiesmentioning

confidence: 99%

Phase-polarized visualization and processing coherent images of biotissue fractal structures

et al. 1999

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“…Authors of papers [17][18] for the first time performed experiments on the scattering of light by microphotographs of the Koch snowflake in order to get the Fourierimage of it and compared obtained data with the theory using the analytical description of a fractal. The features of Fraunhofer diffraction for other fractal objects (Vicsek fractal, Cantor bar, Sierpinski carpet, etc.…”

Section: Introductionmentioning

confidence: 99%

Foirier Images Quasisymmetry of Generalized Triadic Koch Prefractals

Arzamastseva¹,

Evtikhov²,

Lisovsky³

et al. 2016

RENSIT

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Abstract. The study of the Fourier-images properties was made by numerical methods for the family of flat triadic geometric prefractals with generator in the form of symmetric four-stage broken line with an arbitrary angle at the apex between the central units and the initiator in the form of a straight line (Koch curve) or in the form of an equilateral triangle (the Koch snowflake). To obtain the Fourier images the pictures of fractals were approximated by a grid function on a uniform grid with cells small enough for adequate mapping of high generation prefractal details, and then were digitized in order to use fast Fourier transform for determination the values of the squared modules of the Fourier component, that is, the spectral intensity distribution of diffraction maxima in the Fraunhofer region. An analysis showed that for the values of the vertex or base angles equal to the integer fraction of 180 degrees, Fourier images are the same as for the perfect crystals with the symmetry axes of the 2-nd, 3-th, 4-th and 6-th order, or as for parcuet mosaics or quasicrystals with the axes of quasisymmetry of any order. Really in the Fourier images of the Koch curves with the initiator in the form of a straight line was observed axis of quasisymmetry from 3rd to 9 th and 11-th order. Similar to the above-described properties are also inherent to Fourier images of the Koch snowflake with the initiator in the form of an equilateral triangle. The configuration of the observed Fourier images can be approximately regarded as a radial-annular, at that in the peripheral ("lattice") of the images is dominated by the radial nature of the frequency distribution of diffraction reflections along the radius, and in the central ("fractal") -a ring with self-similarity. The lattice part has a kind of clustering: all the rays have a strong central chain of reflexes along the radii and parallel to it the weaker satellites on both sides. All Fourier images had the center of symmetry, which is an integral attribute of the diffraction patterns in the Fraunhofer zone for any objects, however, the rotational symmetry was not perfect: the positions of the diffraction reflexes when rotating images at angles that correspond to the order of the symmetry axis remain unchanged, but their intensity could vary. The cause of the observed features is that prefractals, unlike crystals, are not a continuum of point objects but two-dimensional set of equal length line segments with different orientation in space. In this set for the considered configurations of the generator it is possible to allocate several two-dimensional subsets with equally oriented segments, each of which contains a number of partial one-dimensional diffraction gratings formed by segments located along the same line. These parallel lattice in the general case contain a different number of segments, and the degree of filling and the distance between adjacent segments, determining the intensity and diffraction reflections distribution structure along the line, depend on the orie...

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Diffraction Fields of Fractally Bounded Apertures

Cited by 15 publications

References 14 publications

Family of Generalized Triadic Koch Fractals: Dimentions and Fourier Images

Family of Generalized Triadic Koch Fractals: Dimentions and Fourier Images

Phase-polarized visualization and processing coherent images of biotissue fractal structures

Foirier Images Quasisymmetry of Generalized Triadic Koch Prefractals

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