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Fresnel zone

About: Fresnel zone is a research topic. Over the lifetime, 2337 publications have been published within this topic receiving 37650 citations.


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Proceedings ArticleDOI
15 Dec 1993
TL;DR: In this paper, the results on x-ray diffractive focusing elements are described: amplitude and phase-contrast Fresnel zone plates as well as freestanding gold gratings.
Abstract: Problems of microelectronics technology applications for diffractive optical elements fabrication have been considered. The results on x-ray diffractive focusing elements are described: amplitude and phase-contrast Fresnel zone plates as well as freestanding gold gratings. The creation of reflected Bragg-Fresnel lenses for soft x-ray range was made on the basis of multilayer x-ray mirrors. Considerable attention was paid to the correction of different distortion factors involved in the electron beam lithography process.

1 citations

Proceedings ArticleDOI
11 Jan 2005
TL;DR: In this paper, the authors presented a general reconstruction model from the perspective of generalized sampling theory, where an approximation of the continuous complex amplitude at the CCD can be synthesized from a set of basis functions with the recorded samples as weights.
Abstract: In digital holography, holograms are recorded by a CCD-array, and the complex amplitude of the object wave is numerically reconstructed via computer. For different recording conditions and different properties of objects, different reconstruction algorithms are required. The conventional reconstruction algorithms were conceived directly by replacing the diffraction integral with summation. Each method has its limitation in the valid range for correctly calculating the diffraction integral. The Single Fourier Transform method is valid for far Fresnel zone hologram, whereas the convolution method is appropriate for near Fresnel holograms. Here, we present a general reconstruction model from the perspective of “Generalized sampling theory”. Given that the function space in which the unknown complex amplitude lies, an approximation of the continuous complex amplitude at the CCD can be synthesized from a set of basis functions with the recorded samples as weights. Back-propagation of the approximated complex amplitude to the original object plane yields an expression relating the continuous complex amplitude of the object with the recorded samples. By adopting different basis functions and different formulas for describing the diffraction process, an optimal reconstruction algorithm can be developed for various recording conditions and different diffraction characteristics of the object. Contrary to the conventional algorithms where values are available only at specific grid, complex amplitude at any position of the object can be obtained using this model. In addition, the effect due to the non-zero fill factor of the CCD can also be incorporated into the reconstruction algorithm to be further compensated by over-weighting the high frequency components. Two basis functions: Dirac delta- and Sinc-, are studied in detail.

1 citations

Dissertation
20 Jun 2001
TL;DR: In this article, a theory based on the first Rytov approximation is developed wherein the effect of finite-frequency wavefields is included, and the developed scattering theory predicts well the arrival time of waves propagating in media with small-scale inhomogeneity that has a characteristic length smaller in size than the width of Fresnel zones.
Abstract: Small-scale heterogeneity alters the arrival time of waves in a way that cannot be explained by ray theory. It is because ray theory is a high-frequency approximation that does not take the finite-frequency of wavefields into account. A theory based on the first Rytov approximation is developed wherein the effect of finite-frequency waves is included. It is found that the developed scattering theory predicts well the arrival time of waves propagating in media with small-scale inhomogeneity that has a characteristic length smaller in size than the width of Fresnel zones. In the regime for which scattering theory is relevant, it is found that caustics are easily generated in wavefields, but this does not influence the good prediction of finite-frequency arrival times of waves by scattering theory. The regime of scattering theory is relevant when the characteristic length of inhomogeneity is smaller than the width of Fresnel zones. By using ray perturbation theory, a condition for the development of triplications is defined for plane wave sources and for point sources in 2-D and 3-D media. This theory is applied to two cases of slowness media: 1-D slowness perturbation models and 2-D Gaussian random media. The focus position in 1-D slowness models is proportional to the inverse of the square root of the relative slowness fluctuations. For Gaussian random media, the distance at which caustics generate is dependent on the relative slowness perturbation to the power of minus two thirds. The developed scattering theory is tested in a 2-D numerical finite-differences experiment using models with small-scale heterogeneity and in a 3-D physical laboratory experiment where ultrasonic waves propagate through samples of granite with small grain-sizes of the minerals. For both kind of modelling experiments, the length-scale of inhomogeneity of the slowness models is smaller than the width of the Fresnel zones. The results of the 2-D and 3- D modelling experiment confirm that the developed scattering theory is better than ray theory in predicting the arrival time of waves propagating in complex media for which the conditions for ray theory are not valid. In general, ray theory overestimates the observed timeshifts of waves or even worse the ray theoretical timeshifts are anti-correlated with the observed ones for waves propagating in media where the effect of scattering is significant. By comparing the characteristic value of the Fresnel zone with the characteristic length of heterogeneity in different experiments from exploration seismics and seismology, it is shown that the resolution in present-day seismological tomography is that the limits of the validity of ray theory. With an emphasis on surface wave tomography, I show that it is important to implement the effect of finite-frequency waves in tomographic imaging techniques in order to retrieve small-scale structured Earth models with the correct theory. The theory for the scattering of waves is applied in global surface wave tomography for Love waves at 40 s and 150s. The estimated tomographic surface wave models derived from ray theory and scattering theory are similar, because a restrictive regularisation condition is incorperated in the inversion so that structures with length-scales smaller than the Fresnel zones are mostly suppressed. I treat a special case of inverse problem theory, namely the spectral leakage problem. The term spectral leakage indicates that observed data affected by structures with a length-scale that is not account for in a given inverse can leak into the long-wavelength structures that are part of the estimated model. In the case of global surface wave tomography, surface wave scattering theory is used in an inversion including the spectral leakage correction of phase velocity measurements for Love waves at periods of 40 s and 150 s. The global phase velocity models from the spectral leakage inversion are obtained without applying any damping, but they show, however, a good correlation with tectonic features such as plate boundaries, ridges and trenches.

1 citations

Patent
28 Aug 1997
TL;DR: In this article, a lensless joint transform correlator optically determines the relative position of two pinholes placed in parallel arms of a Mach-Zehnder interferometer.
Abstract: A lensless joint transform correlator optically determines the relative position of two pinholes placed in parallel arms of a Mach-Zehnder interferometer. The Fraunhaufer diffraction patterns combine to form a joint power spectrum signal in the joint transform plane. Because of the interference of the two pinhole signals, an encoded lens comprising a Fresnel zone is formed in the joint Fraunhaufer diffraction pattern which is illuminated with a plane wave, and the output signal is taken in the focal plane of the Fresnel zone and magnifies the input pinhole displacement by a factor of ten, enhancing its use in precision positioning servo systems for mask alignment.

1 citations

Journal ArticleDOI
TL;DR: A model for the diffraction effects was developed, and the predicted results correspond well to the measurements and some remarkable effects were explained from the theory of Fresnel zones.
Abstract: In a new type of illumination system for reflective liquid-crystal displays, the frontlight, unwanted shadows appear in certain viewing directions. It will be shown that for an accurate description of these shadows the geometrical optics approach is not satisfactory and that Fresnel diffraction has to be taken into account. A model for the diffraction effects was developed, and the predicted results correspond well to the measurements. In addition, some remarkable effects were explained from the theory of Fresnel zones.

1 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202326
202249
202137
202052
201965
201878