Browsing by Subject "Fourier analysis"

Now showing 1 - 8 of 8

Open Access
Approximate fourier domain expression for bloch-siegert shift
(John Wiley and Sons Inc., 2015) Turk, E. A.; Ider, Y. Z.; Ergun, A. S.; Atalar, Ergin
Purpose: In this study, a newsimple Fourier domain-based analytical expression for the Bloch-Siegert (BS) shift-based B1 mapping method is proposed to obtain |B1+| more accurately while using short BS pulse durations and small off-resonance frequencies.Theory and Methods: A new simple analytical expression for the BS shift is derived by simplifying the Bloch equations. In this expression, the phase is calculated in terms of the Fourier transform of the radiofrequency pulse envelope, and thus making the off- and on-resonance effects more easily understandable. To verify the accuracy of the proposed expression, Bloch simulations and MR experiments are performed for the hard, Fermi, and Shinner-Le Roux pulse shapes.Results: Analyses of the BS phase shift-based B1 mapping method in terms of radiofrequency pulse shape, pulse duration, and off-resonance frequency show that |B1+| can be obtained more accurately with the aid of this new expression.Conclusions: In this study, a new simple frequency domain analytical expression is proposed for the BS shift. Using this expression, |B1+| values can be predicted from the phase data using the frequency spectrum of the radiofrequency pulse. This method works well even for short pulse durations and small offset frequencies.
Open Access
Beyond Bouma's window: how to explain global aspects of crowding?
(Public Library of Science, 2019-05) Doerig, A.; Bornet, A.; Rosenholtz, R.; Francis, G.; Clarke, Aaron M.; Herzog, M. H.
In crowding, perception of an object deteriorates in the presence of nearby elements. Although crowding is a ubiquitous phenomenon, since elements are rarely seen in isolation, to date there exists no consensus on how to model it. Previous experiments showed that the global configuration of the entire stimulus must be taken into account. These findings rule out simple pooling or substitution models and favor models sensitive to global spatial aspects. In order to investigate how to incorporate global aspects into models, we tested a large number of models with a database of forty stimuli tailored for the global aspects of crowding. Our results show that incorporating grouping like components strongly improves model performance. Author summary Visual crowding highlights interactions between elements in the visual field. For example, an object is more difficult to recognize if it is presented in clutter. Crowding is one of the most fundamental aspects of vision, playing crucial roles in object recognition, reading and visual perception in general, and is therefore an essential tool to understand how the visual system encodes information based on its retinal input. Hence, classic models of crowding have focused only on local interactions between neighboring visual elements. However, abundant experimental evidence argues against local processing, suggesting that the global configuration of visual elements strongly modulates crowding. Here, we tested all available models of crowding that are able to capture global processing across the entire visual field. We tested 12 models including the Texture Tiling Model, a Deep Convolutional Neural Network and the LAMINART neural network with large scale computer simulations. We found that models incorporating a grouping component are best suited to explain the data. Our results suggest that in order to understand vision in general, mid-level, contextual processing is inevitable.
Open Access
Fourier transform magnetic resonance current density imaging (FT-MRCDI) from one component of magnetic flux density
(IOP Publishing, 2010-05-17) Ider, Y. Z.; Birgul, O.; Oran, O. F.; Arıkan, Orhan; Hamamura, M. J.; Muftuler, L. T.
Fourier transform (FT)-based algorithms for magnetic resonance current density imaging (MRCDI) from one component of magnetic flux density have been developed for 2D and 3D problems. For 2D problems, where current is confined to the xy-plane and z-component of the magnetic flux density is measured also on the xy-plane inside the object, an iterative FT-MRCDI algorithm is developed by which both the current distribution inside the object and the z-component of the magnetic flux density on the xy-plane outside the object are reconstructed. The method is applied to simulated as well as actual data from phantoms. The effect of measurement error on the spatial resolution of the current density reconstruction is also investigated. For 3D objects an iterative FT-based algorithm is developed whereby the projected current is reconstructed on any slice using as data the Laplacian of the z-component of magnetic flux density measured for that slice. In an injected current MRCDI scenario, the current is not divergence free on the boundary of the object. The method developed in this study also handles this situation.
Open Access
Fourier transform plasmon resonance spectrometer using nanoslit-nanowire pair
(American Institute of Physics, 2019) Uulu, Doolos Aibek; Ashirov, Timur; Polat, N.; Yakar, O.; Balcı, S.; Kocabaş, C.
In this paper, we present a nanoscale Fourier transform spectrometer using a plasmonic interferometer consisting of a tilt subwavelength slit-nanowire pair on a metallic surface fabricated by the focused ion beam microfabrication technique. The incident broadband light strongly couples with the surface plasmons on the gold surface, and thus, surface plasmon polaritons (SPPs) are generated. The launched SPPs interfere with the incident light and generate high contrast interference fringes in the nanoslit. The transmitted SPPs through the metal nanoslit can decouple into free space and are collected by an objective in the far field. The spectroscopic information of the incidence light is obtained by fast Fourier transform of the fringe pattern of the SPPs. In our design, there is no need for a bulky dispersive spectrometer or dispersive optical elements. The dimension of the spectrometer is around 200 μm length. Our design is based on inherent coherence of the SPP waves propagating through the subwavelength metal nanoslit structures etched into an opaque gold film.
Open Access
Fundamental structure of Fresnel diffraction: Longitudinal uniformity with respect to fractional Fourier order
(Optical Society of America, 2011-12-24) Özaktaş, Haldun M.; Arik, S. O.; Coşkun, T.
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.
Open Access
Fundamental structure of Fresnel diffraction: natural sampling grid and the fractional Fourier transform
(Optical Society of America, 2011-06-29) Özaktaş, Haldun M.; Arik, S. O.; Coskun, T.
Fresnel integrals corresponding to different distances can be interpreted as scaled fractional Fourier transformations observed on spherical reference surfaces. We show that by judiciously choosing sample points on these curved reference surfaces, it is possible to represent the diffracted signals in a nonredundant manner. The change in sample spacing with distance reflects the structure of Fresnel diffraction. This sampling grid also provides a simple and robust basis for accurate and efficient computation, which naturally handles the challenges of sampling chirplike kernels.
Open Access
Parametric power spectral density analysis of noise from instrumentation in MALDI TOF mass spectrometry
(2007) Shin H.; Mutlu, M.; Koomen J.M.; Markey, M.K.
Noise in mass spectrometry can interfere with identification of the biochemical substances in the sample. For example, the electric motors and circuits inside the mass spectrometer or in nearby equipment generate random noise that may distort the true shape of mass spectra. This paper presents a stochastic signal processing approach to analyzing noise from electrical noise sources (i.e., noise from instrumentation) in MALDI TOF mass spectrometry. Noise from instrumentation was hypothesized to be a mixture of thermal noise, 1/f noise, and electric or magnetic interference in the instrument. Parametric power spectral density estimation was conducted to derive the power distribution of noise from instrumentation with respect to frequencies. As expected, the experimental results show that noise from instrumentation contains 1/f noise and prominent periodic components in addition to thermal noise. These periodic components imply that the mass spectrometers used in this study may not be completely shielded from the internal or external electrical noise sources. However, according to a simulation study of human plasma mass spectra, noise from instrumentation does not seem to affect mass spectra significantly. In conclusion, analysis of noise from instrumentation using stochastic signal processing here provides an intuitive perspective on how to quantify noise in mass spectrometry through spectral modeling.
Open Access
Ultralow threshold laser action from toroidal polymer microcavity
(American Institute of Phycsics, 2009) Tulek, A.; Akbulut, D.; Bayındır, Mehmet
We report laser action from a toroidal microcavity coated with π-conjugated polymer. An ultralow threshold value of ∼200 pJ/pulse is achieved by free space excitation in ambient conditions. This is the lowest threshold energy obtained in microtoroid lasers by free space excitation. The effective refractive index of the polymer, extracted from Fourier analysis of emission spectra, is 1.787, which is very close to measured value of 1.790 indicating that laser modes are located around the circumference of the cavity as whispering gallery resonances. © 2009 American Institute of Physics.