Browsing by Subject "Diffraction"

Now showing 1 - 20 of 45

Open Access
Analysis of the complex light field generated by a deflectable mirror array device
(SPIE, 2006) Ulusoy, Erdem; Onural, Levent; Özaktaş, Haldun M.
An exact analysis of the scalar coherent monochromatic light field produced by a deflectable mirror array device is presented. The three-dimensional light field is related to the tilt angles of the mirrors. The first Rayleigh-Sommerfeld diffraction formula is used to model the diffraction. The analysis is carried out based on the assumption that the mirrors can be tilted with continuously varying angles, so the field produced by a finite (discrete) set of possible tilt angles is included as a special case.
Open Access
Asymmetric transmission in prisms using structures and materials with isotropic-type dispersion
(Optical Society of America, 2015) Gundogdu, F. T.; Serebryannikov, A. E.; Cakmak, A. O.; Özbay, Ekmel
It is demonstrated that strong asymmetry in transmission can be obtained at the Gaussian beam illumination for a single prism based on a photonic crystal (PhC) with isotropic-type dispersion, as well as for its analog made of a homogeneous material. Asymmetric transmission can be realized with the aid of refraction at a proper orientation of the interfaces and wedges of the prism, whereas neither contribution of higher diffraction orders nor anisotropic-type dispersion is required. Furthermore, incidence toward a prism wedge can be used for one of two opposite directions in order to obtain asymmetry. Thus, asymmetric transmission is a general property of the prism configurations, which can be obtained by using simple geometries and quite conventional materials. The obtained results show that strong asymmetry can be achieved in PhC prisms with (nearly) circular shape of equifrequency dispersion contours, in both cases associated with the index of refraction 0 < n < 1 and n > 1. For the comparison purposes, results are also presented for solid uniform nonmagnetic prisms made of a material with the same value of n. It is shown in zero-loss approximation that the PhC prism and the ultralow-index material prism ( 0 < n < 1) can replace each other in some cases without affecting the scenario of asymmetric transmission. Moreover, the PhC prism and the solid dielectric prism can show the same scenario at n > 1. Possible contributions of scattering on the individual rods and diffraction on the wedge to the resulting mechanism are discussed. Analogs of unidirectional splitting and unidirectional deflection regimes, which are known from the studies of PhC gratings, are obtained in PhC prisms and solid uniform prisms, i.e. without higher diffraction orders. ©2015 Optical Society of America.
Open Access
A aurvey of signal processing problems and tools in holographic three-dimensional television
(Institute of Electrical and Electronics Engineers, 2007) Onural, L.; Gotchev, A.; Özaktaş, Haldun M.; Stoykova, E.
Diffraction and holography are fertile areas for application of signal theory and processing. Recent work on 3DTV displays has posed particularly challenging signal processing problems. Various procedures to compute Rayleigh-Sommerfeld, Fresnel and Fraunhofer diffraction exist in the literature. Diffraction between parallel planes and tilted planes can be efficiently computed. Discretization and quantization of diffraction fields yield interesting theoretical and practical results, and allow efficient schemes compared to commonly used Nyquist sampling. The literature on computer-generated holography provides a good resource for holographic 3DTV related issues. Fast algorithms to compute Fourier, Walsh-Hadamard, fractional Fourier, linear canonical, Fresnel, and wavelet transforms, as well as optimization-based techniques such as best orthogonal basis, matching pursuit, basis pursuit etc., are especially relevant signal processing techniques for wave propagation, diffraction, holography, and related problems. Atomic decompositions, multiresolution techniques, Gabor functions, and Wigner distributions are among the signal processing techniques which have or may be applied to problems in optics. Research aimed at solving such problems at the intersection of wave optics and signal processing promises not only to facilitate the development of 3DTV systems, but also to contribute to fundamental advances in optics and signal processing theory.
Open Access
Bessel functions-based reconstruction of non-uniformly sampled diffraction fields
(IEEE, 2007) Uzunov, V.; Esmer, G. Bora; Gotchev, A.; Onural, Levent; Özaktaş, Haldun M.
A discrete computational model for the diffraction process is essential in forward problems related to holographic TV. The model must be as general as possible, since the shape of the displayed objects does not bear any restrictions. We derive a discrete diffraction model which suits the problem of reconstruction of diffraction fields from a set of non-uniformly distributed samples. The only restriction of the model is the wave nature of the field. The derivation takes advantage of changing the spatial and frequency coordinates to polar form and ends up with a model stated in terms of Bessel functions. The model proves to be a separable orthogonal basis. It shows rapid convergence when evaluated in the framework of the non-uniform sampling problem.
Open Access
Calculation of the scalar diffraction field from curved surfaces by decomposing the three-dimensional field into a sum of Gaussian beams
(Optical Society of America, 2013) Şahin, E.; Onural, L.
We present a local Gaussian beam decomposition method for calculating the scalar diffraction field due to a twodimensional field specified on a curved surface. We write the three-dimensional field as a sum of Gaussian beams that propagate toward different directions and whose waist positions are taken at discrete points on the curved surface. The discrete positions of the beam waists are obtained by sampling the curved surface such that transversal components of the positions form a regular grid. The modulated Gaussian window functions corresponding to Gaussian beams are placed on the transversal planes that pass through the discrete beam-waist position. The coefficients of the Gaussian beams are found by solving the linear system of equations where the columns of the system matrix represent the field patterns that the Gaussian beams produce on the given curved surface. As a result of using local beams in the expansion, we end up with sparse system matrices. The sparsity of the system matrices provides important advantages in terms of computational complexity and memory allocation while solving the system of linear equations.
Open Access
Computation of holographic patterns between tilted planes
(SPIE - International Society for Optical Engineering, 2006-05) Esmer, Gökhan Bora; Onural, Levent
Computation of the diffraction pattern that gives the desired reconstruction of an object upon proper illumination is an important process in computer generated holography. A fast computational method, based on the plane wave decomposition of 3D field in free-space, is presented to find the desired diffraction pattern. The computational burden includes two FFT algorithms in addition to a shuffling of the frequency components that needs an interpolation in the frequency domain. The algorithm is based on the exact diffraction formulation; there is no need for Fresnel or Fraunhofer approximations. The developed model is utilized to calculate the scalar optical diffraction between tilted planes for monochromatic light. The performance of the presented algorithm is satisfactory for tilt angles up to 60°.
Open Access
Data from: Maximizing the signal-to-noise ratio of diverging ultrasonic waves in multiple scattering, attenuating, and diffracting media
(Bilkent University, 2022-09) Kumru, Yasin
Open Access
Design of a 360-degree holographic 3D video display using commonly available display panels and a paraboloid mirror
(SPIE, 2017) Onural, Levent
Even barely acceptable quality holographic 3D video displays require hundreds of mega pixels with a pixel size in the order of a fraction of a micrometer, when conventional flat panel SLM arrangement is used. Smaller pixel sizes are essential to get larger diffraction angles. Common flat display panels, however, have pixel sizes in the order of tens of micrometers, and this results in diffraction angles in the order of one degree. Here in this design, an array of commonly available (similar to high-end mobile phone display panels) flat display panels, is used. Each flat panel, as an element of the array, directs its outgoing low-diffraction angle light beam to corresponding small portion of a large size paraboloid mirror; the mirror then reflects the slowly-expanding, information carrying beam to direct it at a certain exit angle; this beam constitutes a portion of the final real ghost-like 3D holographic image. The collection of those components from all such flat display panels cover the entire 360-degrees and thus constitute the final real 3D table-top holographic display with a 360-degrees viewing angle. The size of the resultant display is smaller compared to the physical size of the paraboloid mirror, or the overall size of the display panel array; however, an acceptable size table top display can be easily constructed for living-room viewing. A matching camera can also be designed by reversing the optical paths and by replacing the flat display panels by flat wavefront capture devices.
Open Access
Diffraction and holography from a signal processing perspective
(SPIE, 2006) Onural, Levent; Özaktaş, Haldun M.
The fact that plane waves are solutions of the Helmholtz equation in free space allows us to write the exact solution to the diffraction problem as a superposition of plane waves. The solution of other related problems can also be expressed in similar forms. These forms are very well suited for directly importing various signal processing tools to diffraction related problems. Another signal processing-diffraction link is the application of novel sampling theorems and procedures in signal processing to diffraction for the purpose of more convenient and efficient discrete representation and the use of associated computational algorithms. Another noteworthy link between optics and signal processing is the fractional Fourier transform. Revisiting diffraction from a modern signal processing perspectiv is likely to yield both interesting viewpoints and improved techniques.
Open Access
Diffraction from a wavelet point of view
(Optical Society of America, 1993-06-01) Onural, L.
The system impulse response representing the Fresnel diffraction is shown to form a wavelet family of functions. The scale parameter of the wavelet family represents the depth (distance). This observation relates the diffraction-holography-related studies and the wavelet theory. The results may be used in various optical applications such as designing robust volume optical elements for optical signal processing and finding new formulations for optical inverse problems. The results also extend the wavelet concept to the nonbandpass family of functions with the implication of new applications in signal processing. The presented wavelet structure, for example, is a tool for space-depth analysis.
Open Access
Diffraction inspired unidirectional and bidirectional beam splitting in defect-containing photonic structures without interface corrugations
(American Institute of Physics Inc., 2016) Colak, E.; Serebryannikov, A. E.; Usik, P. V.; Özbay, Ekmel
It is shown that strong diffractions and related dual-beam splitting can be obtained at transmission through the nonsymmetric structures that represent two slabs of photonic crystal (PhC) separated by a single coupled-cavity type defect layer, while there are no grating-like corrugations at the interfaces. The basic operation regimes include unidirectional and bidirectional splitting that occur due to the dominant contribution of the first positive and first negative diffraction orders to the transmission, which is typically connected with different manifestations of the asymmetric transmission phenomenon. Being the main component of the resulting transmission mechanism, diffractions appear owing to the effect exerted by the defect layer that works like an embedded diffractive element. Two mechanisms can co-exist in one structure, which differ, among others, in that whether dispersion allows coupling of zero order to a wave propagating in the regular, i.e., defect-free PhC segments or not. The possibility of strong diffractions and efficient splitting related to it strongly depend on the dispersion properties of the Floquet-Bloch modes of the PhC. Existence of one of the studied transmission scenarios is not affected by location of the defect layer.
Open Access
Dispersion irrelevant wideband asymmetric transmission in dielectric photonic crystal gratings
(Optical Society of America, 2012-11-22) Serebryannikov, A. E.; Colak, E.; Cakmak, A. O.; Özbay, Ekmel
Wideband suppression of zero order and relevant strongly asymmetric transmission can be obtained in photonic crystal gratings that are made of linear isotropic materials and show the broken structural (axial) symmetry, even if zero diffraction order may be coupled to a Floquet-Bloch (FB) wave at the incidence and exit interfaces. The studied mechanism requires that the peculiar diffractions at the corrugated exit interface inspire strong energy transfer to higher orders, including those not coupled to an FB wave. At the opposite direction of incidence, transmission due to zero and some higher orders that may be coupled at the corrugated input interface can vanish. This leads to the alternative scenario of wideband unidirectional transmission, which itself does not need but can coexist with the other scenario based on the merging of asymmetric diffraction and dispersion of the FB mode.
Open Access
Effect of growth pressure on coalescence thickness and crystal quality of GaN deposited on 4H-SiC
(Elsevier, 2010-09-25) Caban, P.; Strupinski, W.; Szmidt, J.; Wojcik, M.; Gaca, J.; Kelekci, O.; Caliskan, D.; Özbay, Ekmel
The influence of growth pressure on the coalescence thickness and the crystal quality of GaN deposited on 4HSiC by low pressure metalorganic vapor phase epitaxy was studied. It was shown that growth pressure has an impact on the surface roughness of epilayers and their crystal quality. GaN coalescence thicknesses were determined for the investigated growth pressures. The GaN layers were characterized by AFM and HRXRD measurements. HEMT structures were also fabricated and characterized. Among the growth pressures studied, 50, 125 and 200 mbar, 200 mbar was found to be most suitable for GaN/SiC epitaxy.
Open Access
Effect of sample locations on computation of the exact scalar diffraction field (in English)
(IEEE, 2012) Esmer, G. B.; Özaktaş, Haldun M.; Onural, Levent
Computer generated holography is one of common methods to obtain three-dimensional visualization. It can be explained by behavior of propagating waves and interference. To calculate the scalar diffraction pattern on a hologram, there are myriad of algorithms in the literature. Some of them employ several approximations, so the calculated fields may not be the exact scalar diffraction field. However, there are algorithms to compute the exact scalar diffraction field with some limitations on the distribution of the given samples over the space. These algorithms are based on "field model" approach. The performance of an algorithm, based on field model, is investigated according to the distribution of given samples over the space. From the simulations, it was observed that the cumulative information provided by the given samples has to be enough to solve the inverse scalar diffraction field. The cumulative information can be increased by having more samples, but there are some scenarios that differential information obtained from the given samples can be infinitesimal, thus the exact diffraction field may not be computed. © 2012 IEEE.
Open Access
Exact solution for scalar diffraction between tilted and translated planes using impulse functions over a surface
(Optical Society of America, 2011-02-04) Onural, L.
The diffraction relation between a plane and another plane that is both tilted and translated with respect to the first one is revisited. The derivation of the result becomes easier when the impulse function over a surface is used as a tool. Such an approach converts the original 2D problem to an intermediate 3D problem and thus allows utilization of easy-to-interpret Fourier transform properties due to rotation and translation. An exact solution for the scalar monochromatic propagating waves case when the propagation direction is restricted to be in the forward direction is presented.
Open Access
Fast integral equation techniques for propagation problems
(IEEE, 2004-09) Babaoğlu, Barış; Tunç, Celal A.; Altıntaş, Ayhan; Ertürk, Vakur B.
In this paper, the Method of Moments (MoM) solution is achieved for scattering problems by using the stationary Spectrally Accelerated Forward-Backward method (FBSA) and the non-stationary Spectrally Accelerated BiConjugate Gradient Stabilized (SA-BiCGSTAB) method, with a storage requirement and a computational cost of O(N) per iteration where N is the number of surface unknowns in the discretized integral equation. The SA-BiCGSTAB method is applied over rough terrain profiles as well as re-entrant surfaces which can not be handled by any conventional stationary iterative technique.
Open Access
Fractional Fourier Optics
(Optical Society of America, 1995-04) Özaktaş, Haldun M.; Mendlovic, D.
There exists a fractional Fourier-transform relation between the amplitude distributions of light on two spherical surfaces of given radii and separation. The propagation of light can be viewed as a process of continual fractional Fourier transformation. As light propagates, its amplitude distribution evolves through fractional transforms of increasing order. This result allows us to pose the fractional Fourier transform as a tool for analyzing and describing optical systems composed of an arbitrary sequence of thin lenses and sections of free space and to arrive at a general class of fractional Fourier-transforming systems with variable input and output scale factors.
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
Impulse functions over curves and surfaces and their applications to diffraction
(Elsevier Science & Technology, 2006-10-01) Onural, L.
An explicit preferred definition of impulse functions (Dirac delta functions) over lowerdimensional manifolds in RN is given in such a way to assure uniform concentration per geometric unit of the manifold. Some related properties are presented. An application related to diffraction is demonstrated.