Theses supervised by Prof. Dr. Levent Onural
10 theses · İhsan Doğramacı Bilkent University
Geniş görüş açılı holografik ekranlar için sayıl dalga alanlarından kutuplanmış optik alanlara dönüşüm teknikleri
Although the optical waves are vector-valued electromagnetic waves in nature, in holographic three-dimensional television (3DTV) research, an optical field to be displayed is usually modeled as a scalar wave field. In this respect, during the display phase, the scalar wave should be mapped to a polarized optical field with the intention that the desired scalar results are obtained through the generated polarized waves. This mapping has usually been implemented by directly equating the scalar field to the transverse field components of a simply polarized electric field. Although this conventional method is valid in paraxial fields, it becomes erroneous in wide-angle fields due to the nonnegligibly large longitudinal component of the electric field. In order to make a quantitative analysis of error arising from this mapping, a 2D linear-shift invariant (LSI) system is derived from Maxwell's equations, where the inputs and the output are the transverse and longitudinal components, respectively. The magnitude responses of the filters used in the system and some discrete simulations also indicate the longitudinal component becomes the dominant term in large propagation angles. In order to obtain desired scalar results in wide-angle fields, we develop two other techniques which can be used for different purposes. In the first technique, we apply a pair of 2D lowpass filters to the scalar field before mapping it to the transverse components, where the lowpass filters are derived so as to equalize the power spectra of the given scalar field and the resulting electric field. It is shown through discrete simulations that the excessive amplification of the longitudinal component and the deteriorations in the electric field intensity in large propagation angles are prevented by the specified lowpass filters. In the second technique, we first impose a constraint on the electric field vector to be generated such that the amplitude vector of a plane wave has a simple polarization state at plane which is orthogonal to the corresponding propagation direction. Then, the components of the vector amplitude of the plane wave at that locally transverse plane are directly matched with the amplitude of the corresponding plane wave component of the scalar field. As a result of the second technique, the desired intensity images can be obtained if an imaging sensor captures a locally paraxial segment of the field on its observation plane; this is the case for common sensors. The validity of the second technique is justified through the computer simulation of a holographic display of a computer generated 3D object. In the simulation, the proposed method outperforms the conventional method and ends up with the correct intensity of the scalar field associated with the object at different tilted and rotated planes. In conclusion, use of the scalar theory of optics becomes possible also in wide-angle fields as a consequence of the developed techniques and the prescribed scalar results can be realized by means of wide-viewing-angle holographic displays.
Eğimli düzlemler arasında holografik desen hesaplanması
ABSTRACTCOMPUTATION OF HOLOGRAPHICPATTERNS BETWEEN TILTED PLANESGükhan Bora EsmeroM.S. in Electrical and Electronics EngineeringSupervisor: Prof. Dr. Levent OnuralJune 2004Holography is a three-dimensional visualization method. This method dependson duplication of information-carrying optical waves which come from a three-dimensional environment in the absence of the original source. Computation ofthe diï¬raction pattern due to an object is the most important process in digitalholography. The diï¬raction pattern due to an object can be calculated by us-ing several methods. Two models are generated and they are based directly onRayleigh-Sommerfeld diï¬raction integral; there is no need for Fresnel or Fraun-hofer approximations. The generated models are used to calculate scalar opticaldiï¬raction between tilted planes for monochromatic light. First model we gener-ate is called pointwise model. The model provides calculation of the diï¬ractionpattern on an observation plane by superposition of the diï¬raction patterns ofthe point light sources that made up the object on a input plane. However, it isa time consuming process. Second model is named plane wave spectrum modeland it is much more faster than the pointwise model. The performances of thepresented models are examined under several scenarios.Keywords: Digital Holography, Plane Wave Spectrum Diï¬raction, Scalar OpticalDiï¬raction, Fresnel Diï¬raction, 3-D Objects.iii
Nokta bulutlarının çok yönlü ortografik izdüşümlerinden geri çatmalarının elde edilmesi
A method to reconstruct 3D point clouds using multi-view orthographic projections isexamined. Point clouds are generated by means of a stochastic process. This stochasticprocess is designed to generate point clouds that mimic microcalcification formation in breasttissue. Point clouds are generated using a Gibbs sampler algorithm. Orthographic projectionsof point clouds from any desired orientation are generated. Volumetric intersection method isemployed to perform the reconstruction from these orthographic projections. Thereconstruction may yield erroneous reconstructed points. The types of these erroneous pointsare analyzed along with their causes and a performance measure based on linear combinationis devised. Experiments have been designed to investigate the effect of the number ofprojections and the number of points to the performance of reconstruction. Increasing thenumber of projections and decreasing the number of points resulted in better reconstructionsthat are more similar to the original point clouds. However, it is observed that reconstructionsdo not improve considerably upon increasing the number of projections after some number.This method of reconstruction serves well to find locations of original points.Keywords: 3D reconstruction, visual hull, shape from silhouettes, volumetric intersection,point clouds, Gibbs sampler, orthographic projection
Öznitelikli nokta sınıflandırması ve eşlemesi
A feature point is a salient point which can be separated from its neighborhood. Widely used definitions assume that feature points are corners. However, some non-feature points also satisfy this assumption. Hence, non-feature points, which are highly undesired, are usually detected as feature points. Texture properties around detected points can be used to eliminate non-feature points by determining the distinctiveness of the detected points within their neighborhoods. There are many texture description methods, such as autoregressive models, Gibbs/Markov random field models, time-frequency transforms, etc. To increase the performance of feature point related applications, two new feature point descriptors are proposed, and used in non-feature point elimination and feature point sorting-matching. To have a computationally feasible descriptor algorithm, a single image resolution scale is selected for analyzing the texture properties around the detected points. To create a scale-space, wavelet decomposition is applied to the given images and neighborhood scale-spaces are formed for every detected point. The analysis scale of a point is selected according to the changes in the kurtosis values of histograms which are extracted from the neighborhood scale-space. By using descriptors, the detected iii non-feature points are eliminated, feature points are sorted and with inclusion of conventional descriptors feature points are matched. According to the scores obtained in the experiments, the proposed detection-matching scheme performs more reliable than the Harris detector gray-level patch matching scheme. However, SIFT detection-matching scheme performs better than the proposed scheme. Keywords: Feature Point Elimination, Feature Point Matching, Digital Video Processing, Feature Point Detection, Feature Points.
Mobil platformlar üzerinde üç-boyutlu video kodlanması
With the evolution of the wireless communication technologies and the multimedia capabilities of the mobile phones, it is expected that three-dimensional (3D) video technologies will soon get adapted to the mobile phones. This raises the problem of choosing the best 3D video representation and the most efficient coding method for the selected representation for mobile platforms. Since the latest 2D video coding standard, H.264/MPEG-4 AVC, provides better coding efficiency over its predecessors, coding methods of the most common 3D video representations are based on this standard. Among the most common 3D video representations, there are multi-view video, video plus depth, multi-view video plus depth and layered depth video. For using on mobile platforms, we selected the conventional stereo video (CSV), which is a special case of multi-view video, since it is the simplest among the available representations. To determine the best coding method for CSV, we compared the simulcast coding, multi-view coding (MVC) and mixed-resolution stereoscopic coding (MRSC) without inter-view prediction, with subjective tests using simple coding schemes. From these tests, MVC is found to provide the best visual quality for the testbed we used, but MRSC without inter-view prediction still came out to be promising for some of the test sequences and especially for low bit rates. Then we adapted the Joint Video Team's reference multi-view decoder to run on ZOOM OMAP34x Mobile Development Kit (MDK). The first decoding performance tests on the MDK resulted with around four stereo frames per second with frame resolutions of 640x352. To further improve the performance, the decoder software is profiled and the most demanding algorithms are ported to run on the embedded DSP core. Tests resulted with performance gains ranging from 25% to 60% on the DSP core. However, due to the design of the hardware platform and the structure of the reference decoder, the time spent for the communication link between the main processing unit and the DSP core is found to be high, leaving the performance gains insignificant. For this reason, it is concluded that the reference decoder should be restructured to use this communication link as infrequently as possible in order to achieve overall performance gains by using the DSP core.
Uzayda dağılmış örneklerden skalar optik kırınım alanı hesaplanması
As a three-dimensional viewing technique, holographyprovides successful three-dimensional perceptions. The technique isbased on duplication of the information carrying optical waves whichcome from an object. Therefore, calculation of the diffraction fielddue to the object is an important process in digital holography. Tohave the exact reconstruction of the object, the exact diffractionfield created by the object has to be calculated. In the literature,one of the commonly used approach in calculation of the diffractionfield due to an object is to superpose the fields created by theelementary building blocks of the object; such procedures may becalled as the ``source model" approach and such a computed field canbe different from the exact field over the entire space. In thiswork, we propose four algorithms to calculate the exact diffractionfield due to an object. These proposed algorithms may be called asthe ``field model" approach. In the first algorithm, the diffractionfield given over the manifold, which defines the surface of theobject, is decomposed onto a function set derived from propagatingplane waves. Second algorithm is based on pseudo inversion of thesystem matrix which gives the relation between the given fieldsamples and the field over a transversal plane. Third and fourthalgorithms are iterative methods. In the third algorithm,diffraction field is calculated by a projection method onto convexsets. In the fourth algorithm, pseudo inversion of the system matrixis computed by conjugate gradient method. Depending on the numberand the locations of the given samples, the proposed algorithmsprovide the exact field solution over the entire space. To computethe exact field, the number of given samples has to be larger thanthe number of plane waves that forms the diffraction field over theentire space. The solution is affected by the dependencies betweenthe given samples. To decrease the dependencies between the givensamples, the samples over the manifold may be taken randomly.Iterative algorithms outperforms the rest of them in terms ofcomputational complexity when the number of given samples are largerthan 1.4 times the number of plane waves forming the diffractionfield over the entire space.
Birçok düşük çözünürlüklü kayıt kullanarak kırınım desenlerinin çözünürlüğünün arttırılması
Holography attempts to record and reconstruct wave fields. The resolution limitationof the recording equipments causes some problems in the reconstructionprocess. An automatic method for the registration and stitching of low resolutiondiffraction patterns to form a higher resolution one is proposed. There is noprior knowledge about the 3D position of the object in the recordings and it is assumedthat there is only one particle in the object field. The method usesWignertransform, Canny edge detection and Hough transform to register the patterns,and some additional iterative methods depending on the local variance of thereconstructed patterns to stitch them. The performance of the overall systemis evaluated against object radius, noise in the original pattern, recording noiseand presence of multiple particles in the object field by computer simulations.
Birden çok uzamsal ışık modülatörlü holografik üç-boyutlu video gösterim sistemleri
Spatial light modulators (SLMs) are commonly used in electro-holographic display systems. Liquid crystal on silicon, liquid crystal, mirror-based, acousto-optic and optically addressed devices are some of the SLM types. Most of the SLMs are digitally driven and pixelated; therefore, they are easy to use. We use phase-only SLMs in our experiments. Resolution and size of currently available SLMs are inadequate for satisfactory holographic reconstructions. Space-bandwidth product (SBP) is a good metric for the quality assessments. High SBP is needed when lateral or rotational motion is allowed for the observer. In our experiments 2D images whose sizes are even larger than the SLM size are reconstructed using single SLM holographic displays. Volume reconstructions are also obtained by using such displays. Either LED or laser illumination is used in our experiments. After the experiments with the single SLM holographic displays, some laboratory prototypes of multiple SLM holographic systems are designed and implemented. In a real-time color holographic display system, three SLMs are used for red, blue and green channels. GPU acceleration is also used to achieve video rates. Beam-splitters and micro-stages are used for the alignments in all multiple SLM designs. In another multiple SLM configuration, SLMs are tiled side by side to form a three by two matrix to increase both vertical and horizontal field of view. Larger field of view gives flexibility to the observer to move and rotate around the reconstructed images of objects. To further increase the field of view, SLMs are tiled in a circular configuration. A single large beam-splitter is used to tile the SLMs side by side without any gap. A cone mirror is used to direct incoming light toward all SLMs. Compared to planar configuration, circularly configured multiple SLMs increase the field of view, significantly. With the help of such configurations holographic videos of ghost-like 3D objects can be observed binocularly. Experimental results are satisfactory.
Sayısal programlanabilir fresnel mercekcik dizilerinin kullanıldığı integral görüntüleme tabanlı üç-boyutlu görüntü çekim ve gösterim sistemi
A Fresnel lenslet array pattern is written on a phase-only LCoS spatial light modulator device (SLM) to replace the regular analog lenslet array in a conventional integral imaging system. We theoretically analyze the capture part of the proposed system based on Fresnel wave propagation formulation. Due to pixelation and quantization of the lenslet array pattern, higher diffraction orders and multiple focal points emerge. Because of the multiple focal planes introduced by the discrete lenslets, multiple image planes are observed. The use of discrete lenslet arrays also causes some other artefacts on the recorded elemental images. The results reduce to those available in the literature when the effects introduced by the discrete nature of the lenslets are omitted. We performed simulations of the capture part. It is possible to obtain the elemental images with an acceptable visual quality. We also constructed an optical integral imaging system with both capture and display parts using the proposed discrete Fresnel lenslet array written on a SLM. Optical results, when self-luminous objects, such as an LED array, are used indicate that the proposed system yields satisfactory results. The resulting system consisting of digital lenslet arrays offers a flexible integral imaging system. Thus, to increase the visual performance of the system, previously available analog solutions can now be implemented digitally by using electro-optical devices. We also propose a method and present applications of this method that converts a diffraction pattern into an elemental image set in order to display them on a display-only integral imaging setup. We generate elemental images based on diffraction calculations as an alternative to commonly used ray tracing methods. Ray tracing methods do not accommodate the interference and diffraction phenomena. Our proposed method enables us to obtain elemental images from a holographic recording of a 3D object/scene. The diffraction pattern can be either numerically generated or digitally acquired from optical input. The method shows the connection between a hologram (diffraction pattern) of a 3D object and an elemental image set of the same 3D object. We obtained optical reconstructions with a display-only integral imaging setup where we used a digital lenslet array. We also obtained numerical reconstructions, again by using the diffraction calculations, for comparison. The digital and optical reconstruction results are in good agreement. Finally, we showed a method to obtain an orthoscopic image of a 3D object. We converted an elemental image set that gives real pseudoscopic reconstruction into another elemental image set that gives real orthoscopic reconstruction. Again, we used wave propagation simulations for this purpose. We also demonstrated numerical and optical reconstructions from the obtained elemental image sets for comparison. The results are satisfactory given the physical limitations of the display system.
Eğri bir yüzey üzerinde verilen alana karşılık gelen üç boyutlu skalar optik alanın hesaplanması için lokal sinyal ayrıştırma tabanlı yöntemler
A three-dimensional scene or object can be optically replicated via the three-dimensional imaging and display method holography. In computer-generated holography, the scalar diffraction field due to a field given on an object (curved surface) is calculated numerically. The source model approaches treat the building elements of the object (such as points or planar polygons) independently to simplify the calculation of diffraction field. However, as a tradeoff, the accuracies of fields calculated by such methods are degraded. On the other hand, field models provide exact field solutions but their computational complexities make their application impractical for meaningful sizes of surfaces. By using the practical setup of the integral imaging, we establish a space-frequency signal decomposition based relation between the ray optics (more specifically the light field representation) and the scalar wave optics. Then, by employing the uncertainty principle inherent to this space-frequency decomposition, we derive an upper bound for the joint spatial and angular (spectral) resolution of a physically realizable light field representation. We mainly propose two methods for the problem of three-dimensional diffraction field calculation from fields given on curved surfaces. In the first approach, we apply linear space-frequency signal decomposition methods to the two-dimensional field given on the curved surface and decompose it into a sum of local elementary functions. Then, we write the diffraction field as a sum of local beams each of which corresponds to such an elementary function on the curved surface. By this way, we increase the accuracy provided by the source models while keeping the computational complexity at comparable levels. In the second approach, we firstly decompose the three-dimensional field into a sum of local beams, and then, we construct a linear system of equations where we form the system matrix by calculating the field patterns that the three-dimensional beams produce on the curved surface. We find the coefficients of the beams by solving the linear system of equations and thus specify the three-dimensional field. Since we use local beams in three-dimensional field decomposition, we end up with sparse system matrices. Hence, by taking advantage of this sparsity, we achieve considerable reduction in computational complexity and memory requirement compared to other field model approaches that use global signal decompositions. The local Gaussian beams used in both approaches actually correspond to physically realizable light rays. Indeed, the upper joint resolution bound that we derive is obtained by such Gaussian beams. Keywords: Linear Space-Frequency Signal Decomposition, Gaussian Beam Decomposition, Curved Surfaces, Computer-Generated Holography, Scalar Optical Di?raction, Light Field Representation, Integral Imaging, Ray Optics, Scalar Wave Optics