Showing papers on "Fresnel diffraction published in 2011"

Calculation for computer generated hologram using ray-sampling plane

Abstract: We introduce a new algorithm for calculating computer generated hologram (CGH) using ray-sampling (RS) plane. RS plane is set at near the object and the light-rays emitted by the object are sampled at the plane. Then the light-rays are transformed into the wavefront with using the Fourier transforms. The wavefront on the CGH plane is calculated by wavefront propagation simulation from RS plane to CGH plane. The proposed method enables to reproduce high resolution image for deep 3D scene with angular reflection properties such as gloss appearance.

Complex Fresnel hologram display using a single SLM

Abstract: We propose a novel optical method to display a complex Fresnel hologram using a single spatial light modulator (SLM). The method consists of a standard coherent image processing system with a sinusoidal grating at the Fourier plane. Two or three position-shifted amplitude holograms displayed at the input plane of the processing system can be coupled via the grating and will be precisely overlapped at the system's output plane. As a result, we can synthesize a complex hologram that is free of the twin image and the zero-order light using a single SLM. Because the twin image is not removed via filtering, the full bandwidth of the SLM can be utilized for displaying on-axis holograms. In addition, the degree of freedom of the synthesized complex hologram display can be extended by involving more than three amplitude holograms.

Holographic video at 40 frames per second for 4-million object points.

Abstract: We propose a fast method for generating digital Fresnel holograms based on an interpolated wavefront-recording plane (IWRP) approach. Our method can be divided into two stages. First, a small, virtual IWRP is derived in a computational-free manner. Second, the IWRP is expanded into a Fresnel hologram with a pair of fast Fourier transform processes, which are realized with the graphic processing unit (GPU). We demonstrate state-of-the-art experimental results, capable of generating a 2048 x 2048 Fresnel hologram of around 4 × 10(6) object points at a rate of over 40 frames per second.

Wavelength multiplexing multiple-image encryption using cascaded phase-only masks in the Fresnel transform domain

Abstract: We propose a method of wavelength multiplexing based on a modified Gerchberg–Saxton algorithm (MGSA) and a cascaded phase modulation scheme in the Fresnel transform domain to reduce the cross talk in the multiple-image-encryption framework. First, each plain image is encoded to a complex function by using the MGSA. Next, the phase components of the created complex functions are multiplexed with different wavelength parameters, and then they are modulated before being combined together as a phase-only function, which is recorded in the first phase-only mask (POM). Finally, the second POM is generated by applying the MGSA again on the amplitude derived from the summation of the total created complex functions. Simulation results show that the cross talk between multiplexed images has been significantly reduced compared with an existing similar method. Therefore, the multiplexing capacity in encrypting multiple gray-scale images can be increased accordingly.

Integrated Polarization Analyzing CMOS Image Sensor for Material Classification

Abstract: Material classification is an important application in computer vision. The inherent property of materials to partially polarize the reflected light can serve as a tool to classify them. In this paper, a real-time polarization sensing CMOS image sensor using a wire grid polarizer is proposed. The image sensor consist of an array of 128 × 128 pixels, occupies an area of 5 × 4 mm2 and it has been designed and fabricated in a 180-nm CMOS process. We show that this image sensor can be used to differentiate between metal and dielectric surfaces in real-time due to the different nature in partially polarizing the specular and diffuse reflection components of the reflected light. This is achieved by calculating the Fresnel reflection coefficients, the degree of polarization and the variations in the maximum and minimum transmitted intensities for varying specular angle of incidence. Differences in the physical parameters for various metal surfaces result in different surface reflection behavior, influencing the Fresnel reflection coefficients. It is also shown that the image sensor can differentiate among various metals by sensing the change in the polarization Fresnel ratio.

Electromagnetically induced Talbot effect

Abstract: By modulating transmission function of a weak probe field via a strong control standing wave, an electromagnetically induced grating can be created in the probe channel. Such a nonmaterial grating may lead to self-imaging of ultracold atoms or molecules in the Fresnel near-field regime. This work may offer a nondestructive and lensless way to image ultracold atoms or molecules.

Polarization-independent and high-diffraction-efficiency Fresnel lenses based on blue phase liquid crystals.

Abstract: A polarization-independent and high-diffraction-efficiency Fresnel lens is developed based on blue phase liquid crystals (BPLCs). The optically isotropic characteristic of BPLCs is used to produce a polarization-independent Fresnel lens. The small optical phase shift of BPLCs that is induced by the Kerr effect is sufficient for the BPLC Fresnel lens to have high theoretical and experimental diffraction efficiencies of 41% and ∼34%, respectively. An electrically erasable memory effect in the focusing diffraction at an electric field E>4.44 V/μm is observed. The electro-optical properties of the BPLC Fresnel lens are analyzed and discussed.

2-D/3-D Switchable Display by Fresnel-Type LC Lens

Abstract: We demonstrate a multi-electrode Fresnel-type 2-D/3-D switchable display with electrically controlled birefringence mode liquid crystal (LC) lenses. By applying a discontinuous nonuniform electric field, the display with this structure can form a Fresnel-type refractive-index distribution to generate 3-D images. Compared to a normal LC lens, the Fresnel-type LC lens can achieve faster switching speed for dynamic applications. It can also replace the high sag solid lens for 3-D applications with relatively small cell gap. Furthermore, a Fresnel lens with suitable refractive-index profile is proposed to reduce the crosstalk in the 3-D displays.

A Uniform Asymptotic Solution for the Diffraction by a Right-Angled Dielectric Wedge

Abstract: We propose a uniform asymptotic solution for the field diffracted by a lossless right-angled dielectric wedge illuminated by a plane wave at normal incidence. The diffraction problem is solved by splitting the observation domain in the inner region of the wedge and the surrounding free-space. The scattered electric field in each region is assumed to be originated by a set of equivalent electric and magnetic surface currents involved in the well-known radiation integral. Such currents are localized on the interior and exterior faces of the wedge, and expressed in terms of the corresponding geometrical optics field. Useful analytical manipulations and asymptotic evaluations of the resulting integrals allow one to obtain the diffraction coefficients in terms of the Fresnel's reflection and transmission coefficients of the structure and the transition function of the uniform geometrical theory of diffraction. The related diffracted field compensates the discontinuities of the geometrical optics field and gives total field levels in good agreement with finite difference time domain results.

Joint DOA, Range, and Polarization Estimation in the Fresnel Region

Abstract: A new algorithm of joint direction-of-arrival (DOA), range, and polarization estimation is proposed to localize multiple polarized sources in the Fresnel region. The algorithm is based on a sparse linear array composed of dual-polarization sensors with symmetric subarray partition. By the symmetric property of sparse linear array, the steering vector of the polarized array can be expressed as the product of a complex matrix with the signal's DOA and a complex matrix with the signal's range and a complex vector with the signal's polarization. A spectral rank reduction (RARE) algorithm is presented to estimate the DOA independent from the range and polarization. With each estimated DOA, the range of each source is accordingly estimated by defining the 1-D range RARE function. For each DOA and range of source, a MUSIC algorithm is finally adopted for the signal's polarization. The DOA and range identifiability of the proposed algorithm are discussed, and the range ambiguity issues caused by sparse linear array are analyzed. The proposed algorithm employs only second-order statistics and 1-D search so that its computational burden is reduced. The limitation of inter-element spacing (d ≤ λ/4) is overcome. By numerical examples, it is shown that the proposed algorithm can enhance the angle resolution even with the limited number of sensors.

Two-Photon Imaging with Entangled and Thermal Light

Abstract: Two‐photon “ghost” imaging, based on the second‐order intensity correlation, was first realized with entangled light, but has now been demonstrated with true thermal light. Following our work on lensless and high‐order ghost imaging with thermal light, we have recently shown that both entangled and thermal light may be used to produce two‐photon correlation Talbot effects. In the Talbot effect, first observed in 1836, a periodic object illuminated with coherent light can give rise to repeated self‐images at specific positions within the Fresnel diffraction field without any lens. Using an incoherent thermal light source, we have experimentally observed second and higher order Talbot self‐images, including fractional and phase‐reversal images, at multiples of the Talbot length in a lensless setup containing two optical paths. We have also recently observed another surprising imaging phenomenon which does not depend on the second‐order correlation function, and can produce both negative and positive images of a nonlocal object. It is expected that these types of imaging will find novel applications in both the microscopic and macroscopic regimes.

Optics for Engineers

Abstract: Introduction Why Optics? History Optical Engineering Electromagnetics Background Wavelength, Frequency, Power, and Photons Energy Levels and Transitions Macroscopic Effects Basic Concepts of Imaging Overview of the Book Problems Basic Geometric Optics Snell's Law Imaging with a Single Interface Reflection Refraction Simple Lens Prisms Reflective Systems Problems Matrix Optics Matrix Optics Concepts Interpreting the Results The Thick Lens Again Examples Problems Stops, Pupils, and Windows Aperture Stop Field Stop Image-Space Example Locating and Identifying Pupils and Windows Examples Problems Aberrations Exact Ray Tracing Ellipsoidal Mirror Seidel Aberrations and OPL Spherical Aberration for a Thin Lens Chromatic Aberration Design Issues Lens Design Problems Polarized Light Fundamentals of Polarized Light Behavior of Polarizing Devices Interaction with Materials Fresnel Reflection and Transmission Physics of Polarizing Devices Jones Vectors and Matrices Partial Polarization Problems Interference Mach-Zehnder Interferometer Doppler Laser Radar Resolving Ambiguities Michelson Interferometer Fabry-Perot Interferometer Beamsplitter Thin Films Problems Diffraction Physics of Diffraction Fresnel-Kirchhoff Integral Paraxial Approximation Fraunhofer Diffraction Equations Some Useful Fraunhofer Patterns Resolution of an Imaging System Diffraction Grating Fresnel Diffraction Problems Gaussian Beams Equations for Gaussian Beams Gaussian Beam Propagation Six Questions Gaussian Beam Propagation Collins Chart Stable Laser Cavity Design Hermite-Gaussian Modes Problems Coherence Definitions Discrete Frequencies Temporal Coherence Spatial Coherence Controlling Coherence Summary Problems Fourier Optics Coherent Imaging Incoherent Imaging Systems Characterizing an Optical System Problems Radiometry and Photometry Basic Radiometry Spectral Radiometry Photometry and Colorimetry Instrumentation Blackbody Radiation Problems Optical Detection Photons Photon Statistics Detector Noise Photon Detectors Thermal Detectors Array Detectors Nonlinear Optics Wave Equations Phase Matching Nonlinear Processes Appendix A Notation and Drawings for Geometric Optics Appendix B Solid Angle Appendix C Matrix Mathematics Appendix D Light Propagation in Biological Tissue Appendix E Useful Matrices Appendix F Numerical Constants and Conversion Factors Appendix G Solutions to Chapter Problems References Index

Coherent x-ray wavefront reconstruction of a partially illuminated Fresnel zone plate

Abstract: A detailed characterization of the coherent x-ray wavefront produced by a partially illuminated Fresnel zone plate is presented. We show, by numerical and experimental approaches, how the beam size and the focal depth are strongly influenced by the illumination conditions, while the phase of the focal spot remains constant. These results confirm that the partial illumination can be used for coherent diffraction experiments. Finally, we demonstrate the possibility of reconstructing the complex-valued illumination function by simple measurement of the far field intensity in the specific case of partial illumination.

Uniform Ray Description for the PO Scattering by Vertices in Curved Surface With Curvilinear Edges and Relatively General Boundary Conditions

Abstract: A new high-frequency analysis is presented for the scattering by vertices in a curved surface with curvilinear edges and relatively general boundary conditions, under the physical optics (PO) approximation. Both, impenetrable (e.g., impedance surface, coated conductor) as well as transparent thin sheet materials (e.g., thin dielectric, or frequency selective surface) are treated, via their Fresnel reflection and transmission coefficients. The PO scattered field is cast in a uniform theory of diffraction (UTD) ray format and comprises geometrical optics, edge and vertex diffracted rays. The contribution of this paper is twofold. First, we derive PO-based edge and vertex diffraction coefficients for sufficiently thin but relatively arbitrary materials, while in the literature most of the results (especially for vertex diffraction) are valid only for perfectly conducting objects. Second, the shadow boundary transitional behavior of edge and vertex diffracted fields is rigorously derived for the curved geometry case, as a function of various geometrical parameters such as the local radii of curvature of the surface, of its edges and of the incident ray wavefront. For edge diffracted rays, such a transitional behavior is found to be the same as that obtained heuristically in the original UTD. For vertex diffracted rays, the PO-based transitional behavior is a novel result providing offers clues to generalize a recent UTD solution for a planar vertex to treat the present curved vertex problem. Some numerical examples highlight the accuracy and the effectiveness of the proposed ray description.

Investigation of the partially coherent effects in a 2D Talbot interferometer

Abstract: The recent use of a one-dimensional (1D) X-ray Talbot interferometer has triggered great interest in X-ray differential phase contrast imaging. As an improved version of a 1D interferometer, the development of two-dimensional (2D) grating interferometry strongly stimulated applications of grating-based imaging. In the framework of Fresnel diffraction theory, we investigated the self-image of 2D-phase gratings under partially coherent illumination. The fringe visibility of the self-image has been analyzed as a function of the spatial coherence length. From the viewpoint of self-image visibility, it is possible to find the optimal 2D grid for 2D X-ray grating interferometer imaging. Numerical simulations have been also carried out for quantitative evaluation. Results, in good agreement with theoretical analysis, indicate the spatial coherence requirements of the radiation illuminating a 2D grating interferometer. Moreover, our results can be used to optimize performances of a 2D grating interferometer and for further theoretical and experimental research on grating-based imaging systems.

Carrier fringes in the two-aperture common-path interferometer

Abstract: We present a method to introduce a linear phase into an interference pattern. This phase is introduced when a grating is placed outside of the Fourier plane of a two-aperture common-path interferometer, which is built using a 4f optical imaging system. Based on an analysis of near-field diffraction, the introduction of the carrier fringes is mathematically justified. It is important to note that no tilt between the two beams is requested to produce this effect, and it turns out to be simpler, easier, and more versatile than other existing methods. The main attributes and advantages of the setup will be discussed and illustrated in detail with experimental fringe patterns.

Influence of various growth conditions on Fresnel diffraction patterns of bacteria colonies examined in the optical system with converging spherical wave illumination

Abstract: The novel optical system based on converging spherical wave illumination for analysis of bacteria colonies diffraction patterns, is proposed. The complex physical model of light transformation on bacteria colonies in this system, is presented. Fresnel diffraction patterns of bacteria colonies Escherichia coli, Salmonella enteritidis, Staphylococcus aureus grown in various conditions, were examined. It was demonstrated that the proposed system enables the characterization of morphological changes of colony structures basing on the changes of theirs Fresnel diffraction patterns.

Fraunhofer diffraction of a Laguerre–Gaussian laser beam by fork-shaped grating

Abstract: In this article we present a theoretical study for Fraunhofer diffraction of a Laguerre–Gaussian laser beam with zeroth radial mode number and azimuthal mode number l by a diffractive grating with embedded fork-shaped dislocations of integer order p. Analytical expressions describing the diffracted wave field amplitude and intensity distributions in the Fourier plane are deduced and analyzed. They are also followed by the vortex radii expressions.

Fraunhofer computer-generated hologram for diffused 3D scene in Fresnel region.

Abstract: A Fraunhofer computer-generated hologram (CGH) is proved to be valid in display for three-dimensional (3D) objects from the Fresnel to the far-field region without a Fourier lens for reconstruction. To quickly compute large and complicated 3D objects that consist of slanted diffused surfaces in the Fresnel region, a Fraunhofer-based analytical approach using a basic-triangle tiling diffuser is developed. Both theoretical and experimental results reveal that Fraunhofer CGH can perform the same effects as Fresnel CGH but require less calculation time. Impressive 3D solid effects are achieved in the Fresnel region.

Reversible transition between thermodynamically stable phases with low density of oxygen vacancies on the SrTiO3(110) surface.

Abstract: We report the first experimental observation of quantum Talbot effects with single photons and entangled photon pairs. Both the first-and second-order quantum Talbot self-images are observed experimentally. They exhibit unique properties, which are different from those produced by coherent and incoherent classical light sources. In particular, our experiments show that the revival distance of two-photon Talbot imaging is twice the usual classical Talbot length and there is no net improvement in the resolution, due to the near-field effect of Fresnel diffraction, which is different from the case of previous proof-of-principle quantum lithography experiments in the far field.

Integral imaging using phase-only LCoS spatial light modulators as Fresnel lenslet arrays.

Abstract: We present a digital integral imaging system. 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. Because of 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 artifacts 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.

On Diffraction Fresnel Transforms for Boehmians

Abstract: The theory of the diffraction Fresnel transform is extended to certain spaces of Schwartz distributions. In the context of Boehmian spaces, the diffraction Fresnel transform is obtained as a continuous function. Convergence with respect to and is also defined.

Fresnel zone plate and ordinary lens antennas: Comparative study at microwave and terahertz frequencies

Abstract: A number of lens antennas with single-dielectric phase-correcting Fresnel zone plate (FZP) lenses have been designed and studied numerically at microwave and terahertz frequencies, and contrasted to a similar in size and parameters ordinary refractive lens antenna. In a confined frequency band the terahertz grooved-dielectric FZP lenses/antennas with four or more phase-correction steps have gain, beamwidth, cross-polar isolation and input-mismatch comparable to those of the corresponding ordinary lens antenna. An examined 1.5-THz FZP lens antenna designed according to the here-proposed correction in FZP design equation can prevail in gain the ordinary lens antenna, but this finding is not valid for the examined 38-GHz (microwave) FZP lens antenna. Thus, the terahertz FZP lenses are thinner, lighter and effective options to the similar in diameter, focal length and building material ordinary lens for lens antennas construction.

Fundamental structure of Fresnel diffraction: natural sampling grid and the fractional Fourier transform.

Abstract: 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.

Two and three slit electron interference and diffraction experiments

Abstract: Current nanotechnology techniques make possible the preparation of slits in the submicrometer range so that electron interference and diffraction experiments can be done even with a conventional electron microscope. If the instrument is also equipped with a field emission source, it is possible to follow almost in real time the transition from the image of the slits to their Fraunhofer pattern through the intermediate Fresnel diffraction images. We discuss our results for the two-slit experiment and illustrate them for the three-slit case.

Phase-only hologram generation based on integral imaging and its enhancement in depth resolution

Abstract: We introduce a phase-only hologram generation method based on an integral imaging, and propose an enhancement method in representable depth interval. The computational integral imaging reconstruction method is modified based on optical °ow to obtain depth-slice images for the focused objects only. A phase-only hologram for multiple plane images is generated using the iterative Fresnel transform algorithm. In addition, a division method in hologram plane is proposed for enhancement in the representable minimum depth interval.

Particle-wave discrimination in Poisson spot experiments

Abstract: Matter?wave interferometry has been used extensively over the last few years to demonstrate the quantum-mechanical wave nature of increasingly larger and more massive particles. We have recently suggested the use of the historical Poisson spot setup to test the diffraction properties of larger objects. In this paper, we present the results of a classical particle van der Waals (vdW) force model for a Poisson spot experimental setup and compare these to Fresnel diffraction calculations with a vdW phase term. We include the effect of disc-edge roughness in both models. Calculations are performed with D2 and with C70 using realistic parameters. We find that the sensitivity of the on-axis interference/focus spot to disc-edge roughness is very different in the two cases. We conclude that by measuring the intensity on the optical axis as a function of disc-edge roughness, it can be determined whether the objects behave as de Broglie waves or classical particles. The scaling of the Poisson spot experiment to larger molecular masses is, however, not as favorable as in the case of near-field light-grating-based interferometers. Instead, we discuss the possibility of studying the Casimir?Polder potential using the Poisson spot setup.

Direct calculation of a three-dimensional diffracted field

Abstract: We present an approach to calculating the complex amplitude of a three-dimensional (3D) diffracted light field in the paraxial approximation based on a 3D Fourier transform. Starting from the Huygens–Fresnel principle, the method is first developed for the computation of the light distribution around the focus of an apertured spherical wave. The method, with modification, is then extended to treat the 3D diffraction of an aperture with an arbitrary transmittance function.