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For the most popular method of scan formation in Optical Coherence Tomography (OCT) based on plane-parallel scanning of the illuminating beam, we present a compact but rigorous K-space description in which the spectral representation is used to describe both the axial and lateral structure of the illuminating/received OCT signals. Along with the majority of descriptions of OCT-image formation, the discussed approach relies on the basic principle of OCT operation, in which ballistic backscattering of the illuminating light is assumed. This single-scattering assumption is the main limitation, whereas in other aspects, the presented approach is rather general. In particular, it is applicable to arbitrary beam shapes without the need for paraxial approximation or the assumption of Gaussian beams. The main result of this study is the use of the proposed K-space description to analytically derive a filtering function that allows one to digitally transform the initial 3D set of complex-valued OCT data into a desired (target) dataset of a rather general form. An essential feature of the proposed filtering procedures is the utilization of both phase and amplitude transformations, unlike conventionally discussed phase-only transformations. To illustrate the efficiency and generality of the proposed filtering function, the latter is applied to the mutual transformation of non-Gaussian beams and to the digital elimination of arbitrary aberrations at the illuminating/receiving aperture. As another example, in addition to the conventionally discussed digital refocusing enabling depth-independent lateral resolution the same as in the physical focus, we use the derived filtering function to perform digital "super-refocusing." The latter does not yet overcome the diffraction limit but readily enables lateral resolution several times better than in the initial physical focus. [ABSTRACT FROM AUTHOR]

This research focuses on the analysis of the free propagation of Hermite-Gaussian beams diffracted by a symmetrical annular aperture placed at the beam waist plane. The propagation is studied analytically and numerically using the angular spectrum method and the 2D fast Fourier transformation. Numerical simulation examples illustrate the propagation characteristics of the Hermite-Gaussian beams diffracted by an annular aperture. The beam truncation parameters and obscuration ratio influence Hermite-Gaussian beam diffraction properties. [ABSTRACT FROM AUTHOR]

• This paper proposes a holographic curved waveguide system for near-eye display. • An iterative algorithm is established based on angular spectrum theory to simulate the whole propagation process and analyze the behavior of light beam in the curved waveguide. • A phase compensation measures for overmodulation during beam propagation in the waveguide have been proposed. • Experiments have proven that the overmodulation can be diluted with the appropriate compensation phase over an effective distance. Generally, current type of waveguide used for near-eye displays is planar waveguide, which belongs to flat panel display. Compared to display system in three-dimensional space, flat panel display limits people's view of the 3-D world and is not conducive to the integration of virtual and reality. This paper proposes a holographic curved waveguide system for near-eye display. In order to analyze the propagation process of light beam in waveguide, an iterative algorithm is established based on angular spectrum theory to get the intensity distribution from each total internal reflection point. According to the simulation results and experimental phenomenon, we have developed phase compensation measures for overmodulation during beam propagation in the waveguide. The research shows that using curved waveguide can achieve beam transmission with less aberration after introducing an appropriate phase compensation in a distance, and it can also achieve beam transmission with lossless energy within a large radius range. Experiments have proven that the final coupling effect is basically consistent with the simulation results, this means that our proposal about curved waveguide has potential application value in near-eye display systems. [ABSTRACT FROM AUTHOR]

• Proposing a fast point-based hologram generation method using high-frequency information extraction. • Using the Gaussian filter to separate high-frequency information and low-frequency information of the 3D objects. • Improving the calculation speed by over 65%. • Combining different algorithms and leveraging their respective advantages. Computer-generated hologram based holographic 3D display is an important development direction of holographic 3D display. However, the heavy amount of calculation affects the generation speed of the holograms, which limits the further development of real-time holographic 3D display. In this paper, a fast point-based hologram generation method using high-frequency (HF) information extraction is proposed. Firstly, an image information processing method based on the Gaussian filter is proposed to separate the HF information and low-frequency (LF) information of 3D object. Then, the HF hologram is calculated by using the novel-look-up-table algorithm, while the LF hologram is calculated by the angular spectrum algorithm. Finally, the final hologram is obtained by overlaying HF hologram and LF hologram. Compared with the traditional method, the proposed method improves the generation speed of the hologram by more than 65%. Moreover, the details of 3D object can be fully reconstructed, and the quality of the reconstructed image is slightly improved with lower speckle noise. Experimental results verify the feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

In this study the role of vergence in relation to age-dependent scaling of eye and photoreceptor parameters is studied. The underlying hypothesis is that the size and packing of outer segments is matched to the pupil size outdoors in photopic conditions. Vergence is analysed in relation to the angular spectrum of waves being incident using age-dependent data from the literature for the actual geometry and density of photoreceptor cones and rods. This approach is used to derive simple relations for the angular confinement of light along outer segments. Only with a small photopic pupil can leakage and crosstalk for both central and peripheral photoreceptors be entirely ruled out due to the finite length of the outer segments. A limiting 3 mm pupil size is found for children in the school age. Larger pupils will increase the likelihood of leakage and crosstalk that may therefore impact on emmetropization. This study has introduced a new paradigm in myopia research by considering vergence across the 3-D retina as being matched to the angular spectrum of waves being incident from the eye pupil. Emmetropization suggests a delicate balance between photoreceptor outer segment length and density in relation to pupil size. Only when balanced will leakage and crosstalk between adjacent outer segments be effectively suppressed thereby ensuring the highest possible light capture efficiency by visual pigments in the outer segments whether an image is formed on the retina or not. [ABSTRACT FROM AUTHOR]

The interactions between body tissues and a focused ultrasound beam can be evaluated using various numerical models. Among these, the Rayleigh–Sommerfeld and angular spectrum methods are considered to be the most effective in terms of accuracy. However, they are computationally expensive, which is one of the underlying issues of most computational models. Typically, evaluations using these models require a significant amount of time (hours to days) if realistic scenarios such as tissue inhomogeneity or non-linearity are considered. This study aims to address this issue by developing a rapid estimation model for ultrasound therapy using a machine learning algorithm. Several machine learning models were trained on a very-large dataset (19,227 simulations), and the performance of these models were evaluated with metrics such as Root Mean Squared Error (RMSE), R-squared (R²), Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC). The resulted random forest provides superior accuracy with an R2 value of 0.997, an RMSE of 0.0123, an AIC of -82.56, and a BIC of -81.65 on an external test dataset. The results indicate the efficacy of the random forest-based model for the focused ultrasound response, and practical adoption of this approach will improve the therapeutic planning process by minimizing simulation time. [ABSTRACT FROM AUTHOR]

Microwave holography utilizes an antenna to record the hologram. In a phase shifting microwave holographic method, the antenna has to perform the 2D scanning over an area corresponding to each phase shift in reference wave. Since this methodology requires phase shifting in each scan, this makes the process lengthy and laborious. In this work, a numerical 4‐step phase shifting method is presented for generating the microwave hologram, in which a single (0° phase) hologram is recorded experimentally and the other three holograms are generated numerically by shifting the phase in reference wave. The amplitude and phase information of object is extracted using angular spectrum diffraction method. An error introduced by various components in experiments is calculated and corrected to enhance the accuracy of reconstructed phase values. The calculated phase step error for the experiment is 0.0501 rad. The quantitative and qualitative results along with the experimental phase shifting phase results are shown to envision the applications of numerical phase shifting microwave holography in imaging of metallic objects and highly scattered biological phantom. [ABSTRACT FROM AUTHOR]

The feature size of holographic diffuser is an important parameter which affects the display resolution when the holographic diffuser is used as an exit-pupil expander device in head up display. However, there is currently a lack of relevant research work on it. Here, we derive the amplitude and phase properties of the scattering light based on a statistical model of the surface undulations of ground glass. Combining with angular spectrum diffraction theory, a method for accurately simulating the speckle pattern is developed. The speckle patterns in the far-field and near-field diffraction areas of light passing through ground glass is calculated, then compared with estimation and experimental results. The comparison shows that the speckle feature size obtained by the traditional estimation method is quite different from the experimental results in the nearfield diffraction area. While the results obtained by our simulation method is in good agreement with the experiment in both near-field and far-filed diffraction areas. This work provides an effective method for the design and preparation of small feature size holographic diffuser elements. [ABSTRACT FROM AUTHOR]

In this work, a compact indirect microwave holographic setup is proposed and developed by utilizing the low cost, specifically designed directive antennae as transmitter and receiver. Microwave holograms are recorded while scanning the 2D plane using (x‐y) motorized translation stage. The recorded holograms are then reconstructed numerically employing the angular spectrum diffraction phenomenon. The quality of the reconstructed amplitude image is further enhanced through the deep neural network, in order to combat with the low resolution of reconstructed images. The quantitative and qualitative results exploit the possibility of developing the miniaturized indirect microwave holographic system for near field applications. [ABSTRACT FROM AUTHOR]

Imaging distance plays an essential role in image formation in computational ghost imaging (CGI). Uncertain or unknown imaging distance often leads to the deterioration of the image quality or, even worse, to the failure of imaging. Here we present a CGI technique that provides high-quality image reconstruction in an uncertain distance environment. We propose a method to generate a stable speckle field, where the size of the field remains invariant and the field does not distort during light transmission, and find that the use this field removes the constraint imposed by the imaging distance. We experimentally and numerically verify the performance of the technique by applying it to a single-detector CGI system. The results show that the proposed technique provides excellent imaging performance, even when the imaging distance is uncertain, and can be extended to existing computational-based ghost-imaging schemes. • A computational ghost imaging technique is proposed. • The technique can realize image reconstructions with an uncertain distance. • A method is developed to generate a stable speckle field. • The technique can be extended to existing computational-based ghost-imaging schemes. • The technique possesses excellent performances and wide potential applications. [ABSTRACT FROM AUTHOR]

We numerically investigated lateral Goos-Hänchen shifts a two-dimensional Airy beam experiences when it is reflected at the interface between air and an epsilon-near-zero metamaterial. Angular spectrum theory is employed to decompose Airy beam into plane waves, followed by beam vectorization to overcome the paraxial propagation assumption. The reflected light field can then be obtained by integrating plane waves weighted by Fresnel reflection coefficients. Results show that Airy beam experiences nonzero GH shift at normal incidence due to asymmetric angular spectrum. Influences of beam parameters and permittivity are further investigated. Our study provides foundation for deep understandings of Airy beam in epsilon-near zero metamaterials. [ABSTRACT FROM AUTHOR]

While rotational dynamics of anisotropic nanoobjects has often been limited in plasmonic and fluorescent nanomaterials, here we demonstrate the capability of a surface plasmon resonance microscopy (SPRM) to determine the orientation of all kinds of anisotropic nanomaterials. By taking CdS nanorods as an example, it was found that two-dimensional Fourier transform of the asymmetrical wave-like SPRM image resulted in a peak in its angular spectrum in k space. Consistency between the peak angle and the geometrical orientation of the nanorod was validated by both in situ scanning electron microscope characterizations and theoretical calculations. Real-time monitoring of the rotational dynamics of single CdS nanorods further revealed the accelerated rotation under appropriate reaction conditions for photocatalyzed hydrogen generation. The driving force was attributed to the asymmetric production of hydrogen molecules as a result of inhomogeneous distribution of reactive sites within the nanorod. The present work not only builds the experimental and theoretical connections between the orientation of anisotropic nanomaterials and its SPRM images; the general suitability of SPRM also sheds light on broad types of nonfluorescent and nonplasmonic anisotropic nanoobjects from semiconductors to bacteria and viruses. [ABSTRACT FROM AUTHOR]

The paper describes a theoretical study of horizontal anisotropy of dynamic ocean noise. It is shown that the anisotropic distribution of the ocean noise field is governed by the effect of its scattering by wind waves. The dependence of the degree of noise anisotropy on the mode number and wind speed is discussed. [ABSTRACT FROM AUTHOR]

In the lithography process, overlay describes the position errors of placing one mask layer pattern over an existing pattern on the wafer, and overlay metrology is one of the key challenges in semiconductor manufacturing. With the increase of process complexity especially for multiple patterning technologies in advanced nodes, the demand for accuracy, precision and process robustness in overlay metrology continues to tighten. In this paper, we have proposed and demonstrated a novel overlay metrology method with high process robustness. A straightforward theory called interference of diffraction light is developed for explanations why this method works for single layer overlay metrology. The overlay signals with continuous wavelengths and angles are simultaneously acquired in the pupil plane. Therefore, compared with the current monochrome measurement technology, this work can gather and utilize as much overlay information as possible for measurements. Experiments illustrate that this technique can achieve better measurement repeatability, faster measurement speed and better process robustness than current monochrome method, and thus this method has great potential to meet the higher node requirements for measurement accuracy. What’ more, our work provides a novel idea for scatterometry technology in the field of micro-nano measurement. [ABSTRACT FROM AUTHOR]

Abstract: A method is proposed to automatically evaluate the focal planes of spherical particles. This method compares the correlation coefficients of multiple reconstructed planes relative to a reference plane. The particles are located where a minimum correlation is found, and reconstructions are made using an angular spectrum propagator. The Hough transform is employed to segment the hologram, thereby enabling the detection of circular shapes, such as Airy patterns, and the edges of the particles themselves. The autofocus is improved by creating a correlation matrix using an iterative process, which reduces the computational cost of the particle display processes in their respective focal planes. A theoretical model was studied to estimate the longitudinal and transverse magnifications of the focused particles caused by the influence of aberrations in the reconstruction of digital holograms due to the spherical reference wave used. Experimentally, laser light was used to illuminate 5-μm latex particles, which was recorded by a CCD camera with a 9.9-μm pixel size. The reconstructions measured an average particle radius of 71.3 ± 16.3 μ m in the average focal plane, which was estimated to be 60.65 ± 0.22 mm from the hologram where the magnifications were considered. [ABSTRACT FROM AUTHOR]

The moments of a plane wave scattered at low grazing angles from a one-dimensional perfectly reflecting rough surface are considered. The mean intensity and autocorrelation of the scattered field and the corresponding angular spectrum are obtained to second order in surface height. The derivations are based on an operator expansion of the extended (two-way) parabolic integral equation solution. The resulting operator series describes successively higher-order surface interactions between forward and backward going components. The expressions derived may be regarded as backscatter corrections to those obtained via the standard (one-way) parabolic integral equation method. [ABSTRACT FROM PUBLISHER]

Ultrasound wave reflection from one of the crystal faces is the convenient way to arouse the acoustic beam with a desired propagation direction in acousto-optic cells with collinear and quasi-collinear interaction geometries. The reflection process effects on the ultrasound field amplitude and phase structure. The method to simulate the reflected finite ultrasound beam structure in the case of acoustically anisotropic media is presented in this paper. The investigation is carried on the example of two quasi-collinear acousto-optic cells fabricated on the base of tellurium dioxide crystal. The cells have special geometry that allows to obtain extremely long acousto-optic interaction length and to achieve unprecedented spectral resolution. The influence of reflection process in the acousto-optic diffraction characteristics was also examined. [ABSTRACT FROM AUTHOR]

• Envelope phase method is presented to generate parallel Bessel arrays with high SNR. • The calculation method of the incomplete axicon phase holograms is deduced. • Three different methods for generating Bessel arrays are proposed. • The number, length and axial intensity distribution of the Bessel arrays can be adjusted by the programmable SLM. Bessel beam arrays have important applications in ultra-laser processing, but most of its implementation methods have the disadvantages of complex process, high cost or poor effect. In this paper, a Bessel beam array generation method is proposed based on envelope phase holograms. Applying the programmable characteristics of spatial light modulator (SLM), the parallel Bessel beam array with adjustable spacing, quantity and intensity is simulated. The diffraction pattern of the Bessel array is discussed based on the angular spectrum diffraction theory. The phase expression of the envelope superposition morphology is deduced based on the analysis of the transmission function of the axicon. Three different methods are introduced and the quality of the arrays generated by these methods are compared. Simulation and experimental results show that the diffraction pattern of Bessel beam array generated by the envelope phase holograms can keep the Bessel beams as parallel with high signal noise ratio. The research of this paper will provide a theoretical basis for the development and application of the parallel Bessel beam array. [ABSTRACT FROM AUTHOR]

This research aims to make a comparison between the analytical and numerical methods of simulation of the Gaussian beam propagation in free space. This comparison brings evaluation of the accuracy and applicability limitations of the angular spectrum diffraction algorithm. In this approach, planar harmonic waves are assumed as basic components of a propagating wave, so the algorithm combines the angular spectrum technique and the 2D fast Fourier transformation procedures. It means a quite different approach than the well-established Huygens–Fresnel–Rayleigh–Sommerfeld one, based on spherical waves. The Gaussian beam is a rare case of the exact analytical 3D solution of a specific wave diffraction problem, in paraxial scalar approximation. Gaussian beam form has been chosen here as an evaluation reference. It allows to avoid comparisons between two numerical procedures, both of which may suffer from imperfections. In this comparison, the respective 2D cross-sections of calculated 3D complex valued wave fields distributions are presented. Also values of specific Gaussian beam parameters like full phase and Gouy phase shift and wave-front curvature radius are presented. The comparison between that form and the results of the angular spectrum algorithm brings information about the performance quality of that algorithm. [ABSTRACT FROM AUTHOR]

This research aims to make a comparison between the analytical and numerical methods of simulation of the Gaussian beam propagation in free space. This comparison brings evaluation of the accuracy and applicability limitations of the angular spectrum diffraction algorithm. In this approach, planar harmonic waves are assumed as basic components of a propagating wave, so the algorithm combines the angular spectrum technique and the 2D fast Fourier transformation procedures. It means a quite different approach than the well-established Huygens–Sommerfeld one, based on spherical waves. The Gaussian beam is a rare case of the exact analytical 3D solution of a specific wave diffraction problem, in paraxial scalar approximation. Gaussian beam form has been chosen here as an evaluation reference. It allows to avoid comparisons between two numerical procedures, both of which may suffer from imperfections. In this comparison, the respective 2D cross-sections of calculated 3D complex valued wave fields distributions are presented. Also values of specific Gaussian beam parameters like full phase and Gouy phase shift and wave-front curvature radius are presented. The comparison between that form and the results of the angular spectrum algorithm brings information about the performance quality of that algorithm. [ABSTRACT FROM AUTHOR]

A controllable energy method, which considers the undersampling issue of the transfer function and valid spectral energy of a source signal, is proposed to implement angular spectrum diffraction calculation in near and far fields. The proposed method provides an optimized frequency boundary f C E within which it always keeps controllable energy to be diffracted. The controllable energy angular spectrum method significantly reduces the number of samples while having the same accuracy as previous angular spectrum methods, implying a higher calculation efficiency. The new perspective of analyzing spectral energy is shown to improve the performance of relevant diffraction calculations. • The proposed controllable-energy angular spectrum method (CE-ASM) can be widely applied to near-field or far-field diffraction. • The proposed CE-ASM has the same lightweight computational load as the adaptive sampling ASM, while the computational accuracy of the adaptive sampling ASM decreases with increasing distance; in addition, it provides the same high-quality results as the band expansion ASM, which has a huge computational load. • The proposed method was applied to holographic calculations and proved to have high performance. [ABSTRACT FROM AUTHOR]

The coupled wave equations for second harmonic generation of flat-topped beam propagating in birefringent uniaxial anisotropic medium are presented. Based on them, specific physical models of single and twin BBO crystals have been established and numerically computations have been carried out. The influences of beam waist, medium structure on second harmonic generation are analyzed. The calculation results indicate that a wider beam waist can make a better phase matching, therefore the second harmonic beam will maintain the flat-topped property better but with a lower intensity and twin crystals can eliminate beam walk-off in some way. [ABSTRACT FROM AUTHOR]

We consider an oscillating electric dipole, embedded in a uniform medium with relative permittivityand relative permeability. The dipole is located near an interface with a layer with uniform material parametersand, and the second interface borders a uniform medium with parametersand. We have obtained the solutions for the electric and magnetic fields in the various regions, without any restrictions on the parameters and for any state of oscillation of the dipole (elliptical, in general). The solution involves a set of auxiliary functions, which are given as integral representations containing the Fresnel coefficients for plane waves. With this solution, the field lines of energy flow can be obtained, and we have considered the flow pattern for the simple case of a dipole oscillating perpendicular to the interface. When the material of the layer is optically thicker than the embedding medium of the dipole, energy flows more or less along straight lines. At an interface, the field lines refract, similar to optical rays. When the layer material is optically thinner, the energy flow lines curve. A portion of the energy that propagates toward the interface bends away from it before reaching the interface. Other field lines of energy flow cross the interface, but then return to the area of the dipole by crossing the interface again. This leads to an oscillation of energy back and forth through the interface. In the neighborhood of this oscillation, a concentric set of vortex tori appears. [ABSTRACT FROM AUTHOR]

The geometrical optical method has been used to discuss the far-field distribution characteristics of a continuous phase plate. The gradient histogram of the plate’s surface has been calculated. It has been proved that the gradient histogram can be used to show the angular spectrum of a phase plate. The gradient histogram can simplify the analysis process of the angular spectrum and describe the focal spot morphology more intuitively. [ABSTRACT FROM AUTHOR]

Abstract: We consider the transmission of electric dipole radiation through an interface between two dielectrics, for the case of a vertical dipole. Energy flows along the field lines of the Poynting vector, and in the optical near field these field lines are curves (as opposed to optical rays). When the radiation passes through the interface into a thicker medium, the field lines bend to the normal (as rays do), but the transmission angle is not related to the angle of incidence. The redirection of the radiation at the interface is determined by the angle dependence of the transmission coefficient. This near-field redistribution is responsible for the far-field angular power pattern. When the transmission medium is thinner than the embedding medium of the dipole, some energy flows back and forth through the interface in an oscillating fashion. In each area where field lines dip below the interface, an optical vortex appears just above the interface. The centers of these vortices are concentric singular circles around the dipole axis. [Copyright &y& Elsevier]

Abstract: Coupled wave equations that consider two-dimensional distribution and phases of gratings are derived by using weak grating and slow varying approximation. The result of angular selectivity on rand binary data page shows that each minimum is nonzero and each maximum that is not the middle maximum is a little bit smaller than that on plane wave volume hologram. Angular multiplexing is also modeled using the same method, and the middle page is read out in two different angular spacings. The relationship about PSNR versus angular spacing at different multiplexing pages is analyzed to reflect crosstalk between pages. All simulative results show this method is effective for volume holograms simulation. [Copyright &y& Elsevier]

In this paper, carbon quantum dot-labelled β-lactoglobulin antibodies were used for refractive index magnification, and β-lactoglobulin was detected by angle spectroscopy. In this method, the detection light is provided by a He-Ne laser whose central wavelength is the same as that of the porous silicon microcavity device, and the light source was changed to a parallel beam to illuminate the porous silicon microcavity' surface by collimating beam expansion, and the reflected light was received on the porous silicon microcavity' surface by a detector. The angle corresponding to the smallest luminous intensity before and after the onset of immune response was measured by a detector for different concentrations of β-lactoglobulin antigen and carbon quantum dot-labelled β-lactoglobulin antibodies, and the relationship between the variation in angle before and after the immune response was obtained for different concentrations of the β-lactoglobulin antigen. The results of the experiment present that the angle variations changed linearly with increasing β-lactoglobulin antigen concentration before and after the immune response. The limit of detection of β-lactoglobulin by this method was 0.73 μg/L, indicating that the method can be used to detect β-lactoglobulin quickly and conveniently at low cost. [ABSTRACT FROM AUTHOR]

Abstract: Power of an electromagnetic field in a plane is derived exactly as a function of the angular spectrum of only electric field components at another plane based on Maxwell equations and Poynting vector. Then, this quantity is acquired as a function of the electric field components. In this calculation, a function appears that is general and does not depend on the electromagnetic field function. [Copyright &y& Elsevier]

With an upbeat in petroleum exploration efforts in the Middle and Upper Benue Trough, emphasis is increasingly laid on the structural setting of the basin. This work reports the results of the analysis of aeromagnetic data over the Middle Benue Trough, Nigeria. It is well known that the expression of the spectrum (radial and angular) for the total-field magnetic anomaly field has been extensively used in a variety of geologic applications ranging from depth estimates to magnetic body tops and bottoms and estimates of polarization directions and other linear features. In the same vein, matched filters are capable of separating magnetic anomalies of individual magnetic layers from the total magnetic field anomaly. Consequently, the spectra of the different layers can be separated through the matching of the observed spectra to the spectra of equivalent sources at different depths. This technique can also yield dipole equivalent layers, which might be magnetic ensemble discontinuities. The angular spectrum of the magnetic anomaly, on the other hand, is capable of yielding information on the directions of polarization vectors, as this spectrum is usually maximum in these directions. These processing tools have been briefly examined and applied to the aeromagnetic anomaly data of the Middle Benue Trough, Nigeria. The performances of the radial spectrum and matched filtered output of the field are compared. Results from the plot of log radial spectrum against the frequency numbers indicate five discernable linear segments giving depths corresponding to magnetic layers ranging from 20.62 km (highest) to 0.26 km (lowest). Results from the spectral matching yielded three dipole equivalent source layers at 0.89, 4.33, and 18.22 km, giving two corridor bands. With the sensed magnetic discontinuities at depths of 18.10 to 20.50 km (from ground level), the temperature gradient probably over the area lies between 28.80 and 25.40°C/km for the Curie temperature of 520°C. Finally, we have computed the angular spectrum of the field over this area. It is found that the angular spectrum in the mid and high frequency bands shows two peaks at 62° and 145°. Also there are peaks corresponding to the direction of polarization and the rectangular tapered window used in the analysis. [ABSTRACT FROM PUBLISHER]

We report the experimental results of geometric parameter measurement of the single-mode fiber by use of digital holographic micro-tomography technology. Tomography of the single-mode fiber is performed by a filtered back-projection algorithm and a Fourier diffraction algorithm, respectively, to reconstruct the three-dimensional (3-D) map of refractive index. According to this map, we can further get the dimensions of the single-mode fiber by the relate edge detection algorithm of image processing. Experimental results show that compared to the filtered back-projection reconstruction, diffraction tomography based on the Rytov approximation resembles the dimensions of the single-mode fiber. It provides a new way for the nondestructive and on-site measurement of tiny weakly diffracting objects with a cylindrically symmetric structure, such as the single-mode fiber. [ABSTRACT FROM AUTHOR]

A simple Gaussian model for engineering calculations of radar signals passed through the propagation channel with random inhomogeneities is considered. The set of parameters introduced to the model allows spatiotemporal and polarization properties of the signal to be described by a random vector function of the vector argument. [ABSTRACT FROM AUTHOR]

Introduction: CR-39 detectors are widely used for Radon and progeny measurement in the air. In this paper, using the Monte Carlo simulation, the possibility of using the CR-39 for direct measurement of Radon and progeny in water is investigated. Materials and Methods: Assuming the random position and angle of alpha particle emitted by Radon and progeny, alpha energy and angular spectrum that arrive at CR-39, the calibration factor, and the suitable depth of chemical etching of CR-39 in air and water was calculated. In this simulation, a range of data were obtained from SRIM2008 software. Results: Calibration factor of CR-39 in water is calculated as 6.6 (kBq.d/m3)/(track/cm2) that is corresponding with EPA standard level of Radon concentration in water (10-11 kBq/m3). With replacing the skin instead of CR- 39, the volume affected by Radon and progeny was determined to be 2.51 mm3 for one m2 of skin area. The annual dose conversion factor for Radon and progeny was calculated to be between 8.8-58.8 nSv/(Bq.h/m3). Conclusion: Using the CR-39 for Radon measurement in water can be beneficial. The annual dose conversion factor for Radon and progeny was calculated to be between 8.8-58.8 nSv/ (Bq.h/m3). [ABSTRACT FROM AUTHOR]

Abstract: The performance of orthogonal-frequency-division-multiplexing (OFDM) technology in the multimode fiber (MMF) optical communication system is investigated numerically. The mode dispersion in MMF is analyzed by utilizing the optical angular spectrum analysis method. Simulation results in terms of bit-error-rate (BER) and signal-to-noise ratio (SNR) show that the transmission distance can reach up to 2.5-km at 10−3 BER for 40-Gb/s data. Results of different modulation formats further indicate that better performance can be achieved by adopting multi-level modulation format. [ABSTRACT FROM AUTHOR]

We used digital interference holography (DIH) for in vitro imaging of human optic nerve head and retina. Samples of peripheral retina, macula, and optic nerve head from two formaldehyde-preserved human eyes were dissected and mounted onto slides. Holograms were captured by a monochrome CCD camera (Sony XC-ST50, with 780 × 640 pixels and pixel size of ∼9 µm). Light source was a solid-state pumped dye laser with tunable wavelength range of 560-605 nm. Using about 50 wavelengths in this band, holograms were obtained and numerically reconstructed using custom software based on NI LabView. Tomographic images were produced by superposition of holograms. Holograms of all tissue samples were obtained with a signal-to-noise ratio of approximately 50 dB. Optic nerve head characteristics (shape, diameter, cup depth, and cup width) were quantified with a few micron resolution (4.06-4.8 µm). Multiple layers were distinguishable in cross-sectional images of the macula. To our knowledge, this is the first report of DIH use to image human macular and optic nerve tissue. DIH has the potential to become a useful tool for researchers and clinicians in the diagnosis and treatment of many ocular diseases, including glaucoma and a variety of macular diseases. [ABSTRACT FROM AUTHOR]

Surface reconstruction for micro-samples with large discontinuities using digital holography is a challenge. To overcome this problem, multi-incidence digital holographic profilometry (MIDHP) has been proposed. MIDHP relies on the numerical generation of the longitudinal scanning function (LSF) for reconstructing the topography of the sample with large depth and high axial resolution. Nevertheless, the method is unable to reconstruct surfaces with large gradients due to the need of: (i) high precision focusing that manual adjustment cannot fulfill and (ii) preserving the functionality of the LSF that requires capturing and processing many digital holograms. In this work, we propose a novel MIDHP method to solve these limitations. First, an autofocusing algorithm based on the comparison of shapes obtained by the LSF and the thin tilted element approximation is proposed. It is proven that this autofocusing algorithm is capable to deliver in-focus plane localization with submicron resolution. Second, we propose that wavefield summation for the generation of the LSF is carried out in Fourier space. It is shown that this scheme enables a significant reduction of arithmetic operations and can minimize the number of Fourier transforms needed. Hence, a fast generation of the LSF is possible without compromising its accuracy. The functionality of MIDHP for measuring surfaces with large gradients is supported by numerical and experimental results. [ABSTRACT FROM AUTHOR]

In the recent works on Mathieu beams, the angular spectrums commonly used are even and odd angular Mathieu functions with an angular variation vary between 0 to 2 π. In this work, we propose to introduce a new index m characterizing the rotation repetitions (m- times) of the structure of the original angular spectrum of Mathieu beams on the total circle in the frequency space. With this index, the angular spectrum of Mathieu beams rotation can be controlled to change the beam symmetry. We study the effect of these repetitions of the angular spectrum on the even and odd Mathieu modes features when they propagate through a paraxial optical system. We show that rotated repetitions of the angular spectrum does not affect the nondiffracting property of the beams. To illustrate the rotation repetitions of the angular spectrum, the Fourier transform of the beam is calculated in the focal plane of a thin lens. From the obtained results, we can conclude that the rotation repetitions of the angular spectrum can be used to produce others Mathieu beams shapes and can enrich the applications of these kinds of beams. [ABSTRACT FROM AUTHOR]

Cladding pumping is a common method to amplify signal channels in space-division multiplexing (SDM) systems. A high-power laser pump is directly launched to multi-core doped fiber (MCDF), and depending on the arrangement of cores in the MCDF, a small fraction of power goes to each core and amplifies the signal. Therefore, we have designed two diffractive optical elements, vortex lens (VL) and beam fanner (BF), to properly form the transverse pump distribution and increase pump power efficiency. Phase-only approximation and angular spectrum (AS) based methods are used to design the elements. We have found that using VL and BF allowed a significant increase in the pump power efficiency compared to direct cladding pumping. [ABSTRACT FROM AUTHOR]

Abstract: The angular spectrum propagation technique is applied to modeling of wave propagation through piezoelectric media. The calculations of the angular spectrum propagator are based on the relevant equation for the slowness surface resulting from the solution of the Christoffel equation with piezoelectrically stiffened elastic constants. A two-dimensional FFT algorithm is applied in the final field superposition. We concentrate on the case of Coulomb coupling through local electrical point contacts on both the excitation and detection side. To model that case we superpose solutions for acoustic Green’s functions of different propagation modes convoluted with equivalent distributed effective sources. Calculated results are in good agreement with the measured ones. [Copyright &y& Elsevier]

Abstract: We present a solution to the problem of reflection and transmission of a polarized paraxial light beam at an interface between two homogeneous media by using a two-form amplitude and an extension matrix to represent the vectorial angular spectrum of a three-dimensional (3D) light beam. We derive general formulas for the Imbert–Fedorov (IF) shift of the reflected and transmitted beams of a polarized paraxial light beam. The IF shift of two different types of polarized beams is calculated, and the influence of the polarization state and the polarization feature of the vectorial angular spectrum on the IF shift is discussed. [Copyright &y& Elsevier]

Abstract: The notion of a spherical angular spectrum leads to the representation of an electromagnetic wave as a superposition of spherical waves. It provides a direct way of interpreting the role of the pupil in the theory of image formation. The spherical angular spectrum propagation takes the same form as the field amplitude transfer from a spherical emitter to a spherical receiver. To cite this article: P. Pellat-Finet, P.-E. Durand, C. R. Physique 7 (2006). [Copyright &y& Elsevier]

Abstract: Based on the relationship between separable solutions of the Helmholtz equation, we expanded the field’s amplitude associated with Mathieu beams in terms of Bessel beams. By using the expansion of the circ function into a finite sum of complex Gaussian functions, we derived an approximated analytical expression of the amplitude distribution of Mathieu beams at the output plane of any apertured paraxial ABCD optical system. Some numerical calculations are performed and it is shown that our approach can substitute the usual numerical integration of the Helmholtz equation or the numerical calculation of the diffraction integral. [Copyright &y& Elsevier]

Abstract: We present an optical theorem for evanescent (near field) electromagnetic wave scattering by a dielectric structure. The derivation is based on the formalism of angular spectrum wave amplitudes. The optical theorem shows that an energy flux at scattering is emitted in the direction of incident evanescent wave decay. [Copyright &y& Elsevier]

We present a numerical modelling of the harmonic sound in two isotropic media, one liquid and the other solid separated by a plane interface. This numerical modelling is carried out by the angular spectrum method. This latter is applied to calculate the displacement potential generated by a rectangular transducer with a Gaussian profile and with an uniform profile. The rigorous modelling of the field needed to find the optimal parameters of the decomposition according to the transducer aperture and the ultrasonic wave frequency. [Copyright &y& Elsevier]

In this paper the optical distribution in the near-field region of solid immersion lens (SIL) is investigated from the viewpoint of angular spectrum. Because of the big numeric aperture (NA) of objective in SIL storage system, the polarization of incident laser is also considered. Based on this investigation, a kind of high-pass angular spectrum filter method is proposed to decrease the optical spot size. The effect of filter in SIL system is analyzed in detail. Our theoretical analysis shows that this kind of filter can decrease the spot size by nearly 40% and light intensity loss by around 11%. [Copyright &y& Elsevier]

An iterative inversion in angular spectral domain based on the quasi Newton's procedure is presented. Angular spectral-domain reconstruction is shown to be more insensitive to the noise in the scattered field than configuration domain reconstruction. It is also shown by closed-form solution of a homogeneous circular cylinder that the local minima hindering this inversion process exist in the cost function. [ABSTRACT FROM AUTHOR]