High-order Diffraction Terms Research Articles

Analyzing radiowave multiple diffraction from a low transmitter in vegetated urban areas using a spherical-wave UTD–PO approach

This article introduces a uniform theory of diffraction–physical optics (UTD–PO) formulation for analyzing radiowave multiple diffraction emanating from trees and buildings in green urban areas, considering illumination from a low transmitter and assuming spherical-wave incidence. Based on Babinet’s principle, this solution models buildings as rectangular sections and accounts for the influence of tree crowns (assuming these rise above the average rooftop height) by incorporating appropriate attenuation factors/phasors into the diffraction phenomena of buildings. The validation of the formulation is achieved through measurements made at the 39 GHz 6G mmWave frequency on a scale model of a green urban environment comprising bonsai trees and bricks. The main advantage of the proposed solution is that the calculations only include single diffractions due to recursion, circumventing the need to use higher-order diffraction terms in the diffraction coefficients, thus reducing the computation time and power. Our results may be beneficial for the design of mobile communication systems, including 6G networks, situated in green urban areas and with transmission source positioned lower than the surrounding infrastructure.

Eyebox expansion of a lensless near-eye display using diverging spherical wave illumination and a multiplexed holographic optical element

We expand the eyebox size of a lensless holographic near-eye-display (NED) using passive eyebox replication technique that incorporates a spatial light modulator (SLM) and a holographic optical element (HOE). In holographic NEDs, the space-bandwidth product (SBP) of the SLM determines the exit pupil dimensions and corresponding eyebox size. The base eyebox size is replicated in the horizontal direction by using the horizontal high-order diffractions of an SLM under spherical wave illumination and a multiplexed HOE combiner. When a digital blazed grating and a digital lens phase are added to the computed phase hologram sent to the SLM, two spatially separated, horizontal high-order diffraction terms with identical intensity and information can be uniformly formed without the zero-order term. When the eyebox size is expanded, the field-of-view (FOV) is not sacrificed; spherical divergence wave illumination alleviates the need for a tradeoff between FOV and eyebox size. The astigmatism introduced during HOE fabrication is counterbalanced by pre-correcting the target image using a computer-generated, holographic computation algorithm. The prototype system shows simple and effective, distortion-free eyebox expansion of a wide-angle, lensless, holographic NED.

Plane-Wave UTD-PO Formulations for Multiple-Diffraction by Trees and Buildings at Millimeter-Wave Frequencies

Two uniform theories of diffraction or physical optics (UTD-PO) formulations for the analysis of the multiple-diffraction of millimeter plane waves which is caused by both trees and buildings, in vegetated residential areas, are hereby presented. The two solutions consider the buildings, modeled as knife-edges and rectangular sections (a more complex and realistic shape), respectively, and the influence of the tree canopies—assumed to be higher than the average rooftop height—is taken into account by considering the proper attenuation factors and phasors into the building diffraction phenomenon. The formulations have been validated through comparison with solutions previously published by other authors, and the main advantage of the proposed models is that, thanks to their recursion, only single diffractions are involved in the calculations. This way, the need of higher order diffraction terms in the diffraction coefficients is avoided, thereby lowering the computational effort. The results, focused on the 5G millimeter-wave (mmWave) candidate bands, can be applied in the planning of forthcoming mobile communication systems.

Validation with measurements of plane and spherical-wave UTD-PO propagation models which assume flat-topped obstacles

Two radiowave propagation models which calculate the multiple-building diffraction losses through the corresponding Uniform Theory of Diffraction-Physical Optics (UTD-PO) formulations are validated with measurements performed in different locations of an urban environment. The main advantage of such solutions is that, since they are recursive, the calculations are expressed in terms of single diffractions (high-order diffraction terms are not considered in the diffraction coefficients), thus showing better computational efficiency than other existing methods. Buildings are modeled as flat-topped obstacles and one formulation assumes plane-wave incidence over the obstacles while the other considers a spherical wave impinging over the array of rooftops. The locations in which the spherical-wave model should be used instead of the plane-wave method in order to obtain more realistic results are discussed.

Uniform theory of diffraction (UTD)-based solution for sound diffraction caused by an array of obstacles.

A formulation based on the uniform theory of diffraction (UTD) for the analysis of the multiple-diffraction of a spherical sound wave caused by a series of wedges or knife-edges is hereby presented. The receiver location has to be considered at the same height as the preceding obstacles and at the same inter-obstacle distance from the last wedge. The solution, which is based on a UTD-physical optics formulation for radio-wave multiple-diffraction and has been validated through comparison with a geometrical theory of diffraction acoustic model, is computationally more efficient than other existing methods thanks to the fact that only single diffractions are involved in the calculations (high-order diffraction terms are not considered in the diffraction coefficients), thus allowing for the consideration of a great number of obstacles. In such a way, the proposed solution overcomes the limitations of previous works when multiple acoustic diffraction caused by an array of elements of equal height is to be analyzed. Therefore, the results can be applied in the study of sound propagation in scenarios where multiple-diffraction over a series of edges of equal height and periodical spacing has to be considered, such as the typical audience seating of a concert hall.

Space bandwidth product enhancement of holographic display using high-order diffraction guided by holographic optical element.

A space bandwidth product (SBP) enhancement method for holographic display using high-order diffraction of a spatial light modulator (SLM) is proposed. Among numerous high order diffraction terms, the plus-minus first and the zeroth are adopted and guided by holographic optical elements (HOEs) to an identical direction with the same intensity. By using a set of electro-shutters synchronized with corresponding order component, the system acts as if three SLMs are tiled in the horizontal direction. To confirm the feasibility of using HOE as the guiding optics for the system, several optical characteristics of the recording material are measured before using them. Furthermore, a computer generated hologram algorithm is proposed for compensating the wavefront distortion caused by use of the HOE. The demonstrated system achieves a three-fold increase in SBP of a single SLM. The results are verified experimentally.

UTD-PO Formulation for the Multiple-Diffraction of Spherical Waves by an Array of Multimodeled Obstacles

A hybrid uniform theory of diffraction-physical optics (UTD-PO) solution for the analysis of the multiple-diffraction of spherical waves caused by an array of obstacles, which have been modeled by different shapes, is hereby presented. The formulation, validated with measurements from technical literature, does not need to incorporate high-order diffraction terms (slope diffraction) thanks to a recursive relation, therefore producing an easier, faster solution-when compared with other methods-that, at the same time, achieves accurate results. Such results can be applied in radiowave propagation analysis when multiple-diffraction over obstacles with quite different shapes has to be considered.

A Hybrid UTD-PO Solution for Multiple-Cylinder Diffraction Analysis Assuming Spherical-Wave Incidence

A modified hybrid uniform theory of diffraction-physical optics formulation for the analysis of the multiple diffraction caused by an array of cylinders, assuming spherical-wave incidence, is hereby presented. The solution, validated with numerical data from technical literature, is mathematically less complex and computationally more efficient-particularly for a large number of cylinders-than other existing methods, due to the fact that high-order diffraction terms (slope diffraction) are not considered, without such lack of terms barely entailing any loss in accuracy. Results can be applied in radiowave propagation analysis when multiple diffraction over rounded obstacles has to be considered.

Random facet Fresnel lenses and mirrors

Fresnel-type lenses and mirrors are designed and their performance is simulated. These lenses and mirrors employ random spac- ings between elements to minimize intense higher order diffraction terms while maintaining good overall light concentration.

An efficient representation for radar scattering with the use of the genetic algorithm

In order to obtain a more accurate, efficient representation of scattering behavior for radar targets and to allow better extrapolation of scattering data from the sampled frequency band to a wide range, a modeling procedure is presented for processing scattering data containing high-order diffraction terms. In this procedure, a more realistic fα model for scattering and the maximum-likelihood algorithm are employed. In the model, the restriction of α being an integer multiple of ½ has been removed, which results in highly accurate estimates. In addition, the genetic algorithm is used to overcome the issue of converging to local minima. An iterative simplex downhill minimization method is used to accelerate the optimization process. Computer simulation shows superior noise performance of this modeling procedure. © 1997 John Wiley & Sons, Inc. Microwave Opt Technol Lett 15: 36–39, 1997.