A general solution for two-dimensional volume holograms

Distributions of amplitude and phase for bivariate distributions

Floquet-modal-based analysis is presented to determine self and mutual impedances between array elements. The analysis inherently includes the effects on scattered fields from the neighbouring elements of self and mutual impedances, and, hence, the technique is appropriate for estimating the performance of finite-array antennas with arbitrary amplitude and phase distributions. From analytical and computational aspects, the technique is simple to handle complex-element structures, such as multilayered patch-array antennas. The technique is applied to patch-array antennas and the numerical results compare well with the available measured data.

The properties of volume holograms are investigated for the special 2-dimensional case when the overlap of the inscribing beams is entirely in the interior of the holographic material. The amplitude distributions of the output beams and the power relations are derived on the basis of the model and formulas of Solymar. It is found that the amplitudes of the output beams become strongly varying for sufficiently high values of the coupling coefficient. It is further concluded that, for the beam geometry investigated, the distinction between transmission and reflection holograms is no longer relevant.

Diffractive optical elements able to generate on-axis (zero-order) phase as well as amplitude distributions are described. The proposed elements are surface-relief plates, that is phase-only elements, that are based on concepts of computer-generated masks followed by lithographic and etching processes. The proposed encoding method assumes variable spatial partitioning of the cell and a fixed phase value allocated to each subcell. This method requires the minimal number of etching levels needed for full representation of the wave front, that is three, but can be applied with improved efficiency using more etching levels. The reconstructed amplitude and phase distributions contain some noise owing to the encoding process. Discussion of the error sources is given.

The feasibility of using a Kerr magneto-optic-effect display as the input to a coherent optical computer is discussed and experimentally verified. Simple amplitude and phase distributions were generated on a continuous ferromagnetic thin film and their Fourier transforms were displayed with a lens. An experiment was performed demonstrating spatial filtering of a magneto-optically generated amplitude distribution. Magneto-optic generation of more complicated amplitude distributions requires a matrix-type thin-film structure and this input must be treated as sampled data.

A compact quadriwave lateral shearing interferometer (QWLSI) with strong adaptability and high precision is proposed based on a novel randomly encoded hybrid grating (REHG). By performing the inverse Fourier transform of the desired ±1 Fraunhofer diffraction orders, the amplitude and phase distributions of the ideally calculated quadriwave grating can be obtained. Then a phase chessboard is introduced to generate the same phase distribution, while the amplitude distribution can be achieved using the randomly encoding method by quantizing the radiant flux on the ideal quadriwave grating. As the Faunhofer diffraction of the REHG only contains the ±1 orders, no order selection mask is ever needed for the REHG-LSI. The simulations and the experiments show that the REHG-LSI exhibits strong adaptability, nice repeatability, and high precision.

An approach based on the genetic algorithm is proposed to solve system of coupled differential equation with prescribed boundary conditions. Unsteady, viscous, 2-dimensional incompressible flow over a stretching sheet with outer velocity and aligned magnetic field is considered to illustrate the approach. Coupled partial differential equations are converted to equivalent ordinary differential equation using similarity transform. Results show that this approach may replace traditional shooting technique in solving complex boundary value problems. Comparison with existent methods have been made to show validation of the approach. Graphs and tables are depicted to show impact of aligned magnetic field, stretching parameter on flow and heat transfer over stretching surfaces.

In the previous chapter we discussed the detection of the incident power in an optical or infrared wave, basically ignoring the actual frequency of the wave except in the value of the quantum energy and the wavelength or frequency cutoff of the photon detector. We now consider heterodyne or coherent detection first demonstrated at optical frequencies by Forrester et al. (1955). By using a single-frequency local oscillator as a reference, we may convert the incoming wave’s amplitude and phase to a low frequency in the rf or microwave region. In the following sections we treat the heterodyne case, first for simple constant-amplitude co-planar waves and then in a more general way for an arbitrary amplitude and phase distribution of the local oscillator over the detector surface. We then derive two important theorems that are applicable to heterodyne detection. These are the antenna theorem, which describes the angular response of the detector, and the mixing theorem, which allows the calculation of the mixing efficiency at any arbitrary surface.

Yam is an important food crop in Ghana. It is a delicacy that is eaten after cooking or frying the fresh sample when cut into slices. The powders of the dried yam can be incorporated into soups, baby food and bread as composite flours. However, the high moisture content of yam when harvested (about 70%wb) makes it susceptible to spoilage leading to reduced shelf life and onward rejection by the consumer. This adds to the waste basket. Drying is a worldwide postharvest method for extending the shelf life of agricultural food products such as yam. An energy source that is cheap and clean has always been from the sun. The open sun method has been utilized severally and for many years, but this is subject to various contaminants and thus reducing its quality. A confined solar drying method is a better option but the energy source is limited to the day’s solar energy. Solar adsorption drying is an opportunity to dry day and night in an efficient and product conserving manner with a reduced drying cycle. Prior to this thesis work, several aspects were insufficiently known to really judge the potential. The thesis tackles some of the bottlenecks and problems: lack of knowledge about the drying properties of yam; how to design appropriate solar collectors for drying and regeneration and to share experiences with the actual implementation of the system to see its possibilities an opportunities. In this thesis the sorption properties of yam which gives an indication of the equilibrium moisture content in relation to water activity at constant temperature, but has been given less attention in literature, is studied. The analytical Crank solution to the Fick’s second law has been utilized in the prediction of drying curves of many food products. However the Crank solution puts limitations on the extent to which the equation could be utilized. The limitation is that the particle of food sample to be dried must be infinite, shrinkage should not exist, while moisture diffusion coefficient must be constant. In practice, these limitations are not realistic since most biological food products go through shrinkage together with variable moisture diffusion. Meanwhile the source of energy for drying has largely come from the sun and has led the use of the so-called open sun drying (OSD) method especially in tropical countries, for so many years. This method exposes the food to weather conditions and contaminants reducing the quality of the dried product. Recent research has shown that a confined drying system is most appropriate in terms of reduced drying time and quality of the final product. The shortcoming of the solar drying (SD) method is that, drying is limited to a time interval of 6-9 hours of the day after which the sun’s energy can no more be explored. Solar adsorption drying (SAD), as an alternative drying to solar drying, is an integrated drying method that helps in drying day and night in a continuous manner. Research in solar adsorption drying systems is limited in literature, therefore its performance is yet to be explored. Solar collectors are an integral part of solar and solar adsorption dryers. However, most researchers construct collectors to see what happens or use heuristic rules, whereas others do not link to dryers. The output air temperature has an effect on the quality of the dried food product, therefore much attention must be given to the output temperature of the air that enters the dryer. On the other hand after adsorption drying, the adsorbent needs to be regenerated. The easiest way to regenerate the adsorbent (silica gel), which requires temperatures over 70°C is by conventional ovens, which is costly. In this thesis, the condition and requirements for solar adsorption drying of yam (Dioscorea rotundata) is investigated. The approach is first to investigate the sorption properties of yam, then the drying characteristics of yam by modifying the Crank solution of the Fick’s diffusion equation, subsequently the model based design and construction of solar collectors for drying and regeneration purposes, and then finally, the proof of principle of solar - adsorption for both drying and regeneration. The first part of this thesis concerns investigating the equilibrium moisture isotherms for yam at 25°C and 50°C, both for sorption and desorption, experimentally using the gravimetric method. The strength of this work is that a Dynamic Vapour Sorption (DVS) analyzer, which is very sensitive to micro changes in weight loss during dehydration or rehydration, was used. A graphical presentation of equilibrium moisture content, as a function of water activity from the outcome of nonlinear regression analyses of desorption and adsorption isotherms respectively, is shown. The findings contradict most of the findings in literature. The parameters and their uncertainty range for each of the models (GAB, Henderson, Halsey, Oswin, Smith, BET and Peleg) are estimated. The strength of the statistical analysis is that an objective criteria is used to select the model that best describes the experimental desorption and adsorption isotherms over the relevant range of moisture contents. This has been presented in a table form where statiscally, the standard error (SE), the percent average relative deviation (PRD), Akaike Information Criterion (AIC), coefficient of performance (R2), and most importantly, the 2-σ bound confidence interval of the parameters, in particular those that bear the same unit as the equilibrium moisture content (Xe), have been taken into consideration. The GAB model was selected to describe both the desorption and adsorption isotherms, because it allows a physical interpretation. Next, Crank’s analytical approximation to Fick’s diffusion equation is used to investigate the effect of moisture dependent sample thickness and diffusivity on the drying behavior of yam (Dioscoreaceae rotundata) cubicles. Separate experiments of drying and shrinkage at constant temperatures of 30, 40 and 50oC were conducted in a cabinet dryer. The comparative study shows an interdependence between diffusivity and shrinkage due to water loss during drying. The analytical expression for the diffusion in a slab results in non-Fickian behavior for smaller cubicles and consequently, results in a higher effective diffusion coefficient. The drying rate trajectory shows two stages as a function of moisture ratio. The drying behavior of yam is better described by observing both drying and drying rate curves concurrently. This gives good agreement between observed and model data by a combination of fractal moisture dependent shrinkage and moisture dependent diffusion. The advantage of this modified Crank’s approximation is that the moisture trajectory of finite food cubicles can be predicted appropriately. Coupled partial differential equations are developed to investigate which collector lengths are appropriate for drying and for adsorbent regeneration. The output air temperature of the model was validated with an experiment. The spatially distributed model is a powerful tool to aid in multi-purpose collector design leading to solar dryer and regeneration system construction. The advantage of this model is that, the spatial mean temperature of the absorber plate, a requirement for the determination of the overall heat loss coefficient, which hitherto is absent in the approach of Duffie and Beckmann, is no more a problem. The result shows a spatially distribution of temperature in air, absorber plate, and glass cover as functions of collector length and time (day) at constant air velocity and presented in a graphical from. While the temperature of absorber plate, glass cover and air are functions of time (day), the air temperature additionally varies directly with collector length. The study shows the operational overall heat loss coefficient, radiative and convective heat gain and efficiency as functions of the operational air velocity. There was a good agreement between the observed and the model air output temperature. The proof of principle of solar adsorption drying (SAD) and its benefits, compared to solar drying (SD) and open sun drying (OSD) and the effects of these drying methods on the quality of different yam cultivars and regeneration of silica gel is considered. The drying methods SAD, SD and OSD are compared in terms of drying cycles. The SAD had, the shortest drying cycle while maintaining the whitish colour of yam, followed by SD and OSD. However, due to the night drying, the SAD dried product is longer exposed to the drying medium (air), leading to slightly lower vitamin C content of dried sample compared to SD dried samples. OSD had the worst effect on vitamin C. The study shows that the different cultivars of yam dried at different rates. Drying has no effect on composition. Regeneration was possible with solar energy but more work must be done to obtain the information needed for improved designs and operation strategies for the desorption. Finally the perspective, impact and the potential application of the study has also been discussed.

Mathematical models play a vital role in fuel cell development. Some of the aspects treated with the help of models are the analysis of steady state and transient system behaviour during regular operation or start‐up and shut‐down, optimisation of system design and operating conditions and failure detection by online observation. In this contribution, we present some typical equations for high temperature fuel cell models and demonstrate their numerical treatment. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A method is proposed for the reconstruction of an optical field with the aid of two transparencies. Information on the distribution of the amplitudes and phases of the optical field is recorded by directing radiation into two channels. The distribution of the field amplitudes is recorded in the usual way in one channel, whereas the other channel visualizes the phase distribution and ensures that it is recorded in a phase-sensitive material. Reconstruction involves illumination of these two transparencies used in combination with a plane monochromatic wave.

Holography is the recording of the interference pattern of a reference and light reflected from or transmitted through an 3D object. In conventional digital holography, the interference intensity pattern is recorded on a digital camera. Recording reflection holograms using this device are usually not possible. In this paper, we outline a method to numerically convert digital transmission holograms to digital volume reflection holograms by simulating a reflection grating which incorporates a fast longitudinal variation along with information from the transmission hologram function. This longitudinal variation would from the interference of two counter propagating waves, similar to what would be physically recorded in a bulk medium for a volume reflection grating. Coupled wave theory is then used to read the simulated volume reflection hologram and reconstruct the object. Wavelength multiplexing is readily achieved in this simulated volume hologram recording. Volume reflection holography has the advantage of excellent wavelength selectivity during readout using multispectral or white light. We demonstrate digital volume reflection holography by numerically simulating digital transmission hologram recording using simple objects such as Gaussian beams at two different wavelengths. This is followed by experimentally recording the digital transmission holograms of two objects with different wavelengths and repeating the reflection hologram conversion and readout numerically. Digital volume reflection holography is expected to have applications in 3D color holographic displays.

Holographic optical element (HOE) is one of the most promising solutions for achieving widespread market recognition and rapid implementation of augmented reality (AR) display systems. Nevertheless, the spherical HOE lacks sufficient modulation capability to constrain off-axis aberration, which weakens the competitiveness of the HOE scheme. This paper designs and fabricates HOE with arbitrary phase distributions to correct aberrations and improve the imaging quality of AR display systems. A hybrid optimization algorithm that integrates global and local algorithms is developed to achieve large-scale search and stable convergence. A HOE design framework with a hybrid optimization algorithm as the core, considering application requirements and process constraints, is constructed. HOE with arbitrary phase distributions is designed by the framework to suppress aberrations. The samples are fabricated by a self-made holographic printer according to the design results, and an AR display system prototype is built based on the HOE sample. The distortion, as an imaging indicator, is reduced by 84.9% and 72%, respectively, in the design and experiment after optimization. The high flexibility and performance brought by arbitrary phase distribution will enhance the attractiveness of HOE schemes to AR display systems.

A reflector-antenna synthesis procedure based on the principles of geometrical optics (GO) will be applied to the design of a quasi-optical converter which is used to transform the output of the whispering-gallery-mode (WGM) gyrotron to a freespace beam. The amplitude and phase distributions across both transverse dimensions of the free-space beam are specified as design parameters. The exact reflector surfaces which yield the desired output-beam characteristics are determined self consistently as the solutions of a system of first-order partial differential equations which we solve by progressive integration across the face of the reflectors. The synthesis procedure is anticipated to improve the output-beam characteristics of previous Vlasov-type converter designs where the power distribution could be manipulated in only one dimension across the beam which results in relatively poor free-space propagation charasteristics and reduced coupling efficiency into guided wave systems.

Continuous-wave off-axis and in-line terahertz digital holography with phase unwrapping and phase autofocusing