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William T. Rhodes

Other affiliations: Universidad de Guanajuato
Bio: William T. Rhodes is an academic researcher from Florida Atlantic University. The author has contributed to research in topics: Fourier transform & Coherence (physics). The author has an hindex of 7, co-authored 26 publications receiving 243 citations. Previous affiliations of William T. Rhodes include Universidad de Guanajuato.

Papers
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Journal ArticleDOI
TL;DR: A series of experimental results are presented to confirm the validity of the theoretical model, demonstrating recovery of super- Nyquist frequencies for the first time and how the model can be used to optimize CCD design for lensless DH capture.
Abstract: We examine some fundamental theoretical limits on the abil- ity of practical digital holography DH systems to resolve detail in an image. Unlike conventional diffraction-limited imaging systems, where a projected image of the limiting aperture is used to define the system performance, there are at least three major effects that determine the performance of a DH system: i The spacing between adjacent pixels on the CCD, ii an averaging effect introduced by the finite size of these pixels, and iii the finite extent of the camera face itself. Using a theo- retical model, we define a single expression that accounts for all these physical effects. With this model, we explore several different DH record- ing techniques: off-axis and inline, considering both the dc terms, as well as the real and twin images that are features of the holographic record- ing process. Our analysis shows that the imaging operation is shift vari- ant and we demonstrate this using a simple example. We examine how our theoretical model can be used to optimize CCD design for lensless DH capture. We present a series of experimental results to confirm the validity of our theoretical model, demonstrating recovery of super- Nyquist frequencies for the first time. © 2009 Society of Photo-Optical Instrumen-

113 citations

Journal ArticleDOI
TL;DR: In this paper, the Wigner distribution function and the space bandwidth product were used to identify suitable sampling rates for the Fresnel transform (FST) and the Cai-Wang and Lohmann Type-I optical fractional Fourier transform (OFRT) systems.
Abstract: The numerical calculation of the Fresnel transform (FST) presents significant challenges due to the high sampling rate associated with the chirp function in the kernel. The development of an efficient algorithm is further complicated by the fact that the output extent of the FST is dependent on the propagation distance. In this paper, we implement a recently proposed technique for efficiently calculating the FST in which we apply the Wigner distribution function and the space bandwidth product to identify suitable sampling rates. This method is shown to be suitable for all propagation distances. Our method can also be applied to describe the effect of a thin lens modeled as a chirp modulation transform (CMT). Combining our results for the FST and the CMT, we numerically calculate the light distribution at the output of both Cai-Wang and Lohmann Type-I optical fractional Fourier transform (OFRT) systems. Analytic solutions for the OFRT of rectangular window and circular apertures are presented. The analytical solutions are compared to experimental data and to numerical results for equivalent cases. Finally the numerical method is applied to examine the effect that apertured lenses, in the OFRT system, have on the output distribution.

46 citations

Journal ArticleDOI
TL;DR: For the 4-f imaging system investigated in this paper, the severity of the space variance depends on the relative sizes of the two lens stops and the aperture stops.
Abstract: In the usual model of an imaging system, only the effects of the aperture stop are considered in determining diffraction-limited system performance. In fact, diffraction at other stops—those associated with different lens elements, for example—can also affect system performance and cause the imaging to be space variant, even in the absence of vignetting in the conventional ray optics sense. For the 4-f imaging system investigated in this paper, the severity of the space variance depends on the relative sizes of the two lens stops and the aperture stops. If the diameters of the lenses are equal, the aperture of the first lens has a greater effect on system performance than does that of the second.

15 citations

Journal ArticleDOI
TL;DR: This paper studies some of the practical limits introduced by using a converging spherical lens of finite aperture to produce the illuminating field in the implementation of the SOFT and shows that the worst-case errors in the resulting SOFT can be quantified and avoided.

12 citations

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TL;DR: This paper describes a method that shows promise for diffraction-limited imaging through ground-level turbulence with large apertures and at large distances and takes suitable time averages of the magnitude and phase of the Fourier telescopy signal.
Abstract: The problem of high-resolution imaging through long horizontal-path ground-level turbulence has gone unsolved since it was first addressed many decades ago. In this paper I describe a method that shows promise for diffraction-limited imaging through ground-level turbulence with large (meters) apertures and at large (kilometers) distances. The key lies in collecting image data in the spatial frequency domain via the method of Fourier telescopy and taking suitable time averages of the magnitude and phase of the Fourier telescopy signal. The method requires active illumination of the target with laser light, and the time averages required will likely be over many tens of seconds if not tens of minutes or more. The scheme will thus not be suitable for time-varying scenes. The basic scheme is described, and principle challenges briefly discussed.

12 citations


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TL;DR: In this article, a fast Fourier transform method of topography and interferometry is proposed to discriminate between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour generation techniques.
Abstract: A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

3,742 citations

Journal ArticleDOI
TL;DR: Digital holography is an emerging field of new paradigm in general imaging applications as discussed by the authors, and a review of a subset of the research and development activities in digital holographic microscopy techniques and applications is presented.
Abstract: Digital holography is an emerging field of new paradigm in general imaging applications. We present a review of a subset of the research and development activities in digital holography, with emphasis on microscopy techniques and applications. First, the basic results from the general theory of holography, based on the scalar diffraction theory, are summarized, and a general description of the digital holographic microscopy process is given, including quantitative phase microscopy. Several numerical diffraction methods are described and compared, and a number of representative configurations used in digital holography are described, including off-axis Fresnel, Fourier, image plane, in-line, Gabor, and phase-shifting digital holographies. Then we survey numerical techniques that give rise to unique capabilities of digital holography, including suppression of dc and twin image terms, pixel resolution control, optical phase unwrapping, aberration compensation, and others. A survey is also given of representative application areas, including biomedical microscopy, particle field holography, micrometrology, and holographic tomography, as well as some of the special techniques, such as holography of total internal reflection, optical scanning holography, digital interference holography, and heterodyne holography. The review is intended for students and new researchers interested in developing new techniques and exploring new applications of digital holography.

672 citations

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TL;DR: This is Applied Cryptography Protocols Algorithms And Source Code In C Applied Cryptographic Protocols algorithms and Source Code in C By Schneier Bruce Author Nov 01 1995 the best ebook that you can get right now online.

207 citations

Journal ArticleDOI
TL;DR: This work has considered an approach based on discretizing the continuous LCT, making careful consideration of the consequences for the range and resolution of the output.

123 citations

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TL;DR: This work describes three sampling regimes for FFT-based propagation approaches: ideally sampled, oversampled, and undersampled and describes the form of the sampled chirp functions and their discrete transforms.
Abstract: Accurate simulation of scalar optical diffraction requires consideration of the sampling requirement for the phase chirp function that appears in the Fresnel diffraction expression. We describe three sampling regimes for FFT-based propagation approaches: ideally sampled, oversampled, and undersampled. Ideal sampling, where the chirp and its FFT both have values that match analytic chirp expressions, usually provides the most accurate results but can be difficult to realize in practical simulations. Under- or oversampling leads to a reduction in the available source plane support size, the available source bandwidth, or the available observation support size, depending on the approach and simulation scenario. We discuss three Fresnel propagation approaches: the impulse response/transfer function (angular spectrum) method, the single FFT (direct) method, and the two-step method. With illustrations and simulation examples we show the form of the sampled chirp functions and their discrete transforms, common relationships between the three methods under ideal sampling conditions, and define conditions and consequences to be considered when using nonideal sampling. The analysis is extended to describe the sampling limitations for the more exact Rayleigh-Sommerfeld diffraction solution.

122 citations