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W. Duane Montgomery

Bio: W. Duane Montgomery is an academic researcher from Institute for Defense Analyses. The author has contributed to research in topics: Diffraction & Fresnel diffraction. The author has an hindex of 4, co-authored 8 publications receiving 425 citations.

Papers
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Journal ArticleDOI
TL;DR: In this article, the necessary and sufficient conditions for self-imaging were derived in order that an infinite plane object, illuminated by a plane monochromatic wave of normal incidence, images itself without the aid of lenses or other optical accessories.
Abstract: The necessary and sufficient conditions are derived in order that an infinite plane object, illuminated by a plane monochromatic wave of normal incidence, images itself without the aid of lenses or other optical accessories. This involves a solution of the reduced wave equation which does not satisfy the Sommerfeld radiation condition. The solution is obtained by requiring a geometrical-optics limiting condition as the wavelength λ goes to zero. Two cases of self-imaging are considered. The first case, called weak, deals with the faithful imaging of objects whose spatial frequencies are all much smaller than the (1/λ) value of the illuminating source. The conditions for this case demand that the two-dimensional Fourier spectrum of the object lies on the circles of a Fresnel zone plate. The second case, called strong, deals with the faithful imaging of objects for spatial frequencies up to the natural cutoff of 1/λ. Both doubly- and singly-periodic and nonperiodic objects are considered. For periodic objects the results are shown to agree well with the experimental and theoretical work to date, the latter of which has always employed the Fresnel–Kirchhoff diffraction integral with the parabolic approximation appropriate to Fresnel diffraction.

347 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that there exist fields which image themselves exactly through the diffraction process, i.e., to within a constant positive factor, regardless of whether the screen is applied or not.
Abstract: One of Rayleigh’s diffraction integrals is generalized as to the nature of the functions on which it operates. These functions comprise the well-known Hilbert space ℒ2 of square-integrable functions. The algebraic properties are apparent in the existence of a left inverse for the diffraction operator, and in other places where the ordering of a sequence of operations is important. The conditions for self imaging are completely characterized by a certain part of the mathematical spectrum of the diffraction operator. The contribution of the evanescent waves to this spectrum is clearly shown. Both the infinite- and finite-aperture cases of diffraction are treated. In the infinite-aperture case we can employ a vector theory in which we obtain a complete characterization of self imaging. This self imaging is of an approximate nature. For the finite-aperture case we employ a scalar theory and obtain some partial results. However, in contrast to the infinite aperture we prove, for the case of an arbitrary finite aperture in a black screen, that there exist fields which image themselves exactly through the diffraction process. These fields are the eigenfunctions of a diffraction operator which corresponds to the sequential operations of inserting a screen into the incident field, discarding the evanescent-wave contribution, and diffracting through a distance z. The operator which corresponds to just the first two processes of inserting the screen and discarding the evanescent waves is of the type which generates the so-called generalized prolate spheroidal functions. These functions correspond to fields which have the interesting optical property of giving the same diffraction pattern whether the screen is applied or not (i.e., to within a constant positive factor). A conjecture is put forth concerning the evanescent-wave contribution to measurements that have been taken near the aperture. If the conjecture proves correct, it may be possible to show a consistency between the first Rayleigh diffraction integral and near-aperture measurements.

76 citations

Journal ArticleDOI
TL;DR: The use of complex-valued notation in classical electromagnetic theory is shown to have a more fundamental basis than that of simplifying mathematical manipulations as discussed by the authors, and the appearance and location of the pseudoscopic image in holography is due to the unitary property of the diffraction operator in the absence of evanescent waves.
Abstract: The practice of using complex-valued notation in classical electromagnetic theory is shown to have a more fundamental basis than that of simplifying mathematical manipulations. In the algebraic formulation, the positive and negative time-frequency components of the real-valued field quantities are propagated by two different diffraction operators, each of which is the dual (adjoint) of the other. In addition to the basic distinguishability of these positive and negative time-frequency components, other features distinguish them in general, owing to the constraint of Maxwell’s equations. In the monochromatic case, there are boundary fields for which these other features vanish. For some of these fields, a pseudoscopic image can be propagated. The appearance and location of the pseudoscopic image in holography is shown to be a direct consequence of the unitary property of the diffraction operator in the absence of evanescent waves.

8 citations

Journal ArticleDOI
TL;DR: In this article, the authors developed a method for real-time visual display of wave fields using a wide-angle lens for viewing large solid angles in the visible spectrum, analogous to a recently developed technique of incoherent holography, with the important difference that the sampling performed by an array makes unnecessary any film processing stage.
Abstract: The passive planar arrays used to receive sonic waves through the earth or water or those employed in radio astronomy use mechanical or electronic scanning in order to observe a large solid angle, such as 2π sr. The purpose of the present paper is to develop a method for real-time visual display of such wave fields. It is analogous to the use of a wide-angle lens for viewing large solid angles in the visible spectrum. The method is analogous to a recently developed technique of incoherent holography, with the important difference that the sampling performed by an array makes unnecessary any film-processing stage.

5 citations

Journal ArticleDOI
TL;DR: In this article, the authors derived two original results: the satisfaction of Maxwell's equations in the diffracted field is equivalent to an orthogonality condition on the boundary, and the diffraction process is governed by a one-parameter group of diffraction operators.
Abstract: The diffraction due to a monochromatic source is treated with the use of mathematical distributions. A significant departure from the conventional literature on distributions is manifest in the choice of test functions. These latter are tailored to reflect the important physical properties of the specific problem of electromagnetic diffraction. In this context, we derive two original results. The satisfaction of Maxwell’s equations in the diffracted field is shown to be equivalent to an orthogonality condition on the boundary. The diffraction process is shown to be governed by a one-parameter group of diffraction operators.

3 citations


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Journal Article
TL;DR: The theory of image formation is formulated in terms of the coherence function in the object plane, the diffraction distribution function of the image-forming system and a function describing the structure of the object.
Abstract: The theory of image formation is formulated in terms of the coherence function in the object plane, the diffraction distribution function of the image-forming system and a function describing the structure of the object. There results a four-fold integral involving these functions, and the complex conjugate functions of the latter two. This integral is evaluated in terms of the Fourier transforms of the coherence function, the diffraction distribution function and its complex conjugate. In fact, these transforms are respectively the distribution of intensity in an 'effective source', and the complex transmission of the optical system-they are the data initially known and are generally of simple form. A generalized 'transmission factor' is found which reduces to the known results in the simple cases of perfect coherence and complete incoherence. The procedure may be varied in a manner more suited to non-periodic objects. The theory is applied to study inter alia the influence of the method of illumination on the images of simple periodic structures and of an isolated line.

566 citations

Book ChapterDOI
TL;DR: In this paper, the authors discuss the theoretical and applicational aspects of the self-imaging phenomenon, that is, the property of the Fresnel diffraction field of some objects illuminated by a spatially coherent light beam.
Abstract: Publisher Summary This chapter describes the self-imaging phenomenon and its applications. The self-imaging phenomenon requires a highly spatially coherent illumination. It disappears when the lateral dimensions of the light source are increased. When the source is made spatially periodic and is placed at the proper distance in front of the periodic structure, a fringe pattern is formed in the space behind the structure. The chapter discusses the theoretical and applicational aspects of the self-imaging phenomenon—that is, the property of the Fresnel diffraction field of some objects illuminated by a spatially coherent light beam. The applications of self-imaging are summarized in four main groups—namely, (1) image processing and synthesis, (2) technology of optical elements, (3) optical testing, and (4) optical metrology. The chapter describes the double diffraction systems using spatially incoherent illumination. The first periodic structure plays the role of a periodic source composed of a multiple of mutually incoherent slits. Depending on whether the periods of two periodic structures are equal, the Lau or the generalized Lau effect is discussed. Various applications of incoherent double-grating systems are described in the fields of optical testing, image processing, and optical metrology. After examining some cases of coherent and incoherent illumination, the general issue of spatial periodicities of optical fields and its relevance to the replication of partially coherent fields in space is discussed.

457 citations

Journal ArticleDOI
TL;DR: In this paper, two promising adjacent approaches tackle fundamental limita- tions by utilizing non-optical forces which are, however, induced by optical light fields, namely, dielectrophoretic and photophoretic forces.
Abstract: Optical tweezers, a simple and robust implementa- tion of optical micromanipulation technologies, have become a standard tool in biological, medical and physics research labo- ratories. Recently, with the utilization of holographic beam shap- ing techniques, more sophisticated trapping configurations have been realized to overcome current challenges in applications. Holographically generated higher-order light modes, for exam- ple, can induce highly structured and ordered three-dimensional optical potential landscapes with promising applications in op- tically guided assembly, transfer of orbital angular momentum, or acceleration of particles along defined trajectories. The non- diffracting property of particular light modes enables the op- tical manipulation in multiple planes or the creation of axially extended particle structures. Alongside with these concepts which rely on direct interaction of the light field with particles, two promising adjacent approaches tackle fundamental limita- tions by utilizing non-optical forces which are, however, induced by optical light fields. Optoelectronic tweezers take advantage of dielectrophoretic forces for adaptive and flexible, massively parallel trapping. Photophoretic trapping makes use of thermal forces and by this means is perfectly suited for trapping ab- sorbing particles. Hence the possibility to tailor light fields holo- graphically, combined with the complementary dielectrophoretic and photophoretic trapping provides a holistic approach to the majority of optical micromanipulation scenarios.

338 citations

Journal ArticleDOI
Olof Bryngdahl1
TL;DR: In this paper, two situations in which self-imaging techniques can be applied to advantage are presented: the pinhole-array camera and transmission through an optical fiber, and the experimental procedure and results are presented for the case of a pinhole array illuminated with an extended incoherent object distribution.
Abstract: Two situations in which self-imaging techniques can be applied to advantage are presented: the pinhole-array camera and transmission through an optical fiber. The experimental procedure and results are presented for the case of a pinhole array illuminated with an extended incoherent object distribution. In the Fresnel-image planes, more images are formed than there are pinholes in the array, which is in contrast to the case of the pinhole-array camera. An optical fiber or thin film working in the kaleidoscope mode may form an image, provided that its length fulfills the self-imaging condition.

324 citations

Journal ArticleDOI
TL;DR: In this article, the authors give an overview of recent advances on the effect from classical optics to nonlinear optics and quantum optics, and present the physical aspects of the self-imaging phenomenon.
Abstract: The Talbot effect, also referred to as self-imaging or lensless imaging, is of the phenomena manifested by a periodic repetition of planar field distributions in certain types of wave fields. This phenomenon is finding applications not only in optics, but also in a variety of research fields, such as acoustics, electron microscopy, plasmonics, x ray, and Bose–Einstein condensates. In optics, self-imaging is being explored particularly in image processing, in the production of spatial-frequency filters, and in optical metrology. In this article, we give an overview of recent advances on the effect from classical optics to nonlinear optics and quantum optics. Throughout this review article there is an effort to clearly present the physical aspects of the self-imaging phenomenon. Mathematical formulations are reduced to the indispensable ones. Readers who prefer strict mathematical treatments should resort to the extensive list of references. Despite the rapid progress on the subject, new ideas and applications of Talbot self-imaging are still expected in the future.

310 citations