Self-imaging objects of infinite aperture
01 Jun 1967-Journal of the Optical Society of America (Optical Society of America)-Vol. 57, Iss: 6, pp 772-778
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.
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
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
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
PARC1
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
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
Cites background or methods from "Self-imaging objects of infinite ap..."
...Montgomery [12] proved lateral periodicity to be a sufficient, but not a necessary, condition for self-imaging....
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...The terminology “self-imaging” was introduced by Montgomery [12] and has been used together with the term “Talbot effect” in the literature since the 1970s....
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...The physics of wave propagation ensures the appearance of strict periodicity along the axis of propagation z. Montgomery [12] proved lateral periodicity to be a sufficient, but not a necessary, condition for self-imaging....
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References
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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
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.
550 citations
TL;DR: The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science: Vol. 11, No. 67, pp. 196-205 as discussed by the authors, was the first publication of this paper.
Abstract: (1881). XXV. On copying diffraction-gratings, and on some phenomena connected therewith. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science: Vol. 11, No. 67, pp. 196-205.
473 citations
TL;DR: In this paper, a theory of Fresnel images of plane periodic objects viewed in monochromatic light is presented, which is in agreement with the experimental and computer research available in the literature.
Abstract: A theory of Fresnel images is presented. Only the Fresnel images of plane periodic objects viewed in monochromatic light are considered. The theory is in agreement with the experimental and computer research available in the literature. Photographs of Fresnel images of gratings are shown to verify certain aspects of the theory.
444 citations
01 May 1957
TL;DR: In this article, the Fourier image is used for the imaging of real crystal lattices by light or electron optical systems, and a qualitative appeal to communication theory suggests that it should be possible to devise systems of higher efficiency than the conventional microscope by using a priori knowledge of periodicity.
Abstract: The problem of designing a light or electron optical system specifically for the imaging of periodic objects, such as real crystals, is discussed. A qualitative appeal to communication theory suggests that it should be possible to devise systems of higher efficiency than the conventional microscope by using the a priori knowledge of periodicity. The possibility of deforming the incident wavefront in such a way that the periodic object acts as its own imaging system is considered and a formalism is set up. The particular case of the spherical wavefront is then examined in detail and it is predicted that a new type of image should be formed on certain planes. Since this image is in many ways analogous to the Fourier projection of crystallography, and since it can only be formed by periodic objects, it is named the Fourier image. Fourier images produced experimentally with light optics are presented and shown to be in agreement with theoretical predictions. Patterns on planes other than Fourier image planes are described briefly, but detailed treatment is deferred until Part II. The possibility of application to the imaging of crystal lattices by electron optics is discussed, but a quantitative treatment of the crucial problems of finite source size and coherence are deferred until Part III.
241 citations