Effects of Spatial Coherence on Fourier Imaging of a Periodic Object
TL;DR: In this article, the formation and contrast of Fourier images of a periodic object, especially a sinusoidally transparent object, are investigated under partially coherent illumination, and it becomes apparent that the spatial coherence of light affects seriously the contrast and positions of the Fourier image planes.
Abstract: The formation and the contrast of Fourier images of a periodic object, especially a sinusoidally transparent object, are investigated under partially coherent illumination. It becomes apparent that the spatial coherence of light affects seriously the contrast of Fourier images and the positions of the Fourier image planes.
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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: Fractional Talbot images of optical gratings acting as periodic phase objects have been obtained by use of x rays of 0.069-nm wavelength from a third-generation synchrotron radiation source.
Abstract: Fractional Talbot images of optical gratings acting as periodic phase objects have been obtained by use of x rays of 0.069-nm wavelength from a third-generation synchrotron radiation source. Quantitative evaluation of the data obtained as a function of defocusing distance provides information on the lateral coherence of the beam as well as on the phase modulation in the object.
145 citations
TL;DR: In this article, the authors studied the diffraction field of two spatially separated linear diffraction gratings under incoherent illumination, based on the spatial superposition of many mutually incoherent Talbot (self-imaging) effects.
Abstract: Characteristics of the diffraction field of two spatially separated linear diffraction gratings under incoherent illumination are studied. The analytical model is based on the spatial superposition of many mutually incoherent Talbot (self-imaging) effects. It permits a simple explanation of the basic parameters of the ‘incoherent’ diffraction images: axial localization, spatial period and lateral displacement. The moire fringe formation in space, the imaging of a grating by a second grating, and the Lau effect are considered; the results are compared with the former studies in the literature.
73 citations
TL;DR: In this article, a hard-x-ray imaging microscope consisting of a lens, a sample, and a transmission grating is presented, where the electric field on the image plane is derived for ideal and real lenses.
Abstract: We report on a hard-x-ray imaging microscope consisting of a lens, a sample, and a transmission grating. After the theoretical framework of self-imaging phenomenon by the grating in the system is presented, equations for the electric field on the image plane are derived for ideal and real lenses and an equation for the intensity on the image plane for partially coherent illumination is derived. The equations are simple and similar to those applying to a projection microscope consisting of a transmission grating except that there is no defocusing effect, regardless of whether the grating is in front of or behind the lens. This means that x-ray phase-imaging microscopy can be done without the defocusing effect. It is also shown that, by resolving the self-image on the image plane, high-sensitive x-ray phase-imaging microscopy can be attained without degradation in the spatial resolution due to diffraction by the grating. Experimental results obtained using partially coherent illumination from a synchrotron x-ray source confirm that hard-x-ray phase-imaging microscopy can be quantitatively performed with high sensitivity and without the spatial resolution degradation.
45 citations
References
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Book•
[...]
01 Jan 1959
TL;DR: In this paper, the authors discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals, including interference, interferometers, and diffraction.
Abstract: The book is comprised of 15 chapters that discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals. The text covers the elements of the theories of interference, interferometers, and diffraction. The book tackles several behaviors of light, including its diffraction when exposed to ultrasonic waves.
19,815 citations
[...]
01 Oct 1999
TL;DR: In this article, the authors discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals, including interference, interferometers, and diffraction.
Abstract: The book is comprised of 15 chapters that discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals. The text covers the elements of the theories of interference, interferometers, and diffraction. The book tackles several behaviors of light, including its diffraction when exposed to ultrasonic waves.
19,503 citations
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: 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