scispace - formally typeset
Search or ask a question
Journal Article

On the diffraction theory of optical images

01 Jan 2004-SPIE milestone series (Society of Photo-Optical Instrumentation Engineers)-Vol. 178, pp 108-132
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.
Citations
More filters
01 Jan 1956
TL;DR: In this paper, a review of coherence properties of electromagnetic fields and their measurements, with special emphasis on the optical region of the spectrum, is presented, based on both the classical and quantum theories.
Abstract: This article presents a review of coherence properties of electromagnetic fields and their measurements, with special emphasis on the optical region of the spectrum. Analyses based on both the classical and quantum theories are described. After a brief historical introduction, the elementary concepts which are frequently employed in the discussion of interference phenomena are summarized. The measure of second-order coherence is then introduced in connection with the analysis of a simple interference experiment and some of the more important second-order coherence effects are studied. Their uses in stellar interferometry and interference spectroscopy are described. Analysis of partial polarization from the standpoint of correlation theory is also outlined. The general statistical description of the field is discussed in some detail. The recently discovered universal "diagonal" representation of the density operator for free fields is also considered and it is shown how, with the help of the associated generalized phase-space distribution function, the quantum-mechanical correlation functions may be expressed in the same form as the classical ones. The sections which follow deal with the statistical properties of thermal and nonthermal light, and with the temporal and spatial coherence of blackbody radiation. Later sections, dealing with fourth- and higher-order coherence effects include a discussion of the photoelectric detection process. Among the fourth-order effects described in detail are bunching phenomena, the Hanbury Brown-Twiss effect and its application to astronomy. The article concludes with a discussion of various transient superposition effects, such as light beats and interference fringes produced by independent light beams.

846 citations

Journal ArticleDOI
TL;DR: Optical quality of the eye was measured at eight pupil sizes between 1·5 and 6·6 mm diameter by recording the faint light emerging from the eye; this light was reflected from the bright image of a thin line on the fundus.
Abstract: 1. Optical quality of the eye was measured at eight pupil sizes between 1.5 and 6.6 mm diameter by recording the faint light emerging from the eye; this light was reflected from the bright image of a thin line on the fundus.2. The nature of the fundus reflexion was examined; it was found that the fundus acts very much like a perfect diffuser while retaining polarization.3. Using the result that the fundus acts like a diffuser, the recorded line images were Fourier analysed to provide modulation transfer functions. These functions indicate an optical quality considerably higher than that found in previous physical studies.4. Linespread profiles were then derived from the modulation transfer functions. These profiles are 40% narrower than those of previous physical studies for a 3.0 mm pupil. The narrowest profile occurred with a 2.4 mm pupil.5. Our results demonstrate that physical and psychophysical studies can yield similar estimates of optical quality. The influence of optical factors not common to both techniques is discussed. Evidence for the existence of neural ;image sharpening' mechanisms is reviewed.

841 citations

Journal ArticleDOI
TL;DR: Optical questions arising in the so-called Maxwellian View method of illuminating the retina have been analyzed theoretically and problems discussed in detail include those of photometry, of magnification, of focus and finally of pupil size insofar as it relates to the transmission of spatial frequencies in coherent and incoherent illumination.

477 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, the effect of various arrangements using lenses with annular pupil functions is discussed, and it is found that Type 2 microscopes have improved imaging properties over conventional microscopes and that these may be further improved by use of one or two lenses with ANNular pupils.
Abstract: Fourier imaging in the scanning microscope is considered. It is shown that there are two geometries of the microscope, which have been designated Type 1 and Type 2. Those of Type 1 exhibit identical imaging to the conventional microscope, whereas those of Type 2 (confocal microscopes) display various differences. Imaging of a single point object, two-point resolution and response to a straight edge are also considered. The effect of various arrangements using lenses with annular pupil functions is also discussed. It is found that Type 2 microscopes have improved imaging properties over conventional microscopes and that these may be further improved by use of one or two lenses with annular pupils.

454 citations

References
More filters
01 Jan 1956
TL;DR: In this paper, a review of coherence properties of electromagnetic fields and their measurements, with special emphasis on the optical region of the spectrum, is presented, based on both the classical and quantum theories.
Abstract: This article presents a review of coherence properties of electromagnetic fields and their measurements, with special emphasis on the optical region of the spectrum. Analyses based on both the classical and quantum theories are described. After a brief historical introduction, the elementary concepts which are frequently employed in the discussion of interference phenomena are summarized. The measure of second-order coherence is then introduced in connection with the analysis of a simple interference experiment and some of the more important second-order coherence effects are studied. Their uses in stellar interferometry and interference spectroscopy are described. Analysis of partial polarization from the standpoint of correlation theory is also outlined. The general statistical description of the field is discussed in some detail. The recently discovered universal "diagonal" representation of the density operator for free fields is also considered and it is shown how, with the help of the associated generalized phase-space distribution function, the quantum-mechanical correlation functions may be expressed in the same form as the classical ones. The sections which follow deal with the statistical properties of thermal and nonthermal light, and with the temporal and spatial coherence of blackbody radiation. Later sections, dealing with fourth- and higher-order coherence effects include a discussion of the photoelectric detection process. Among the fourth-order effects described in detail are bunching phenomena, the Hanbury Brown-Twiss effect and its application to astronomy. The article concludes with a discussion of various transient superposition effects, such as light beats and interference fringes produced by independent light beams.

846 citations

Journal ArticleDOI
TL;DR: Optical quality of the eye was measured at eight pupil sizes between 1·5 and 6·6 mm diameter by recording the faint light emerging from the eye; this light was reflected from the bright image of a thin line on the fundus.
Abstract: 1. Optical quality of the eye was measured at eight pupil sizes between 1.5 and 6.6 mm diameter by recording the faint light emerging from the eye; this light was reflected from the bright image of a thin line on the fundus.2. The nature of the fundus reflexion was examined; it was found that the fundus acts very much like a perfect diffuser while retaining polarization.3. Using the result that the fundus acts like a diffuser, the recorded line images were Fourier analysed to provide modulation transfer functions. These functions indicate an optical quality considerably higher than that found in previous physical studies.4. Linespread profiles were then derived from the modulation transfer functions. These profiles are 40% narrower than those of previous physical studies for a 3.0 mm pupil. The narrowest profile occurred with a 2.4 mm pupil.5. Our results demonstrate that physical and psychophysical studies can yield similar estimates of optical quality. The influence of optical factors not common to both techniques is discussed. Evidence for the existence of neural ;image sharpening' mechanisms is reviewed.

841 citations

Journal ArticleDOI
TL;DR: Optical questions arising in the so-called Maxwellian View method of illuminating the retina have been analyzed theoretically and problems discussed in detail include those of photometry, of magnification, of focus and finally of pupil size insofar as it relates to the transmission of spatial frequencies in coherent and incoherent illumination.

477 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, the effect of various arrangements using lenses with annular pupil functions is discussed, and it is found that Type 2 microscopes have improved imaging properties over conventional microscopes and that these may be further improved by use of one or two lenses with ANNular pupils.
Abstract: Fourier imaging in the scanning microscope is considered. It is shown that there are two geometries of the microscope, which have been designated Type 1 and Type 2. Those of Type 1 exhibit identical imaging to the conventional microscope, whereas those of Type 2 (confocal microscopes) display various differences. Imaging of a single point object, two-point resolution and response to a straight edge are also considered. The effect of various arrangements using lenses with annular pupil functions is also discussed. It is found that Type 2 microscopes have improved imaging properties over conventional microscopes and that these may be further improved by use of one or two lenses with annular pupils.

454 citations