Showing papers in "Journal of Modern Optics in 1981"
TL;DR: In this paper, a modal theory describing the diffraction properties of a dielectric lamellar grating is presented and the numerical implementation is shown to be suited to modelling the behaviour of high refractive index gratings.
Abstract: A rigorous modal theory describing the diffraction properties of a dielectric lamellar grating is presented. The numerical implementation is shown to be suited to modelling the behaviour of high refractive index gratings. This suggests that an approach of this type may be successfully applied to the problem of lossy metallic lamellar gratings.
383 citations
TL;DR: In this paper, the cross-correlation functions of speckle intensities before and after deformation were investigated by calculating the crosscorrelation function of the intensity distribution of laser-speckles.
Abstract: Laser-speckles show displacement accompanied by structure change when diffuse objects generating them undergo displacement and/or deformation. This behaviour is theoretically investigated by calculating the cross-correlation functions of speckle intensities before and after the deformation. The dependences of speckle displacement on geometries of object illumination and speckle observation as well as on deformation parameters are clarified. The relations derived are interpreted physically by introducing the shift in diffraction rays due to displacement and deformation of a grating. Distributions of speckle displacement are calculated numerically and shown graphically.
319 citations
TL;DR: In this article, a new method of inversion of the Laplace transform based on its recently discovered eigenvalues and eigenfunctions is applied to the problem of inverting light scattering data from a polydisperse molecular suspension.
Abstract: A powerful new method of inversion of the Laplace transform, based on its recently discovered eigenvalues and eigenfunctions, is applied to the problem of inverting light scattering data from a polydisperse molecular suspension.
295 citations
TL;DR: In this paper, the quantum theory of photodetection from the point of view of quantum measurement has been considered, and it has been shown that the Mandel photon counting formula may lead to unphysical results such as negative probabilities, in some situations just because this modification is not incorporated into the model.
Abstract: We reconsider various approaches to the quantum theory of photodetection from the point of view of the quantum theory of measurement, and show that important differences between them depend upon the manner in which they take into account the modification of the field distribution produced by the presence of the detector. We show that the Mandel photon counting formula may lead to unphysical results, such as negative probabilities, in some situations just because this modification is not incorporated into the model. We also show that the recently developed quantum theory of continuous measurements provides a completely satisfactory framework for discussing photon counting experiments. As an illustration, an exact derivation of the photon statistics of a single-mode free field is presented, and some of the results are shown to be identical to those derived earlier by Mollow and others. We also indicate how our approach can be extended to discuss the photon statistics of fields in interaction with sources an...
241 citations
TL;DR: In this paper, a modal theory describing the diffraction properties of a finitely conducting lamellar grating is presented, which is a generalization to lossy structures of an earlier formalism for the dielectric grating.
Abstract: A rigorous modal theory describing the diffraction properties of a finitely conducting lamellar grating is presented. The method used is the generalization to lossy structures of an earlier formalism for the dielectric lamellar grating. Sample results of the method are given, demonstrating its accuracy and its ability to deal with problems intractable by the widely used integral-equation formalisms of diffraction grating theory.
195 citations
176 citations
TL;DR: In this paper, the authors proposed a method for phase retrieval based on measuring the modulus of the Fourier transform of the unknown function and its product of an exponential and an unknown function.
Abstract: A method for solving the phase retrieval problem is proposed. The method consists of measuring the modulus of the Fourier transform of the unknown function and the modulus of the Fourier transform of the product of the unknown function and an exponential. From these two measurements, the location of the complex zeros of the analytic continuation of the Fourier transform of the unknown function may easily and quickly be deduced and the unknown function constructed.
120 citations
TL;DR: In this article, a Michelson interferometer of extreme sensitivity capable of measuring 10-16 m (i.e. some 10-10 of a wavelength λ of the illuminating laser light) was used for the development of a gravitational wave detector.
Abstract: Our development of a gravitational wave detector requires a Michelson interferometer of extreme sensitivity capable of measuring 10-16 m (i.e. some 10-10 of a wavelength λ of the illuminating laser light). Even after painstaking alignment of the interferometer components, and after considerable improvement of the laser stability, noise contributions much in excess of this goal were observed, due partly to fluctuations of the laser beam geometry. The two most obvious types of geometric beam fluctuations are a lateral beam jitter and a pulsation in beam width; these lead to spurious interferometer signals if the interfering wavefronts are misaligned in their tilts or in their curvatures respectively. The geometry of the laser beam can be considerably stabilized by passing it through an optical resonator. The geometric beam fluctuations, as viewed from this resonator, can be described by a well-centred ground mode TEMoo, contaminated by transverse modes TEM mn , with amplitudes decreasing rapidly with the mo...
105 citations
TL;DR: In this paper, the authors report measurements of the statistical properties of the intensity fluctuations in a He/Ne laser beam which had propagated 1·125 km through the earth's atmosphere, where the beam size was such that the beam propagated as a spherical wave, and atmospheric conditions such that most measurements were made in the saturation region (β 0 ∼ 1-4).
Abstract: We report measurements of the statistical properties of the intensity fluctuations in a He/Ne laser beam which had propagated 1·125 km through the earth's atmosphere. The beam size was such that the beam propagated as a spherical wave, and atmospheric conditions such that most measurements were made in the ‘saturation’ region (β0 ∼ 1-4). We found (1) that the variance of the intensity was considerably larger than that previously reported for plane wave propagation, and (2) that the probability distribution of the intensity and the derived moments were close to the K-distribution and its moments. The origin and significance of the K-distribution in atmospheric propagation is considered. Photon counting techniques were used for all measurements.
101 citations
TL;DR: In this paper, an improved root-finding algorithm was proposed for the solution of the eigenvalue equation associated with the diffraction formalism for lossy lamellar gratings.
Abstract: We outline an improved root-finding algorithm necessary for the solution of the eigenvalue equation associated with the diffraction formalism for lossy lamellar gratings. A numerical example is presented, demonstrating the adequacy of this technique for a highly-conducting aluminium grating.
101 citations
TL;DR: In this article, Abbe's theory of image formation in the Microscope has been studied in the context of image recognition. But this paper is not related to the present paper.
Abstract: (1981). On Abbe's Theory of Image Formation in the Microscope. Optica Acta: International Journal of Optics: Vol. 28, No. 12, pp. 1691-1701.
TL;DR: In this paper, a high-resolution Electron Microscopy (EEM) system was proposed for high resolution electron microscopy, and the authors presented their experimental high resolution EEM system.
Abstract: (1981). Experimental High-resolution Electron Microscopy. Optica Acta: International Journal of Optics: Vol. 28, No. 9, pp. 1173-1173.
TL;DR: In this article, safety with Lasers and other optical sources is discussed and safety with laser sources is investigated in the context of Optica Acta: International Journal of Optics: Vol. 28, No. 10, pp. 1312-1312.
Abstract: (1981). Safety with Lasers and other Optical Sources. Optica Acta: International Journal of Optics: Vol. 28, No. 10, pp. 1312-1312.
TL;DR: In this paper, the concept of the Wigner distribution function is applied to stochastic signals, in particular to partially coherent light, and relations between the distribution function, the power spectrum and related subjects are formulated.
Abstract: The concept of the Wigner distribution function is applied to stochastic signals, in particular to partially coherent light. Relations between the Wigner distribution function, the power spectrum and related subjects are formulated. Some inequalities for the Wigner distribution function are derived; one of these inequalities leads to the definition of an overall degree of coherence. The overall degree of coherence of a stochastic signal remains invariant when the signal propagates through a lossless linear system.
TL;DR: In this paper, a multiple scattering theory of scalar waves from random rough surfaces is presented, where the scattering integral equation is solved by means of an expansion in σ powers (σ being the standard deviation of the corrugation).
Abstract: A multiple scattering theory of scalar waves from random rough surfaces is presented. By using the Ewald-Oseen extinction theorem the scattering integral equation is solved by means of an expansion in σ powers (σ being the standard deviation of the corrugation). Values of the mean scattered intensity until the fourth order of σ are given. The quick convergence of this series for low σ permits us to deal with those situations of small roughness in which the Kirchhoff approximation given by Beckmann and Spizzichino [2] fails. These are the cases in which σ ≳ T and λ ≳ T (λ being the wavelength and T the surface correlation length). Thus this theory can give the intensity for white noise surfaces, and yields the conditions under which the single scattering Kirchhoff approximation works, as well as its percentage of error. As such it is shown that Beckmann's theory gives good results in all cases in which σ /T < 0·05 and, thus, the reason why it is valid for interpreting laser speckle measurements is given. A...
TL;DR: In this article, the authors extended the quantal description of a cavity from the case of constant mass to that of variable mass, corresponding to a decaying or driven cavity, in such a way that both Maxwell's equations and quantal equations of motion are invariant.
Abstract: The quantal description of a cavity is extended from the case of constant mass to that of variable mass, corresponding to a decaying or driven cavity, in such a way that both Maxwell's equations and the quantal equations of motion are invariant. The method is illustrated for the case of a decaying cavity.
TL;DR: In this article, the authors obtained results for the intensity variance in a weakly turbulent medium for the case when the source is spatially incoherent, but has an arbitrary degree of temporal coherence.
Abstract: The measured intensity scintillations of an optical wave in the turbulent atmosphere depend strongly on the coherence properties of the source. In this paper we obtain results for the intensity variance in a weakly turbulent medium for the case when the source is spatially incoherent, but has an arbitrary degree of temporal coherence.
TL;DR: In this paper, La Thermographie Infrarouge is used to describe the properties of a thermodynamic model of a thermal system and its properties in terms of its properties and properties.
Abstract: (1981). La Thermographie Infrarouge. Optica Acta: International Journal of Optics: Vol. 28, No. 7, pp. 882-882.
TL;DR: In this paper, the results derived in part I of this investigation are applied to study the radiant intensity and the degree of spatial coherence of the far field generated by certain types of fluctuating three-dimensional scalar sources.
Abstract: The general results derived in part I of this investigation are applied to study the radiant intensity and the degree of spatial coherence of the far field generated by certain types of fluctuating three-dimensional scalar sources. One class of sources that are considered are the three-dimensional analogues of quasihomogeneous sources, which provide a good representation for many natural sources of light. Three-dimensional analogues of the so-called Schell-model sources are also considered, under the assumptions that both the spatial distribution of the intensity and of the degree of spatial coherence of the source have the form of gaussian distributions. Several general theorems relating to fields generated by sources of both kinds are derived and the main results are illustrated by curves. Various limiting forms of the solutions are also considered.
TL;DR: In this article, the photon statistics of quadratic parametric two-mode processes are derived starting from the results of the first part of this paper and a general theory is presented and particular processes are discussed.
Abstract: The photon statistics of quadratic parametric two-mode processes are derived starting from the results of the first part of this paper. A general theory is presented and particular processes are discussed. Assuming the initial field to be coherent, fluctuations of the pumping field are taken into account. The effects of antibunching and anticorrelation of photons on the photon distribution, its factorial moments, fluctuations in modes and their correlations for the amplification process are demonstrated and their dependence on levels of pumping field fluctuations is shown.
TL;DR: In this article, the theoretical first-order probability density functions of these Stokes parameters were derived assuming a chi-square density for the intensity of orthogonal linear polarized field components, a uniform density for relative phase between the corresponding fields and statistical independence of these stochastic quantities.
Abstract: The polarization properties of scattered monochromatic light fields are described by stochastic Stokes parameters S 0, S 1, S 2 and S 3 which fluctuate in space. We determine the theoretical first-order probability density functions of these Stokes parameters assuming a chi-square density for the intensity of orthogonal linear polarized field components, a uniform density for the relative phase between the corresponding fields and statistical independence of these stochastic quantities. If these assumptions hold, the density of S 0 equals the probability density of a sum of two speckle fields and S 1, S 2 and S 3 are Laplace variates.
TL;DR: In this paper, the integrated univariate and bivariate statistics of the photocount were obtained exactly for detection of single-mode thermal, coherent and free-field cavity radiation, and demonstrated explicitly the relation between the univariate photon counting statistics and the photon statistics.
Abstract: A model for photodetection is presented which permits evolution of the detected field during the detection process. The integrated univariate and bivariate statistics of the photocount are obtained exactly for detection of single-mode thermal, coherent and free-field cavity radiation. The scheme encompasses the results of three hitherto disparate photocounting models, and demonstrates explicitly the relation between the univariate photon counting statistics and the photon statistics of the field. First-order photocount correlation functions are derived and compared with the corresponding cavity photon population correlations. Photocount antibunching is examined and found to be possible in this model.
TL;DR: In this paper, the diffraction of an emplane wave from a wedge with included angle equal to 2 is studied in the case of oblique incidence to the edge, where the boundary conditions are transformed into functional difference equations, which are solved in a closed form.
Abstract: The diffraction of an em-plane wave from a wedge with included angle equal to ~/2 is studied in the case of oblique incidence to the edge. The wedge is characterized by a surface impedance on one face and is a perfect conductor on the other one (soft conditions). We make use of the generalized reflection method, which consists in recognizing, in the amplitude spectrum, pairs of waves which are geometrically the reflection of one another and retaining the two waves of each pair through the reflection matrix appropriate the plane considered. In this way the boundary conditions are transformed into functional difference equations, which are solved in a closed form. The exact solution for the field is given under the form of a Sommerfeld integral of simple trigonometric functions. At large distance from the wedge the non-uniform asymptotic evaluation of the Sommerfeld integral ‘blows up’ on certain critical regions (light/shade boundaries). By resorting to appropriate measures, the blow-up is avoided performi...
TL;DR: A unified treatment of the description of the statistical dynamical properties of two-mode quadratic optical parametric processes with intense coherent or stochastic pumping (parametric amplification, frequency conversion, second subharmonic generation, etc. as special cases are involved) including the lossy mechanism is developed in this article.
Abstract: A unified treatment of the description of the statistical dynamical properties of two-mode quadratic optical parametric processes with intense coherent or stochastic pumping (parametric amplification, frequency conversion, second subharmonic generation, etc. as special cases are involved) including the lossy mechanism is developed. The Heisenberg-Langevin equations are derived and their solutions are used to obtain the quantum characteristic functions and the corresponding quasidistributions. The Fokker-Planck equation approach is adopted as well and the equivalence of both the approaches is explicitly found.
TL;DR: The numerical behavior of the Rayleigh Fourier method for sinusoidal and sawtooth gratings overlying lossless dielectric and metallic substrates is examined in this paper.
Abstract: The numerical behaviour of the Rayleigh-Fourier method is examined for sinusoidal and sawtooth gratings overlying lossless dielectric and metallic substrates The vector of the coefficients of the reflected spectral orders is expressed as a linear transformation of the vector of the corresponding coefficients of a grating with the same profile overlying an infinitely conducting medium (TOG) The pair of fundamental polarization mode solutions of the latter problem are shown to couple into each polarization mode solution of the partially reflecting grating (PRG) problem These facts explain why the Rayleigh theory (RT) generally works less well for the PRG than for the TOG, particularly in the case of metallic substrates with high electrical conductivity Nevertheless, the RT is able to account for all of the features (specular reflection reduction of dielectric gratings, surface plasmon and Wood's anomalies, quasi-Brewster absorption of shallow metallic gratings, etc) of a large variety of experimental r
TL;DR: The optical properties of thin dielectric films prepared by vacuum deposition and r.f. sputtering have been measured using guided waves, ellipsometry and reflectometry to assess the relative merits and disadvantages of the three techniques.
Abstract: The optical properties of thin dielectric films prepared by vacuum deposition and r.f. sputtering have been measured using guided waves, ellipsometry and reflectometry to assess the relative merits and disadvantages of the three techniques. Particular attention has been given to the effect on these measurements of typical film imperfections, for example refractive index inhomogeneity and anisotropy. The guided wave technique is shown to possess the highest precision of measurement, to be relatively insensitive to film inhomogeneity and to provide the most suitable method for studying film birefringence. Ellipsometry has a high sensitivity of measurement that can be usefully applied to thinner films than those required by the other techniques. The method is well suited for studying inhomogeneity, but because of its sensitivity to this film defect, ellipsometric measurements must always be interpreted with care. Reflectometry, although only of limited accuracy in measuring film properties, is widely applica...
TL;DR: In this article, the fundamental parameters of a perfectly conducting grating, at least in the case where only two diffracted orders propagate, were defined and some remarkable properties of these parameters were described.
Abstract: A rigorous phenomenological theory allows us to define the fundamental parameters of a perfectly conducting grating, at least in the case where only two diffracted orders propagate. We describe some remarkable properties of these parameters. In particular, the behaviour of the efficiency curves of sinusoidal gratings when the groove depth increases is explained from a topological point of view. We give also a new interpretation of an anomaly at a Rayleigh wavelength. Finally, we describe a new and surprising phenomenon: a perfect blazing can be obtained for polarized light in a non-zero deviation mount.
TL;DR: In this article, the properties of the radiance associated with a quasihomogeneous planar source and with the optical field it generates are discussed and an estimate is obtained for the distance along a straight line over which the radiances remains substantially unchanged.
Abstract: The properties of the (generalized) radiance associated with a quasihomogeneous planar source and with the optical field it generates are discussed. In the source plane the radiance is found to satisfy the usual postulates of conventional radiometry. An estimate is obtained for the distance along a straight line over which the radiance remains substantially unchanged. If the source is strictly homogeneous or if the field is treated in the paraxial approximation, the radiance is shown to obey the conventional propagation law exactly.
TL;DR: In this paper, the angular coherence of a partially coherent effective source arising from stochastic (e.g., K -correlated) radiation illuminating a deterministic (i.e., lens-like or periodic) phase object is studied.
Abstract: We study the radiant intensity and angular coherence of a novel type of partially coherent effective source arising from stochastic (e.g. K -correlated) radiation illuminating a deterministic (e.g. lens-like or periodic) phase object. We show that parabolic phase profiles lead to unusual far-zone intensity and coherence properties not described by the generalized van Cittert-Zernike theorem. For periodic phase objects we find multi-lobe angular intensity distributions and multi-peak degrees of angular coherence. We discuss the pertinent inverse source problems of retrieving information on the coherence of the illumination when the phase object is known, or vice versa, from the radiant intensity and/or the modulus of the angular coherence.