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ABSTRACT: This paper reports experimental studies on speckles produced by the rough silver films. The speckles on the rough glass/silver surfaces are measured with a microscopic imaging system. The structures of speckle patterns have the characteristics of fractals and multi-scaled sizes. We find that with the increase of the silver film thickness, the contrast of the speckles increases, and the intensity probability density functions gradually transit to exponential decay. We calculate the global and the local correlation functions of the speckle patterns, and find that both the fractal exponent and correlation length of the small-sized speckles decrease with the thickness of the silver films. We use the mechanisms of rough dielectric interface scattering and random surface plasmon waves to give the preliminary explanations for the evolutions of the speckles.
Optics Express 04/2013; 21(7):8831-42. · 3.59 Impact Factor
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ABSTRACT: The relations between the specular reflection component of the intensity scattered by random surfaces and the height distributions
of the surfaces are analyzed theoretically. In the extraction of the height distribution, both the phase and the amplitude
of the specular wave are required. The measured specular intensity data versus the perpendicular component of the wave vector
are used for the retrieval of the phase distribution of the specular wave, in which the Gerchberg-Saxton iterative algorithm
is employed, and the characterization of the height distribution of random surfaces is accomplished. In the experiment, two
samples with Gaussian and quasi-two level height distributions, respectively, are practically measured and the results of
the height probability density function obtained by light scattering method are in good accordance with those by atomic force
microscopy. The method of this paper is of important significance for the characterizations and studies of random surfaces.
Science in China Series G Physics Mechanics and Astronomy 04/2012; 46(5):518-527. · 1.41 Impact Factor
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ABSTRACT: From Helmholtz equation of the harmonic electromagnetic waves, the integral equations of the light field at the medium boundaries
are obtained by use of the Green's theorem and are discretized into linear equation set with the values of the light field
and its derivative as the unknowns. On solving the linear equation set, we realize the rigorous computations of the light
fields at the boundaries. Then the intensities of the light waves scattered by the random self-affine fractal surfaces in
the optical near-field are calculated, and the propagation characteristics, the evolutions of the contrast and the intensity
probability density function of the near-field speckles are studied in detail. The near-field speckles are much different
from the conventional speckles in the diffraction regions and in the imaging systems. There are obvious local fluctuations
in the intensity distributions of the near-field speckles and such fluctuations disappear after propagating a distance of
one wavelength from the medium surfaces. For the random surfaces with smaller lateral correlation lengths, the speckle contrasts
approach the saturation values and the speckle fields approach Gaussian distribution within the near-field, while for the
random surfaces with larger lateral correlation lengths, such evolutions become comparatively slow.
Science in China Series G Physics Mechanics and Astronomy 04/2012; 47(3):365-380. · 1.41 Impact Factor
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ABSTRACT: Diffractions by the one-dimensional high-density grating in the near field with TM and TE polarization illuminations are studied, and the diffraction intensity distributions are calculated with the finite-difference time-domain technique. The calculation results show that the diffractions of the high-density grating with different polarization illuminations are different. The quasi-Talbot image of the grating depends on the polarization of the incident wave, and the existence condition of the quasi-Talbot image of the grating in the near field also changes with the polarization of the incident wave. We present explanations based on the vector distribution of the energy flow density. These studies on the polarization dependence of the quasi-Talbot imaging of the high-density grating are helpful for the application of the grating to near-field photolithography.
Journal of the Optical Society of America A 03/2010; 27(3):366-71. · 1.56 Impact Factor
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ABSTRACT: Theoretical and experimental studies of the diffraction of a two-dimensional reflection grating are performed in this paper. Based on the theory of optical scattering, the light field in the Fraunhofer diffraction region is deduced, and the general expression of the diffraction field is given in the form of the wave vectors of the diffracted wave and the incident wave. Then the coordinate of the diffraction order is obtained. The calculation results show that the diffraction distortion of the grating appears when the grating is illuminated by the oblique incident light wave and the distortion is restricted on the diffraction of the grids varying along the direction perpendicular to the plane of incidence. The orbit equation satisfied by the distortion diffraction orders is presented. The experimental results verify adequately this diffraction distortion rule of the grating, and they agree very well with the theoretical results.
Applied Optics 09/2009; 48(23):4519-25. · 1.41 Impact Factor
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ABSTRACT: On the basis of the finite-difference time-domain technique, the diffraction of the high-density grating in the near field is developed, and the gray-scale pattern of the diffraction intensity distribution of a one-dimensional grating is presented. A detailed analysis shows that the near-field diffraction of the grating is the result of the diffraction of a single slit, the interference of two evanescent waves from neighboring slits, and the interference of the homogeneous waves from the slits. Through many numerical calculations, the condition for obtaining the quasi-Talbot imaging of the grating in the near field is explored, i.e., the period of the grating d is larger than the incident wavelength lambda but smaller than 4lambda. The influence of the opening ratio of the grating on the quasi-Talbot imaging of the grating in the near field is also discussed. This study of the near-field diffraction of the high-density grating may be helpful for understanding the diffraction characteristics of subwavelength structures, and the quasi-Talbot imaging of the high-density grating will contribute to the application of the grating in near-field photolithography.
Journal of the Optical Society of America A 01/2009; 25(12):2945-51. · 1.56 Impact Factor
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ABSTRACT: We analyze theoretically the diffraction of phase gratings in the deep Fresnel field on the basis of the theory of scalar diffraction and Green's theorem and present the general formula for the diffraction intensity of a one-dimensional sinusoidal phase grating. The numerical calculations show that in the deep Fresnel region the diffraction distribution can be described by designating three characteristic regions that are influenced by the parameters of the grating. The microlensing effect of the interface of the phase grating provides the corresponding explanation. Moreover, according to the viewpoint that the diffraction intensity distribution is the result of the interference of the diffraction orders of the grating, we find that the diffraction patterns, depending on the carved depth of the phase grating, are determined by the contributing diffraction orders, their relative power, and the quasi-Talbot effect of the phase grating, which results from the second meeting of the diffraction orders carrying most of the power of the total field, as in the case of the amplitude grating.
Journal of the Optical Society of America A 12/2007; 24(11):3636-43. · 1.56 Impact Factor
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ABSTRACT: Based on the theory of scalar diffraction, the diffraction of gratings in the deep Fresnel diffraction region is developed, and the general formula of the diffraction intensity of the one-dimensional grating is presented by using the Hankel function. Through numerical calculations, some interesting diffraction phenomena are found. In the deep Fresnel diffraction region, the dominant effects, with increasing propagation distance from the grating, are, in order, the geometrical effect, the quasi-geometrical effect, and the interference and diffraction effects. Furthermore, the diffraction intensities vary periodically in the diffraction effect region with increasing propagation distance. Quasi-Talbot imaging of the grating exists in the interference and diffraction regions, and the intensity distributions most similar to the structure of the grating are not at the exact Talbot distances. These phenomena in the deep Fresnel diffraction region are distinct from those in the Fresnel diffraction region. The formation origin of quasi-Talbot imaging of the grating is also discussed, and the numerical calculations powerfully verify the theoretical results.
Journal of the Optical Society of America A 07/2007; 24(6):1656-65. · 1.56 Impact Factor
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ABSTRACT: A Jamin double-shearing interferometer with three changeable schemes is proposed for the measurement of diffraction-limited laser wave front. A concept of detectable wave-front height is thus defined, and on this basis the limits of detectable wave-front height from the suggested schemes of interferometer are analyzed. The design is detailed, the simulation for wave aberrations is given, and the experiment is demonstrated. One of the major features of this interferometer is that it is capable of visually testing a diffraction-limited wave front immediately by the fringes with the matched accuracy and minimum detectable wave-front height on the order of 0.1lambda.
Applied Optics 04/2004; 43(9):1819-24. · 1.41 Impact Factor
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ABSTRACT: By use of a numerical calculation based on Green's integral equation, we study the near-field speckles produced by the random self-affine fractal surfaces of a dielectric medium. The speckle intensities evolve considerably in the near-field region, and the local fluctuations in them disappear before they have traversed the distance of a wavelength. The transition of the speckle contrast either on the surface or in the near field and in the neighborhood non-near-field regions depends on lateral correlation length xi and roughness exponent alpha of the random surfaces.
Optics Letters 10/2003; 28(17):1531-3. · 3.40 Impact Factor
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ABSTRACT: A uniform formulation for the self-imaging of gratings with any kind of partially coherent illumination is developed in terms of the cross mutual spectral density of the partial coherence theory. The formulation includes the time diffractive intensity distribution and the averaged diffractive intensity distribution at self-imaging distances and can be applied to both continuous and temporal illuminations with any kind of spectra. It is found that the averaged intensity distribution is related only to the intensity spectrum of illumination. The continuous polychromatic illumination and the ultrashort laser pulses with or without frequency chirp are then studied by a numerical stimulation. It is shown that the ultrashort laser pulse and the continuous polychromatic illuminations have similar averaged self-image distributions. Thus the Talbot effect may help in the study of the temporal and spectral characteristics of ultrashort laser pulses. An experiment with an LED is given, as well.
Journal of the Optical Society of America A 10/2003; 20(9):1747-54. · 1.56 Impact Factor
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ABSTRACT: We present a method for the extraction of the height–height correlation function of random surfaces from the average intensity of image speckles. The setup of a Fourier transforming and imaging system with a variable aperture is used for both the theoretical analysis and experimental performances. Based on the analytical expression of the image intensity, an algorithm is developed to formulate numerically the intensity data versus the aperture radius into the pair of Bessel–Fourier transform and the inversion, from which the height–height correlation function is reconstructed. Three samples of Gaussian correlation are used for the experimental demonstration. The extracted height–height correlation function and the random surface parameters obtained thereby conform with those obtained by atomic force microscopy. © 2002 American Institute of Physics.
Applied Physics Letters 12/2002; 81(24):4544-4546. · 3.84 Impact Factor
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ABSTRACT: We developed a method for extracting the height probability density of random surfaces by light scattering. Theoretical results show that height probability function is the Fourier transform of the central δ-peak in the light waves of angle-resolved light scattering. Experimentally, we measure the δ-peak intensities at a different angle of incidence in a simple setup. We then reconstruct the phase distributions of the δ-peak versus the perpendicular component of the wave vector from the intensities using the Gerchberg–Saxton inversion algorithm, and then extract the height probability density of the samples. Two different types of samples are measured to verify the validity of the method, and the results are compared with those obtained by atomic force microscopy. © 2002 American Institute of Physics.
Applied Physics Letters 09/2002; 81(11):2124-2126. · 3.84 Impact Factor
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ABSTRACT: Coherent dynamic speckles produced by laser illumination is a subject that is widely studied and has found applications in many fields. This paper extends the study theoretically and experimentally to dynamic speckles with partially coherent illumination, namely, dynamic partially coherent speckles (DPCSs). Starting from the partially coherent theory of light, we carry out a theoretical analysis and obtain the generic form of the spatiotemporal cross correlation function of the intensity fluctuation of DPCSs in the Fresnel and Fraunhofer diffraction regions. Then we discuss in detail various properties of DPCSs such as boiling and displacement. The experimental observation of DPCSs and their boiling is accomplished on the Fraunhofer plane by matching the size of the coherence area with that of the scattering aperture. A system using photon counting is established for the measurement of the intensity and the correlation function, and the measured results conform well with the theoetical predictions.
Journal of Optics A Pure and Applied Optics 09/2002; 4(5):580. · 1.92 Impact Factor
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ABSTRACT: Based on the fact that the half-width of the Fourier transform is inversely proportional to that of a symmetrical primary decay function, the half-width of the intensity profiles of light scattered from self-affine fractal random surfaces in the whole k( perpendicular ) region is studied. The primary function, whose Fourier transform is the intensity profile, is approximated with a simple mathematical decay function by equating their half-widths and maximums. The expression obtained for the half-width of the scattered intensity profiles reduces to the present results in the two extreme cases with the scattering roughness factors being either very small or very large. For a complete verification, we perform a simulation of the light scattering, in which self-affine fractal random surfaces are generated with an algorithm that is an analogy to the formation of laser speckles. The simulated and theoretical results conform well.
Physical Review E 07/2002; 65(6 Pt 1):061104. · 2.26 Impact Factor
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ABSTRACT: We study the Fresnel diffraction of Gaussian beam truncated by one circular aperture, and give the general analytic expression of the Fresnel diffraction of truncated Gaussian beam denoted by Bessel functions. Then the characteristic of the axial diffraction fluctuation and the influence of the caliber of the circular aperture and the wave waist of Gaussian beam on the diffraction distributions are discussed, respectively. Through the numerical calculations, the characteristics of the transverse diffraction are presented and the relationship of the fluctuation of the transverse diffraction profile and the position of the axial point is shown. The physical origin of the fluctuation of Fresnel diffraction intensities of truncated Gaussian beam is expressed in terms of Fresnel half-zone theory. These phenomena and the conclusions are important for the measurement of the parameters of the beam and its applications.
Optik - International Journal for Light and Electron Optics.
