Visualization of light propagation

Abramson has demonstrated that by using the finite coherence properties of light, holograms can be constructed that allow one to visualize the path that a simulated light pulse takes through an optical system. We have demonstrated that using an alternate hologram construction and readout geometry, light with a very long coherence length can also be used to visualize light propagation. Experimental results showing well resolved time-sequence photographs of reflection, refraction, and diffraction in an optical system are given.     

对用空间扩展宽谱光源再现的彩虹全息像的分析

用空间扩展宽谱光源再现的彩虹全息像时,整个光源只在一定的光谱的和空间的“有效宽度”内起作用,本文在此概念的基础上,研究了光源的光谱扩展和空间扩展在其单独作用和联合作用时对全息像的影响。发现当两者联合作用时,对像质的总影响几乎与它们单独作用时一样。给出了用宽谱空间扩展光源所再现的彩虹全息像的分辨率,从而提出了一个实用的狭缝宽度。     

Construction of spatial-coherence spectral filters using a Fourier-achromat system

Theoretical investigations made not long ago regarding the construction of spatial-coherence spectral filters (SCSFs) are rendered into experiments by designing and fabricating a Fourier-achromat experimental setup analyzed in the theoretical studies. It is shown that the phenomenon of spectral shift due to spatial coherence also known as the Wolf effect can be exploited to make special types of low-pass and band-pass spectral filters with special spectral characteristics that are not shown by the conventional filters. A Fourier-achromat is employed to construct the SCSFs. The experimental results within the experimental limitations and measurement uncertainty agree well with the theory. These filters might find applications in (i) astronomy (in the search of particular spectral lines) (ii) developing spectrum-selective optical interconnects or (iii) in cryptography.     

Interference approach applied to dual-grating dielectric resonant grating reflection filters

The resonant mechanisms associated with dual-grating dielectric resonant grating reflection filters are described by use of an interference approach. These structures consist of two modulated regions of equal period separated by a higher-index film region. We show that the spectral linewidth is dependent on the separation between the modulated regions and can range from theoretically zero to approximately four times what would be obtained by use of a single-grating geometry.     

Beam radiated from quasi-homogeneous uniformly polarized electromagnetic source scattering on quasi-homogeneous media

We study the coherence properties of the field generated by beam radiated from quasi-homogeneous (QH) electromagnetic source scattering on QH media. Formulas for the spectral density and spectral degree of coherence of the three dimensional scattered field are derived. The results show under assumption that the diagonal correlation coefficients of the source are proportional to each other, the far field of the scattered light satisfy two reciprocity relations analogous to that in the scalar case, that, the spectral density is proportional to the convolution of the spectral density of the source and the spatial Fourier transform of the correlation coefficient of the scattering potential; the spectral degree of coherence is proportional to the convolution of the diagonal correlation coefficients and the strength of the scattering potential.     

Apparent transfer function for partially coherent optical information processing

In this paper, the general formulations of the apparent transfer function for the partially coherent optical processor will be derived. Although these formulas show that the apparent transfer function is dependent upon the degree of spatial and temporal coherence, there is actually more variability in the spatial coherence. We note that the obtained formulas may also be used as a criterion in the selection of source size and spectral bandwidth of an incoherent light source. Thus a specific optical information processing operation can be carried out with an incoherent source.     

Study on the spatial coherence of vortex Gaussian beams passed atmospheric turbulence

In this paper, the spectral degree of coherence formula was derived by using the generalized Huygens–Fresnel principle and the method of Rytov phase structure function quadratic approximation. The spatial coherence of vortex Gaussian beams passed atmospheric turbulence was studied. It showed that the spatial coherence was mainly affected by the coherence of light source, the number of topological charges and the transmission distance. The distance of transmission was farther, the spatial coherence of beam was better. The number of topological charges were more, the spatial coherence of beam was better. In a certain transmission distance, the coherence of light source was better, the spatial coherence of beam was worse. In addition, there were coherent vortexes which spectral degree of coherence was zero after the partially coherent vortex beams getting through atmospheric turbulence transmission.     

Spatial correlation properties of apertured partially coherent beams propagating through atmospheric turbulence

The spatial correlation properties of apertured partially coherent beams propagating through atmospheric turbulence are studied in detail. By using the quadratic approximation of the Rytov’s phase structure function and the finite complex Gaussian expansion of the aperture function, the closed-form expression for the spectral degree of coherence of apertured partially coherent beams in turbulence is derived. It is shown that the larger the aperture width h is, and the smaller the spatial correlation length σ₀ of the source is, the less the spatial correlation is affected by turbulence. Specially, the influence of turbulence on the spatial correlation for unapertured partially coherent beams is less than that for apertured ones. The spectral degree of coherence is shown to possess phase singularities for apertured partially coherent beams, but the phase singularities behavior disappears when the turbulence is strong enough, which is very different from the behavior of unapertured partially coherent beams. In addition, a comparison between the width of the spectral degree of coherence and that of the spectral intensity of apertured partially coherent beams in turbulence is also given, and some interesting results are obtained. The results are interpreted physically. PACS  42.68.Bz; 42.79.Ag; 42.25.Fx     

Computer generated holograms using personal computers

Holography or the method of wave-front reconstruction to produce an image was introduced by D. Gabor in 1948. Normally a laser is necessary to produce holograms in the laboratory. This paper introduces the usage of the high resolution display of the IBM-PC and a graphics printer to generate holograms. The advantages of using this method are that holograms of real or fictitious objects can be made, since all objects can be represented by a collection of points and one does not need an elaborate set up to make the holograms. This method is also useful for making Fourier transform holograms, image plane holograms, spatial filters, optical elements, etc.^1,2     

Modeling of the Spectral Characteristics of Reflection Holograms in Photopolymeric Materials

The dependences of the spectral characteristics of reflection holograms on various parameters are investigated for the model of multilayered thin films and in the context of the Kotel'nikov theory of coupled waves. The practically important cases of the influence of the recording layer thickness shrinkage, the Bragg angle mismatch, and the recording of multicolored reflection holograms are considered. A comparative analysis of the experimental data and the results of computer modeling is made.     

Experimental study of coherence vortices: local properties of phase singularities in a spatial coherence function

By controlling the irradiance of an extended quasimonochromatic, spatially incoherent source, an optical field is generated that exhibits spatial coherence with phase singularities, called coherence vortices. A simple optical geometry for direct visualization of coherence vortices is proposed, and the local properties and the spatial evolution of coherence vortex are experimentally investigated. To our knowledge, this is the first direct and quantitative experimental measurement of a generic coherence vortex.     

Electric field selectivity and multiplexing of volume holograms in LiNbO3

Theoretical and experimental investigations of electric field multiplexing and selectivity of reflection volume holograms in LiNbO₃ are reported. Recording of at least five holograms is demonstrated. Equivalent spectral selectivity (5Ƽ.5 pm for the case of three electrically tunable holograms and (5ǁ pm for the case of five electrically tunable holograms are estimated.     

Source encoding for partially coherent optical processing

A relation between spatial coherence function and source encoding intensity transmittance function is presented. Since the spatial coherence is depending upon the information processing operation, a strictly broad spatial coherence function may not be required for the processing. The advantage of the source encoding is to relax the constraints of strict coherence requirement, so that the processing operation can be carried out with an extended incoherent source. Emphasis of the source encodings and experimental demonstrations are given. The constraint of temperal coherence requirement is also discussed.     

Spatial coherence resonance induced by coloured noise and parameter diversity in a neuronal network

Spatial coherence resonance in a two-dimensional neuronal network induced by additive Gaussian coloured noise and parameter diversity is studied. We focus on the ability of additive Gaussian coloured noise and parameter diversity to extract a particular spatial frequency (wave number) of excitatory waves in the excitable medium of this network. We show that there exists an intermediate noise level of the coloured noise and a particular value of diversity, where a characteristic spatial frequency of the system comes forth. Hereby, it is verified that spatial coherence resonance occurs in the studied model. Furthermore, we show that the optimal noise intensity for spatial coherence resonance decays exponentially with respect to the noise correlation time. Some explanations of the observed nonlinear phenomena are also presented.     

Coherence and polarization properties of a three-dimensional, primary, quasi-homogeneous, and isotropic source and its far field

We study the spatial coherence properties of a three-dimensional, primary, quasi-homogeneous, and isotropic source and the far field that it generates. We assess the spectrum, degree of polarization, electromagnetic degree of coherence, and effective degree of coherence of the source and of the far field. We also demonstrate the formalism for a spherical Gaussian Schell-model current source. The polarization properties of light are fully accounted for in the analysis, and it is found that certain results pertaining to scalar coherence theory are reproduced also within the electromagnetic treatment.     

Crosstalk caused by incoherence of the readout light in wavelength-division multiplexing of reflection holograms

The effect of incoherence of the readout light on the level of crosstalk in wavelength-division multiplexing of reflection holograms is studied. The level of crosstalk is determined theoretically as a function of the spectral width of the readout light, the total number of multiplexed holograms, and the frequency difference between neighboring holograms. Good agreement is obtained between the theory and experiment for the case of two sinusoidal gratings. Zh. Tekh. Fiz. 69, 110–114 (September 1999)     

杨氏实验远场的光谱位移和光谱开关

从部分相干光的传输定律出发，研究了杨氏双缝实验远场的光谱变化。指出杨氏实验中光谱开关在远场也会出现.缝的衍射和光的空间相干性是产生光谱开关的物理原因，增大缝参量ε和源的空间相关度△光谱开关效应越显著。作了详细的数值计算以说明远场光谱位移和光谱开关的特性，并与已有的工作进行了比较。     

Resolution in X-ray Holography

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High-fidelity image reproduction using angular distribution of reflected spectral intensity

A method to reproduce images of an object under various observation conditions is presented. In this method, a series of multispectral images is captured by rotating the object under a point light source of which spectral power distribution and the position are known. The captured images are decomposed into diffuse and specular reflection component images based on the dichromatic reflection and the Lambertian models. Next, the incident angle of the illumination light and the angle between viewing direction and regular reflection are calculated based on observation geometry. Finally, the image under observation geometry is synthesized using the light-ray rearrangement technique. The experiments are carried out using two-dimensional objects, leather and fabric. Most of the synthesized images are shown to be the same as the images actually captured under the assumed illumination geometry, even if the object has complex reflection like fabric for which it is difficult to apply the reflection model used in computer graphics.     

衍射扭曲高斯-谢尔模型光束在远场的光谱移动和光谱开关

从部分相干光的传输理论出发,研究了被光阑衍射扭曲高斯-谢尔模型光束远场的光谱变化规律。结果表明,扭曲高斯-谢尔模型光束在远场也会出现光谱移动和光谱开关效应。与衍射高斯-谢尔模型光束情况相比,光谱移动和光谱开关效应不仅与光束空间相关性、截断参量和源光谱谱宽有关,光束的扭曲因子也会对衍射扭曲高斯-谢尔模型光束远场的光谱移动和光谱开关效应产生影响。通过数值计算结果详细讨论了光束扭曲因子影响衍射扭曲高斯-谢尔模型远场光谱的规律。