Forward scattering from the sea surface and the van Cittert-Zernike theorem

The van Cittert-Zernike theorem is used to generate models for the spatial coherence of a sound field that has been forward scattered from the sea surface. The theorem relates the spatial coherence of an observed wave field to the distant source intensity distribution associated with this field. In this case, the sea surface upon ensonification is taken to be the source, and the sea-surface bistatic cross section corrected for transmission loss is taken as a surrogate for the source intensity distribution. Improvements in methodology for generating an estimate of the 2D autocorrelation function for sea surface waveheight variation, necessary to compute the bistatic cross section, are documented in the Appendix. Upon invoking certain approximations, simple expressions for the characteristic length scales of vertical, horizontal, and horizontal-longitudinal coherence, are derived from the theorem. The three coherence length scales identify a coherence volume for the spatial coherence of a sound field arriving via the surface bounce channel. Models for spatial coherence derived from the van Cittert-Zernike theorem without these approximations compare reasonably well with measurements of complex vertical coherence made at 8 kHz and 20 kHz in the East China Sea as part of the 2001 ASIAEX field program. In terms of the ASIAEX field geometries and sea-surface conditions, at frequency of 20 kHz the coherence volume is a vertical layer 0.5 m thick by 3 m in each of the two horizontal dimensions; at 8 kHz these dimensions increase by a factor of 2.5, representing the ratio of the two frequencies.     

Spatial coherence properties of light from optical fibres

The mutual intensity of the optical field in the Fraunhofer diffraction region produced from the end of an optical fibre under illumination of a coherent beam, is theoretically analysed by using an optical fibre-end source model. In this source model, the optical field at the end of the fibre is expressed as an aggregation of independent plane waves with random directions and phases, because the guided modes propagating through the fibre may be regarded as a stochastic process. It is found that the optical field in the diffraction region from the multimode optical fibre is not homogeneous butquasi homogeneous in a statistical sense. The spatial coherence properties in the field are discussed in connection with theV number (the normalized frequency) of the fibre and in comparison with those in the field produced from an incoherent source obeying the van Cittert-Zernike theorem.     

A radiometric generalization of the Van Cittert-Zernike theorem for fields generated by sources of arbitrary state of coherence

New formulae are derived for the cross-spectral density function and the complex degree of coherence of light in the far zone of a field generated by a planar source of any state of coherence. The formulae are analogous to those encountered in the far-zone formulation of the Van Cittert-Zernike theorem that applies to light from a spatially incoherent source; the only essential difference is that the average light intensity across the source is replaced by the generalized radiance function of the source, with a symmetrized directional variable. In the limiting case of a spatially incoherent source our formulae reduce to expressions that are in agreement with the Van Cittert-Zernike theorem. In the other limiting case, that of spatially fully coherent source, they reduce to results that are to be expected on the basis of the Huygens-Fresnel principle.     

Fiber coupling efficiency for random light and its applications to lidar

Employing the van Cittert-Zernike theorem of classical coherence theory, we derive a general expression for the efficiency with which quasi-monochromatic random light can be coupled to an optical fiber by means of a lens. For the important case of a source with Gaussian intensity distribution, we obtain and discuss the dependence of the coupling efficiency to single-mode fibers on the lens-to-fiber coupling geometry as well as on the ratio of lens size to speckle size. A specialization to the emerging fields of both incoherent and coherent fiber-based lidar applications shows that a maximum coupling efficiency of ~42% can be obtained for a monostatic system.     

Decrease in spatial coherence of light propagating in free space

It is shown that a highly spatially incoherent light distribution may be generated from a highly coherent one on propagation in free space. This result essentially demonstrates that there exists an inverse of a classic result of optical coherence theory, namely, the van Cittert-Zernike theorem. The analysis also indicates that the technique of phase conjugation may be used to reverse changes in the coherence properties of light, at least those which are generated on propagation in free space.     

Extension of the van Cittert-Zernike theorem for completely polarized incoherent electromagnetic beam propagating through non-Kolmogorov turbulence

Based on the 2 × 2 cross-spectral density matrix, the van Cittert-Zernike extended theorem is developed for the completely polarized incoherent beams propagation through the paraxial non-Kolmogorov turbulence. On the consequence of the extended theorem and the definition of general spectral degree of cross-polarization of a beam, we found that the spectral degree of cross-polarization of the resultant field is independent of the refractive index structure constant of atmospheric turbulence. We investigated the influences of the propagation distance and the distance of two detection points on the degree of coherence and the spectral degree of cross-polarization.     

Spatial coherence of bending magnet radiation and application limit of the van Cittert-Zernike theorem

In this paper we discuss how the first-order spatial coherence of bending magnet radiation is determined. We present an analytical representation of the coherence and compare it with the numerical calculations based on the first principles. It is shown that if the electron-beam size is so large that some conditions are satisfied, the van Cittert-Zernike theorem can be used without any modification in the vertical and horizontal directions. The formalism presented will be useful in judging whether or not the electron-beam size in the storage ring can be estimated directly from the van Cittert-Zernike theorem using the synchrotron radiation interferometer.     

Space-variant polarization manipulation for far-field polarimetry by use of subwavelength dielectric gratings

A method for polarimetric measurement that uses a discrete space-variant subwavelength dielectric grating is presented. One retrieves the polarization state by measuring the far-field intensity of a beam emerging from the grating followed by a polarizer. The analysis for a partially polarized, quasi-monochromatic beam is performed by use of the beam coherence polarization matrix along with an extended van Cittert-Zernike theorem. We experimentally demonstrate polarization measurements of both fully and partially polarized light.     

Is the Van Cittert-Zernike Theorem Applicable to Spatially Incoherent Broadband Spectral Source?

This paper deals with the propagation law of mutual intensity and cross-spectral density of the light emitted from an extended broadband spectral source that is spatially incoherent. The mutual intensity of light does not obey the same mathematical formalism as the Van Cittert-Zernike theorem applicable to quasi-monochromatic light, although the cross-spectral density of light does in the propagation zone of the Fresnel diffraction region.     

Measurement of the Mutual Coherence Function of an Incoherent Infrared Field with a Gold Nano-wire Dipole Antenna Array

The first direct measurement of the mutual coherence function of a spatially incoherent infrared beam was performed at 10.6 μm using a pair of infrared dipole nano-wire antennas that were connected to a common bolometer in the center of the pair by short lengths of coplanar strip transmission line. A spatially incoherent source was constructed by dithering a BaF2 diffuser near the focus of a CO2 laser beam. The distance from the diffuser to the nano-wire antenna pair was held constant while the distance from the focus of the laser beam to the diffuser was varied to control the effective diameter of the source. The measured bolometer signal was proportional to the magnitude of the mutual coherence function at the plane of the antennas. The experimental results were found to match the predicted performance closely. If this technology can be extended to large arrays, a form of synthetic aperture optical imaging based on the Van Cittert-Zernike theorem is possible, similar to that performed at microwave frequencies now by astronomers. This has the potential to greatly increase the angular resolution attainable with optical instruments.     

大功率单色LED的空间相干特性

基于van Cittert-Zernike定理,从理论上计算出大功率单色发光二极管(LED)辐出光,在空间中传输后的空间相干性分布。计算结果表明,自发辐射的LED光源其辐射光在空间中传输后,由非相干光变为部分相干光,且其空间相干性与LED芯片的结构有关。实验上采用双缝干涉对LED辐射光的空间相干性进行测量,由干涉条纹的可见度与两点间的相干度之间的关系得出,非相干LED光源的辐射光在传输后为部分相干光。而采用间隔可调的双缝干涉测量两点间的相干度后发现,LED的芯片发光区域决定了其辐射光在传输中的空间相干性分布。理论计算的空间相干性分布与实验测量结果基本吻合。     

The van Cittert-Zernike theorem in atom optics

The van Cittert-Zernike theorem of classical optics is generalized to the situation of matter-wave optics. Applying a Green's function method the first- and second-order correlation functions of the matter field emitted from an incoherent source are calculated, and the results are compared to the case of electromagnetic waves.     

Use of the van Cittert-Zernike theorem for partially polarized sources

We introduce an extension of the van Cittert-Zernike theorem to spatially incoherent sources with partial polarization. We show through a simple example that fields generated by such sources can possess correlation matrices with interesting properties. In particular, we show that by suitable modulation of the polarization state across the incoherent source, the correlation between the orthogonal components of the field as well as the degree of polarization may drastically change on propagation.     

Effects of Spatial Coherence and Dispersive Diffraction on a Change in Optical Spectrum

This paper describes a change in optical spectrum on propagation in free space for a particular class of spatially partially coherent fields emanating from a polychromatic secondary source. A rectangular opening aperture in an opaque screen, illuminated with an extended incoherent polychromatic primary source, works as the secondary source. The spectral change is explored in detail theoretically and experimentally in association with spatial coherence in the secondary source as well as dispersive diffraction by the secondary source. The peak shift of the spectrum is associated with the coherence area for characterizing the secondary source. The peak shift becomes maximum if the secondary source is spatially coherent, but no shift occurs if the secondary source is spatially incoherent.     

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.     

编码栅在光信息处理中的应用

本文从编码栅对光源、物函数、谱函数的调制原理出发,从三个方面分析了编码栅在光信息处理中的作用及应用实例。     

Generation of highly directional beams from a globally incoherent source

We have carried out a series of observations of the far field intensity distribution produced by a class of partially coherent planar sources. Our results confirm that, under the Collett-Wolf quasi-homogeneity conditions, highly directional beams can be produced even from a source which is globally incoherent. The far-zone pattern is shown to be largely independent of the intensity profile in the source plane and that the beam radius varies as predicted by Foley and Zubairy in the paraxial approximation. We show experimentally how the coherence length in the source plane can be measured directly from the far zone intensity distribution.     

Partially coherent Fresnel diffraction by a slit aperture. IV. Effect of the phase term in the coherence function

A formula was derived in paper 1 of the this series for investigating the Fresnel diffraction field of a slit aperture when the mutual coherence function of the illumination contains a quadratic phase term. That formula is applied to study the intensity distribution in the Fresnel diffraction field of a slit aperture illuminated by a quasi-monochromatic incoherent slit source. The phase term has a big effect on the features of Fresnel diffraction.     

Two-dimensional temporal coherence coding for super resolved imaging

In this paper, we present an approach that can be used for transmission of 2D spatial information through space-limited systems capable of transmitting even only a single spatial pixel. The input 2D object is illuminated with temporally incoherent illumination. The axial coherence length is very short and it equals only a few microns. Attached to the input object spatial random phase mask generates different axial shift for every pixel of the input. The temporal delays of the encoding (axial shifts) of every pixel are longer than the coherence length of the illuminating source. Therefore no temporal correlation exists between the various pixels of the input. A lens combines all spatial pixels into one point at its focal plane. Although the various spatial pixels were mixed together, since the random mask provided axial delay which was larger than the coherence length of the light source, the orthogonality between the spatial content of every pixel is preserved. The decoding system includes a lens that is positioned at the output of the resolution reduction system and it converts the output light into a plane wave containing all the spatial information of the original image mixed together in all of its pixels. By interfering this plane wave with the same plane wave after passing through the same random spatial coding mask, the spatial information of every pixel of the input object is recovered.     

The Van Cittert-Zernike theorem for optical fibres

The Van Cittert-Zernike theorem determines the degree of coherence γ of light from a source radiating in a uniform medium in terms of the angular size α of the source. For the fields within an optical fibre far from the source, γ is found by replacing α by the critical angle for total internal reflection.