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.     

Adaptive Optics as a Spatial Coherence Modifier

The possibility of adaptive optics as a spatial coherence modifier is discussed. The initial field to be corrected is produced in such a way that a quasi-monochromatic plane wave of light is incident on a moving diffuser plate, so that it is spatially partially coherent. It is shown that adaptive optics serves to enhance the spatial coherence of the resultant field and that the magnitude of the enhancement depends on the spatial coherence of the initial field to be corrected. The results are illustrated by numerical examples based on an idealized low-order adaptive optics system.     

Spatial coherence and information entropy in optical vortex fields

We show how a vortex structure manifests itself in the one-dimensional projection of a vortex field. We calculate the extent of spatial coherence and entropy of such projections. We quantify the spatial coherence and discuss the properties of the Wigner functions for the projected field.     

Influence of the spatial coherence of X-ray radiation on mirror reflection from multilayered mirrors

The influence of the degrees of spatial coherence of random modulated X-ray radiation on the intensity of the diffractive reflection of such radiation from a multilayered mirror, and on the spatial coherence function of the reflected field (depending on the statistical characteristics of the incident radiation and the parameters of the multilayered periodic structure), is considered.     

What type of coherence of the optical field is observed in the Michelson interferometer

The types and corresponding coherence functions of the optical field are considered depending on the frequency and angular spectra of the field. The main concepts of the theory of coherence effects in the interference experiment with the amplitude splitting of the initial field are discussed. It is shown that, in strict correspondence with the theory of coherence of the random wave fields, the Michelson interferometer reveals manifestations of the transverse and longitudinal spatial (rather than temporal, as it is commonly adopted) coherence of the optical field; the purely temporal coherence of the optical field is revealed only under special conditions of the interference experiment. Beyond these conditions, either spatial or spatiotemporal coherence is revealed.     

孪生光束干涉法测量光源的空间相干性

定量测定光源空间相干性在部分相干光成像, 非相干全息术及光信息处理领域具有重要的研究价值. 本文基于三角全息干涉光路提出了一种测量光源空间相干性的新方法. 利用三角干涉全息光路系统中分束镜产生的孪生光束进行干涉获得干涉图, 通过调整光源中心位置在写入平面内偏离光轴的量, 改变两孪生光束空间分离量的大小, 采集对应的一系列干涉图, 计算干涉图样的对比度, 从而对光源照明空间的波前上一系列不同距离的点对之间的空间复相干度进行测量. 实验系统光路配置较为简单且不需要使用特殊加工的光学元件. 针对一个准单色的扩展光源设计并进行实验, 结果表明利用文中提出的方法可以准确的测量光源的空间相干性, 实验结果相对于理论计算值的误差仅为3.8%. 关键词： 相干性 全息干涉 干涉仪 光学应用     

Three-dimensional generalization of the Van Cittert-Zernike theorem to wave and particle scattering

Coherence properties of primary partially coherent radiations (light, X-rays and particles) elastically scattered from a 3D object consisting of a collection of electrons and nuclei are analyzed in the Fresnel diffraction region and in the far field. The behaviour of the cross-spectral density of the scattered radiation transverse and along to the local direction of propagation is shown to be described by respectively the 3D Fourier and Fresnel transform of the generalized radiance function of a scattering secondary source associated with the object. A relativistic correct expression is derived for the mutual coherence function of radiation which takes account of the dispersive propagation of particle beams in vacuum. An effect of the spatial coherence of radiation on the temporal one is found; in the Fresnel diffraction region, in distinction to the field, both the longitudinal spatial coherence and the spectral width of radiation affect the longitudinal coherence. A solution of the 3D inverse scattering problem for partially coherent radiation is presented. It is shown that squared modulus of the scattering potential and its 2D projections can be reconstructed from measurements of the modulus and phase of the degree of transverse spatial coherence of the scattered radiation. The results provide a theoretical basis for new methods of image formation and structure analysis in X-ray, electron, ion, and neutron optics.     

Modification of Spatial Coherence by Means of Low-Order Zernike-Mode Adaptive Optics

Spatial coherence of the field modified by low-order adaptive optics is analyzed to establish a theoretical basis for the recent idea of using adaptive optics as a spatial coherence modifier. In this context low-order adaptive optics has the ability to correct some of the low-order aberrations specified by Zernike polynomials. The initial field to be modified is assumed to be a spatially partially coherent one resulting from phase disturbance. It is demonstrated, as in the previous study, that low-order adaptive optics serves to enhance the spatial coherence of the resultant field and that the effect of the enhancement becomes stronger as the spatial coherence of the initially partially coherent field increases. Potential applications of low-order adaptive optics as a spatial coherence modifier are briefly discussed.     

Pattern formation in a passive incoherent ring resonator system based on nonlinear material with the self-focusing non-instantaneous Kerr response

We have analyzed the pattern formation in a nonlinear medium with self-focusing non-instantaneous Kerr response by employing the passive incoherent ring resonator system. In such a system, coherence time of the light is much shorter than the time of one round trip in the resonator. This delayed response of the nonlinearity can amplify the noise of certain spatial frequencies of the perturbed wave field and thus patterns can form when nonlinear gain (i.e., amplification of the noises) overcomes the loss (i.e., a well defined cavity threshold set by the coherence properties) in a single pass. The expression for the spatial spectral density of the perturbed wave field, which is the characteristic parameters of the pattern formation, have been derived in the case of lowest order approximation. It is found that for a specific value of the spatial frequency of the perturbed wave field, the intensity feedback of the cavity is much effective factor rather than the crystal thickness of the nonlinear media and amplitude of the incoming beam in the cavity for the enhancement of the spatial spectral density of the intensity pattern, which greatly improved the performance and applications of the pattern formation such as information processing, symmetry-breaking, and dynamics in non-equilibrium systems.     

用于制作光纤光栅的Talbot干涉仪的分析与建模

对用于制作光纤光栅的Talbot干涉仪进行了分析.当考虑准分子激光器的空间相干性和时间相干性时,几何光学中的光线法并不能给出Talbot干涉仪干涉场的真实强度分布情况,而通过光的电磁理论,则可以提供对干涉场的详细描述.基于电磁理论,建立了一个Talbot干涉仪干涉场计算模型,并首次将Talbot干涉仪的反射镜转角作为模型计算参数加以考虑,随后进行了一系列的计算.计算结果显示了干涉场的分布,同时表明空间相干性对Talbot干涉仪的近场干涉和远场干涉影响都很大,其中远场干涉对空间相干性的要求更严格,且对于远场干涉,反射镜转角的影响不可忽视.     

On the van Cittert-Zernike theorem

The van Cittert-Zernike theorem states that the spatial coherence over a space illuminated by an incoherent extended source is described by the Fourier transform of the intensity distribution over the source. The theorem is usually used in a restricted case of the spatial coherence in a plane parallel to the source plane and illuminated by an incoherent extended source of uniform intensity distribution. In this paper we re-examine the van Cittert-Zernike theorem by reviewing it in an original formulation and extend the theorem to the spatial coherence at any two points of a light field illuminated by an incoherent extended source having a non-uniform intensity distribution.     

Longitudinal pure spatial coherence of a light field with wide frequency and angular spectra

We have observed the longitudinal pure spatial coherence of a light field in an interference experiment when the length of the temporal coherence is significantly smaller than the length of the longitudinal spatial coherence of the light field. We introduce into consideration new spatial and temporal scales of a light field: the length of the coherent (free) run and the coherent time (the time of life) of a wave train.     

Is there a fundamental limitation on the measurement of spatial coherence for highly incoherent fields?

We investigate a fundamental limitation on the measurement of spatial coherence for highly incoherent fields. We model the near-field detection scheme, required for such a measurement, with pointlike induced dipoles. We find that this fully vector model sets a characteristic length scale beyond which the spatial coherence of an optical field cannot be accurately measured. This length scale forms an uncertainty relationship with the photodetector integration time.     

强非局域非线性介质中的非相干孤子研究

本文从一维强非局域非线性模型出发,推导出非相干光满足的非线性薛定谔方程.按照相干密度描述方法,写出非相干光的描述方式,求出了非相干光孤子的形成条件和孤子形式,还得到了相干光和非相干光在强非局域非线性介质中形成孤子的临界功率,结果说明非相干光形成孤子时,需要更高的能量.当非相干光孤子的条件不满足时,非相干光束以呈现振荡行为.空间振荡周期仅与介质、入射的非相干光的光功率有关,而与光源的非相干角功率谱宽度及具体组分无关.同时,我们还数值模拟了这种非相干光束的振荡行为和单一组分、一对组分的非相干强度演化过程.     

深远海线性内波条件下声场时间相关性的空间分布

深海声场特定的干涉结构导致其时间相关性的空间起伏,研究这种空间特性可以为水声信号的探测与处理提供重要参考。利用抛物方程声场仿真模型,联合Monte-Carlo数值方法计算分析了深远海线性内波条件下声场时间相关性的空间分布特性。与现有的研究相比,给出了时间相关性的距离和深度起伏特征。结果表明,当接收达到一定距离,声场时间相关性的空间分布具有与声场干涉条纹类似的结构,声场干涉越强,时间相关性越好。此外,声源频率和声速标准差的变化会引起时间相关性空间分布规律的改变,且会聚区传播模式下的改变强于深海声道传播模式。      

Longitudinal purely spatial coherence of a light field

The effects of longitudinal purely spatial coherence of light and the results of observation of these effects in an interference experiment are considered under the condition that the length of temporal coherence l _c is considerably smaller than the length of longitudinal spatial coherence ρ_‖ of the field. It is shown that, for l _c ? ρ_‖, the longitudinal purely spatial coherence of the light field in fact governs the coherence of the wave train in the process of its propagation. The length and the time of coherent (“free”) path of the wave train are considered as new spatial and temporal scales of a partially coherent light field.     

The coherence of reverberant sound fields

A new method of measuring spatial correlation functions in reverberant sound fields is presented. It is shown that coherence functions determined with appropriate spectral resolution contain the same information as the corresponding correlation functions, and that measuring such coherence functions is a far more efficient way of obtaining this information. The technique is then used to verify theoretical predictions of the spatial correlation between various components of the particle velocity in a diffuse sound field. Other possible applications of the technique are discussed and illustrated with experimental results obtained in an ordinary room.     

第三代同步辐射光源X射线相干性测量研究

随着高性能第三代同步辐射光源的建成开放,基于X射线相干特性的实验方法得到了快速发展和广泛应用.作为一个典型的例子,X射线相位衬度成像已经成为常规的X射线实验方法并向用户开放.相干散射、相干衍射成像、光子关联谱等X射线实验方法正日益受到重视,在高空间分辨、时间分辨等研究领域已显示出其独特的优越性.因此,研究和测量第三代同步辐射的空间相干特性对进一步发展这些新的实验方法具有重要意义.基于Talbot自成像原理成功测量了上海光源X射线成像线站发射的X射线的空间相干长度,并进而测得了相应光源的空间尺度.光子能量为33.2 keV时,测得的X射线光束垂直方向空间相干长度为8.84μm,对应的光源尺寸为23μm,测量结果与理论分析相符.     

Optical Information Processing by Synthesis of the Coherence Function–Selective Masking of 2-D Information by Synthesis of Notch-Shaped Coherence Function–

We have proposed an optical information processing system adopting synthesis of the optical coherence function by using direct frequency-modulation of a laser diode.1’ Optical coherence function having notch shape is discussed theoretically and experimentally. Applying the notch shaped coherence function to this system, to mask selectively a two-dimensional (2-D) information from a three-dimensional (3-D) object can be carried out. After showing the experimental results on selective masking, the performance deterioration factors are discussed in detail.     

自聚焦透镜的三维相干成像特性分析

运用傅里叶光学方法，分析并推导了自聚焦透镜的三维相干成像公式。研究表明，虽然自聚焦透镜中介质折射率是径向渐变折射率分布，不同于薄透镜中的均匀分布，但是由于它的三维相干成像性质却类似于薄透镜，从而使自聚焦透镜可以在成像和光学信息处理系统中有效地代替薄透镜，实现光学系统的微型化。