Experimental measurement of the four-dimensional coherence function for an undulator x-ray source

A full measurement of the four-dimensional coherence function from an undulator beam line is reported. The analysis is based on the observation that the data are consistent with a coherence function that is mathematically separable. The effective source size can be altered by changing the width of the exit slit, and the complete coherence function is presented for two settings. We find, to within experimental error, that the four-dimensional complex degree of coherence can be described as a real Gaussian function that depends only on the difference of the spatial coordinates.     

Shearing interferometer for quantifying the coherence of hard x-ray beams

We report a quantitative measurement of the full transverse coherence function of the 14.4 keV x-ray radiation produced by an undulator at the Swiss Light Source. An x-ray grating interferometer consisting of a beam splitter phase grating and an analyzer amplitude grating has been used to measure the degree of coherence as a function of the beam separation out to 30 microm. Importantly, the technique provides a model-free and spatially resolved measurement of the complex coherence function and is not restricted to high resolution detectors and small fields of view. The spatial characterization of the wave front has important applications in discovering localized defects in beam line optics.     

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.     

Effects of a modified spectral model on the spatial coherence of a laser beam

The influence of a modified (bump) spectrum of refractive index fluctuations on the spatial coherence of an optical wave is studied here and compared with that based on a von Karman spectrum. Analytical expressions are derived for the mutual coherence function (MCF) and wave structure function (WSF) of a lowest-order Gaussian beam wave from which the beam spot size and degree of coherence are deduced. The qualitative behaviour of beam spreading and coherence length is basically the same for both spectral models. Also, when the radius of the Fresnel zone and initial beam radius are of comparable size, the presence of a spectral bump appears to have minimal effect on spatial coherence for all beams. However, the choice of spectral model is important for certain ranges of parameters. In particular, the implied spatial coherence length for a collimated beam based on the modified spectrum is significantly smaller than that based on the von Karman spectrum whenever the Fresnel zone is either much larger or much smaller than the initial beam radius, whereas for a focused beam the predicted coherence length based on the modified spectrum is slightly larger when the Fresnel zone size is much smaller than the initial beam radius.     

激光聚变驱动器的光束相干性及其控制:回顾与展望

高功率强激光与物质相互作用蕴藏着丰富的非线性效应,激光聚变驱动器的光束具有高度相干性,它在光束传输过程中极大地凸显了这种效应,并不可避免地制约着激光功率的提升和激光能量的有效利用。回顾激光聚变驱动器的发展史,在提升激光输出能力的主线外,还存在一条与光束相干性做斗争的暗线贯穿其中。以激光与物质相互作用为牵引,从高功率强激光传输中非线性效应抑制和激光等离子体相互作用的抑制两方面回顾了激光聚变驱动器光束相干性的控制现状,并针对潜在需求,展望了未来高功率激光发展的创新技术。     

Characterization of spatial coherence of synchrotron radiation with non‐redundant arrays of apertures

A method to characterize the spatial coherence of soft X‐ray radiation from a single diffraction pattern is presented. The technique is based on scattering from non‐redundant arrays (NRAs) of slits and records the degree of spatial coherence at several relative separations from 1 to 15 µm, simultaneously. Using NRAs the spatial coherence of the X‐ray beam at the XUV X‐ray beamline P04 of the PETRA III synchrotron storage ring was measured as a function of different beam parameters. To verify the results obtained with the NRAs, additional Young's double‐pinhole experiments were conducted and showed good agreement.     

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.     

高斯谢尔光束通过湍流大气漫射目标的散射统计

基于广义惠更斯菲涅耳原理分析了高斯谢尔光束通过湍流大气漫射目标的散射统计特性。假定相位结构函数起主导作用,根据高斯谢尔光束的交叉密度函数,推导了散斑场的互相干函数表达式,进而得出接收面处的散斑尺寸大小和强湍流起伏的时延协方差函数表达式。数值分析了源相干长度、波长、湍流强度对互相干函数的影响。对理想漫射目标,接收面的散斑尺寸大小由束腰宽度、源相干长度和湍流强度确定,随着湍流强度的增加,散斑尺寸变小;在弱湍流区,散斑尺寸由源相干长度决定,当湍流增强时,散斑尺寸大小逐渐趋于一致。     

Shallow water narrowband coherence measurements in the Florida Strait

A set of measures of coherence are defined and applied to the CALOPS experiment, conducted off the coast of Florida in the summer of 2007. A set of narrowband CW tones were transmitted from a towed source received on a 118-element bottom mounted horizontal line array (206 m aperture) with broadside oriented along the 250 m isobath. Two coherence measures are based upon the eigenvalue spread: the power factor and the eigenvalue ratio. This approach is not sensitive to array element error or model mismatch. Two measures are based upon phase residuals; these include the rms-phase error and the coherence function. Three measures are based upon power responses: beam width, array signal gain degradation, and array gain. These approaches have varying sensitivity to array location errors, model mismatch, signal-to-noise ratio, and the structure of the noise field. A Gaussian noise model is used to infer a coherence length from most of the coherence measures. The primary result is that coherence lengths increase with frequency and are on the order of 200 m, the length of the array. The frequency increased coherence length with frequency goes against conventional wisdom, which is to define the coherence length as a fixed number of wavelengths.     

Changes in the coherence of quasi-monochromatic electromagnetic Gaussian Schell-model beams propagating through turbulent atmosphere

Based on the extended Huygens-Fresnel principle, the mutual coherence function of quasi-monochromatic electromagnetic Gaussian Schell-model (EGSM) beams propagating through turbulent atmosphere is derived analytically. By employing the lateral and the longitudinal coherence length of EGSM beams to characterize the spatial and the temporal coherence of the beams, the behavior of changes in the spatial and the temporal coherence of those beams is studied. The results show that with a fixed set of beam parameters and under particular atmospheric turbulence model, the lateral coherence of an EGSM beam reaches its maximum value as the beam propagates a certain distance in the turbulent atmosphere, then it begins degrading and keeps decreasing along with the further distance. However, the longitudinal coherence length of an EGSM beam keeps unchanging in this propagation. Lastly, a qualitative explanation is given to these results.     

部分相干洛伦兹-高斯光束在湍流大气中的峭度参数

基于广义惠更斯-菲涅耳衍射积分公式和洛伦兹函数的厄米-高斯展开,导出了部分相干洛伦兹-高斯光束在湍流大气中经傍轴ABCD光学系统的峭度参数的解析表达式,对该峭度参数进行了数值计算。结果表明:空间相干长度和结构常数对峭度参数的影响与部分相干洛伦兹-高斯光束本身的光束参数有关;当空间相干长度小于光束参数时,其影响显著;当洛伦兹部分的光束参数较大或高斯部分的光束参数较小时,结构常数的影响较明显且随传输距离的增大而增强。     

湍流大气传输高斯谢尔光束的到达角起伏

研究了在弱大气湍流起伏环境下以窄带宽高斯谢尔光束为激光光源的大气通信问题,分析了大气湍流强度和光源空间相干度对通信光束到达角起伏的影响.采用窄带宽光场的交叉谱密度函数代替光场互相干函数的近似方法和采用包含大气湍流内外尺度的简化折射率谱密度函数,得出了湍流大气中传输高斯谢尔光束的波结构函数(WSF) 和到达角起伏方差解析近似关系.分析表明,光源的空间相干度和传输光束的湍流扩展是影响高斯谢尔光束的相位起伏结构函数和传输光束到达角起伏的重要因素.     

非均匀拉盖尔-高斯关联光束及其传输特性

提出了一种新型特殊关联部分相干光束即非均匀拉盖尔-高斯关联光束,其在x和y方向上的关联结构函数分别为非均匀关联和拉盖尔-高斯关联函数.基于广义惠更斯-菲涅耳衍射积分公式,推导了这种光束交叉谱密度函数在自由空间以及大气湍流中的传输式,并计算了该光束经过自由空间和湍流大气传输的光强分布和关联结构函数分布演化特性.研究发现,该光束光强分布在传输过程中展现出自聚焦、自偏移和自分裂等奇异特性,同时发现控制关联结构函数参数可以有效地降低湍流大气的影响.关联结构调控为操控光束传输行为提供了一种新颖而有效的手段,在大气激光通信、微粒操控等领域具有重要的应用前景.     

大气湍流对斜程传输准单色高斯-谢尔光束空间相干性的影响

由湍流大气中斜程传输时准单色高斯-谢尔(GSM)光束互相干函数的解析式导出了该光束的复相干度.然后,利用表征光束空间相干性的横向相干长度,研究了斜程传输时大气湍流对准单色GSM光束空间相干性的影响.研究结果表明：1)当传输路径偏离水平方向较大(即θ≤88°)时,准单色GSM光束横向相干长度随传输距离均为先迅速增加,后缓慢增加,最后基本保持不变.2)当传输路径接近水平方向(即θ≥89°)时,准单色GSM光束横向相干长度随传输距离均为先增大,达到一个最大值后开始下降并持续减小.3) 关键词： 大气光学 空间相干性 高斯-谢尔光束 斜程传输     

大气湍流对多色高斯-谢尔模型光束扩展的影响

基于广义惠更斯-菲涅耳原理,采用Rytov相位结构函数二次近似和硬边窗口函数的复高斯展开法,推导了受光阑限制的多色高斯-谢尔模型(GSM)光束在大气湍流中的二阶矩束宽公式。研究表明:二阶矩束宽随着大气湍流折射率结构常数、源光谱带宽和光束传输距离的增加而增大,随着光束截断参数和光束相干参数的增加而减小;并且,当源光谱带宽越大、光束截断参数和光束相干参数越小,则湍流对受光阑限制的多色GSM光束扩展的影响就越小。关键词:      

Spatial information transmission using orthogonal mutual coherence coding

We use the coherence of a light beam to encode spatial information. We apply this principle to obtain spatial superresolution in a limited aperture system. The method is based on shaping the mutual intensity function of the illumination beam in a set of orthogonal distributions, each one carrying the information for a different frequency bandpass or spatial region of the input object. The coherence coding is analogous to time multiplexing but with multiplexing time slots that are given by the coherence time of the illumination beam. Most images are static during times much longer than this coherence time, and thus the increase of resolution in our system is obtained without any noticeable cost.     

同步辐射的相干模式

在分析了光源相干相体积的基础上，重点研讨了第三代同步辐射中波荡器（ｕｎｄｕｌａｔｏｒ）辐射的相干模式，能谱亮度，相干光子通量等，这对提高光束线相干能量的传输效率和软Ｘ光相干学束线的设计具有重要意义。     

Measurement of spatial coherence of a copper vapour laser beam using a reversal shear interferometer

We measured the spatial coherernce of a copper vapour laser (CVL) beam with an unstable resonator by the reversal shear interferometer. By this method, we can evaluate the spatial coherence function from a single-shot measurement. The spatial coherence width was 5 mm when an unstable resonator with a magnification factor of 60 was used. Moreover we verified the result by the theoretical calculation on the basis of the passive resonator model.     

Slant path average intensity of finite optical beam propagating in turbulent atmosphere

The average intensity of finite laser beam propagating through turbulent atmosphere is calculated from the extended Huygens Fresnel principle. Formulas are presented for the slant path average intensity from an arbitrarily truncated Gaussian beam. The new expressions are derived from the modified von Karman spectrum for refractive-index fluctuations, quadratic approximation of the structure function,and Gaussian approximation for the product of Gaussian function and Bessel function. It is shown that the form of average intensity is not a Gaussian function but a polynomial of the power of the binomial function, Gaussian function, and the incomplete gamma function. The results also show that the mean irradiance of a finite optical beam propagating in slant path turbulent atmosphere not only depends on the effective beam radius at the transmitting aperture plane, propagation distance, and long-term lateral coherence length of spherical wave, but also on the radius of emit aperture.     

Beams generated by Gaussian quasi-homogeneous sources

An explicit expression is presented for the cross-spectral density function of the light in any cross-section perpendicular to the axis of a beam generated by a planar, steady-state, quasi-homogeneous source, whose intensity distribution and degree of spatial coherence are both gaussian. The result is used to discuss some properties of such a beam. It is found, in particular, that the ratio of the transvers (spatial) coherence length of the light to the beam width is the same for every cross-section perpendicular to the beam axis.