Sixth-order coincidence fractional Fourier transform implemented with partially coherent light

The sixth-order coincidence fractional Fourier transform (FRT) with incoherent and partially coherent light is introduced as an extension of the recently introduced fourth-order coincidence FRT. An optical system for implementing sixth-order coincidence FRT is designed. It is found that the visibility of the sixth-order coincidence FRT pattern of an object is always much higher than that of the fourth-order coincidence FRT pattern. The visibility is closely related to the transverse width and the transverse coherence length of the light source and also depends on the fractional order of the optical system.     

Lensless imaging with partially coherent light

Based on the fourth-order correlation of light, lensless imaging with incoherent or partially coherent light is investigated theoretically by use of classical optical coherence theory. A novel lensless optical system for implementing imaging is proposed. The visibility and quality of the image are influenced by the coherence and transverse size of the light source. The results suggest useful imaging applications in x-ray, gamma-ray, or other wavelengths where no effective lens is available, and they have potential applications in optical metrology and holography.     

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。     

部分相干厄米-高斯光束杨氏实验中的光强分布

将杨氏干涉实验作为双缝衍射现象处理,以部分相干厄米-高斯(H-G)光束为例,研究分析了多模部分相干光的杨氏双缝干涉光强和干涉条纹可见度的空间分布。数值计算说明,多模部分相干光束的空间相干参数、模阶数和缝遮拦比对衍射场中光强的空间分布(干涉花样)都有影响。当多模部分相干光的阶数为奇数时,轴上光强与光束的相干性会出现相消干涉;当多模部分相干光的阶数为偶数时,轴上光强与光束的相干性会出现相长干涉等。     

Direct measurement of transverse coherence length of hard X rays from interference fringes

We propose a simple interferometric technique for hard x-ray spatial coherence characterization, recording a Fresnel interference pattern produced by a round fiber or a slit. We have derived analytical formulas that give a direct relation between a visibility of interference fringes and either the source size or the transverse coherence length. The technique is well suited to third-generation synchrotron radiation sources and was experimentally applied to determine the spatial coherence length and the source size at the European Synchrotron Radiation Facility.     

普通光源的时空相干度分析

在分析光源的非单色性和宽度对干涉条纹可见度影响的基础上,推导出普通光源的时空相干度计算公式,并定义了相干线域、相干面域和相干体域等概念.     

Third-order ghost interference with thermal light

A scheme for third-order ghost interference with thermal light is proposed. The visibility and resolution of the interference fringe related to the bandwidth of the spatial frequency spectrum of the source are analysed. The results show that the visibility of the third-order ghost interference fringe is much higher than that of the second-order one.     

Signal-to-noise ratio of lensless ghost interference with thermal incoherent light

Factors influencing the signal-to-noise ratio (SNR) of lensless ghost interference with thermal incoherent light are investigated.Our result shows that the SNR of lensless ghost interference is related to the transverse length of the object,the position of the object in the imaging system and the transverse size of the light source.Furthermore,the effects of these factors on the SNR are discussed in detail by numerical simulations.     

Spatial coherence of an optical turbulent beam in a biased photorefractive crystal due to the spatiotemporal modulation instability

We report the experimental observation of the dynamic pattern formation of a broad coherent light beam in a biased photorefractive crystal due to the spatiotemporal modulation instability. When the nonlinearity exceeds a specific threshold, the coherent light beam not only breaks up into light spots due to the modulation instability but also fast fluctuates both spatially and temporally, forming an optical turbulent beam, which behaves as a quasi-homogeneous speckled beam or a partially incoherent beam. We investigate the spatial coherence property of an optical turbulent beam from the visibility of the averaged double-slit interference fringe. We also numerically demonstrate the visibility variation of the instantaneous interference fringe of an optical turbulent beam.     

Visibility enhancement in two-dimensional lensless ghost imaging with true thermal light

We report an experimental demonstration of two-dimensional(2D) lensless ghost imaging with true thermal light. An electrodeless discharge lamp with a higher light intensity than the hollow cathode lamp used before is employed as a light source. The main problem encountered by the 2D lensless ghost imaging with true thermal light is that its coherence time is much shorter than the resolution time of the detection system. To overcome this difficulty we derive a method based on the relationship between the true and measured values of the second-order optical intensity correlation, by which means the visibility of the ghost image can be dramatically enhanced. This method would also be suitable for ghost imaging with natural sunlight.     

Visibility in differential phase-contrast imaging with partial coherence source

This paper gives theoretical analysis of visibility of fringes, which is influenced by distances, temporal and spatial coherence of source, in hard x-ray differential phase-contrast imaging with microfocus x-ray source. According to the character of longitudinal periodicity of the interferogram, the setup is insensitive to mechanical drift and vibrations. The effect of temporal coherence of x-ray source is investigated and its related bandwidth is derived. Based on the theory of partially coherent light, it shows that the requirement for the spatial coherence of x-ray source is not strict and can be met by the general microfocus x-ray tube for x-ray differential phase-contrast imaging.     

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.     

Experimental investigation on partially coherent higher-order non-diffractive beams

We experimentally study the generation of a partially coherent non-diffractive beam by focusing a partially coherent vortex beam with an axicon. The investigation results show that when the partially coherent vortex beam is focused by the axicon, the beam is transferred into a partially coherent higher-order non-diffractive beam. In the non-diffractive zone, the transverse intensity distribution of the partially coherent higher-order non-diffractive beam is invariant during propagation. In addition, the range of the non-diffractive zone is related to the coherence of the partially coherent vortex beam. The poorer the coherence of the partially coherent vortex beam, the shorter the range of the non-diffractive zone.     

Spectral intensity characteristics of partially coherent flattened multi-Gaussian beams with an axial shadow passing though paraxial ABCD optical systems

Based on the beam model for the flattened multi-Gaussian beams (FMGBs) with an axial shadow and partially coherent theory, the expression for cross-spectral density of partially coherent FMGBs with an axial shadow has been given, and the analytical expression for the spectral intensity of partially coherent FMGBs with an axial shadow passing through paraxial ABCD optical systems has been derived. The spectral shift of partially coherent FMGBs with an axial shadow focused by a thin lens has been analyzed quantitatively. The effects of the beam profile, spatial coherence parameter and the system parameters on the relative spectral shift have been discussed in detail. Our results show that the spectral intensity and the spectral shift of partially coherent FMGBs with an axial shadow passing through paraxial ABCD optical systems depend on the source spectral density, the generalized Fresnel number of the system, the transverse coordinate, the spatially coherence parameter, as well as the beam orders.     

Resolution and visibility of two-color pseudothermal lensless ghost imaging

Two-color (or nondegenerate-wavelength) lensless ghost imaging using pseudothermal light source is investigated theoretically by use of classical optical coherence theory. We find that for two-color pseudothermal lensless ghost imaging the visibility and resolution is determined by (Δ) the product of the wavelength and the corresponding path length rather than the wavelength for each path or the path length. We also confirm our theoretical conclusion by numerical simulations. The result shows we must make a trade-off between resolution and visibility in devise practical experiments, as the resolution of the imaging can be improved by decreasing Δ but with visibility getting poor, and vice versa.     

Effects of atmospheric turbulence on the orbital angular momentum of multi-Gaussian Schell model beams

The effects of multibeams and partially coherent source on the orbital angular momentum transmission of multi-Gaussian Schell model beams in an atmospheric turbulence channel are analyzed. An effective crosstalk probability model of the orbital angular momentum is derived which leads to crosstalk probability function for eigenmodes of different orbital angular momentum states and beamlets. The work shows that the evolution of the effective spatial coherence radius with growing the rms width of the correlation of the partially coherent source and the number of the beamlet in multi-Gaussian model beams. The crosstalk probability of the orbital angular momentum of an effective Gaussian-Schell model beam decreases as increasing of the degree of the spatial coherence of the partially coherent source and the beamlet number of the multi-Gaussian Schell model beams.     

Partially coherent multiple-beam interference

The general formula for multiple-beam interference due to regular slit arrays illuminated with partially coherent quasi-monochromatic light is derived. The correlation functions chosen for partially coherent light assume Gaussian, sinc and besinc forms of correlation. The intensity distribution in the interference patterns is presented and discussed as a function of the spatial coherence condition. It is shown that spatial coherence of the illumination largely affects the features of multiple-beam interference patterns.     

Partially coherent beam and its applications

The recent progresses on the propagation, generation and application of partially coherent beam (PCB) are reviewed in this paper. A new tensor ABCD law for treating the propagation of partially coherent Gaussian-Schell model (GSM) beams through a paraxial optical system is derived. The focusing, spectral shift and fractional Fourier transform of the GSM beam are investigated by using the tensor method. The generation of PCB with special optical resonator is studied both theoretically and experimentally. Furthermore, the ghost imaging and superluminal propagation of the PCB is discussed. The results show clearly that the coherence of light have strong influences on the ghost imaging and superluminal propagation.      

高斯型非均匀部分相干光的大气湍流传输特性

基于广义惠更斯-菲涅耳原理和交叉谱密度函数,对高斯型非均匀关联的部分相干光束在大气湍流中的传输特性进行了研究.结果表明,部分相干光的相干度的变化和源平面的高斯调制半宽、传输距离等有着密切关系.在传输过程中,初始平面相干度分布存在突变,在传输过程中消失;光束中两点的相干度随着传输距离的增加先增大后减小,并且相干度的分布由非均匀分布变成均匀分布.这种非均匀关联的部分相干光束在激光通信领域具有广阔的应用前景.     

四个部分相干点源的完全相消干涉特性

使用部分相干光的干涉定律,对部分相干光照明呈正方形对称四孔干涉仪的干涉场做了研究.结果表明,一定条件下,可出现完全相消干涉,并存在光强和光谱相干度的相位奇点.与二个、三个部分相干点源的干涉做了比较.对所得结果物理上可解释为：虽然四个点源是部分相干的,但从两个点源出射场之和与从另外两个点源出射场之和却可能是完全相关的. 关键词： 相关奇点光学 完全相消干涉 部分相干光 刃型位错线