Real time measurement of the spatial coherence using non-redundant two-dimensional aperture array

In this paper, two-dimensional real time method of measuring the complex degree of spatial coherence of a laser light field is presented. Far-field interferogram is generated by a two-dimensional mask with non-redundant multiple apertures in the focal plane of the lens. The Fourier spectrum of the interferogram is analyzed in the term of classes of aperture pairs. Through using heights of the peaks in the magnitude spectrum, as well as intensities in the apertures, the modulus of the complex degree of spatial coherence was determined. The available experimental data of Young interferometry, confirmed the graphs obtained with the above methods.     

1维部分相干光束的Z扫描理论分析

 对使用高斯-谢尔模型光束的Z扫描做了理论分析,研究了光阑半径和空间相干度变化对Z扫描曲线的影响。研究发现：随着光阑半径的变大,Z扫描峰谷透过率之差逐渐减小直至为零,其作用效果与完全相干光一致;随着空间相干度的增加,峰谷透过率之差也逐渐增大,当空间相干度大于某一定值后,峰谷透过率之差达到饱和不变。部分相干光束的Z扫描实验为测量其空间相干度提供了一种可行的方法。     

Beam shaping by spatial coherence modulation based on spatial coherence wavelets

A novel technique for designing specific shapes of power distributions is presented. It bases on the modulation of the spatial coherence of the optical field in amplitude and phase. The modulating functions are synthesized from the phase-space diagram of the field, provided by the marginal power spectrum. Numerical results for the phase modulation of the complex degree of spatial coherence are presented. This beam shaping technique is suitable in applications that require specific shapes and sizes.     

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     

Spatial coherence and coherent interactions of broadband dispersed laser beams

Analytical expressions are obtained that describe the changes in the degree of coherence and in the thickness of the coherence layers occurring upon propagation of a dispersed broadband laser beam. It is found that the greater the tilting of the coherence layers with respect to the phase fronts, the more rapidly the spatial coherence is violated with increasing distance. A comparison with the case of an undispersed beam is performed. It is shown that, as the beam propagates, the decrease in the degree of coherence is accompanied by the appearance of spatial fluctuations of this parameter. The degree of mutual coherence of intersecting dispersed beams with parallel correlated coherence layers, which determines the efficiency of their coherent interaction, is investigated. The existence of spatial fluctuations of the degree of mutual coherence is established.     

Interference-pattern image formation in an optical system with a random phase screen in the space-frequency plane

The process of interference-pattern image formation in an optical system with a random phase screen in the space-frequency plane is analyzed. It is shown that an optical system of this kind can function, under certain conditions, as a shearing interferometer, which determines the dependence of contrast of the average intensity fringes in the interference pattern image on the normalized correlation function of the random phase screen complex transmittance. The dependence of the fringe contrast on the pattern period and aperture of the field of view is established, as well as dependence of the optical transfer function of the system under study on spatial coherence of the light in the pupil of the system with the random phase screen.     

Partially coherent fresnel diffraction by a slit aperture. 1. Theoretical analysis

A formulation is developed for investigating the intensity distribution of Fresnel diffraction by a slit aperture illuminated with partially coherent light. The formulation is further extended to the case that the complex degree of coherence of the illumination contains a quadratic phase term.     

Spatial coherence measurements through turbulent atmosphere using a computer-aided interferometer

The complex degree of coherence over a telescope aperture is measured by processing instantaneous values of the complex degree of coherence fluctuated by turbulent atmosphere. Fringe patterns produced by a computer-controlled wave-front folding interferometer are analyzed in a short time by a photodiode array to calculate the instantaneous values of the complex degree of coherence. The system is applied to one-dimensional simulation experiments.     

Retrieving the complex degree of spatial coherence of electron beams

The possibility to characterize the coherence properties of an electron source is presented. The method, based on the determination of centered-reduced moments of the beam spot, allows the evaluation of both amplitude and phase of the complex degree of spatial coherence. The experimental results are in agreement with a different approach based on the Fourier analysis and with calculations according to the Van Cittert—Zernike theorem.     

Study correlation vortices in the near-field of partially coherent vortex beams diffracted by an aperture

We have derived the analytical expression of the electric cross-spectral density in the near-field of partially coherent vortex beams diffracted by an aperture. Taking the Gaussian Schell-model vortex beam as a typical example of partially coherent vortex beams, the spatial correlation properties and correlation vortices in the near-field of partially coherent vortex beams diffracted by a rectangle aperture are studied. It is shown that the off-axis displacement, spatial degree of coherence parameter, propagation distance, and the opening factor of the aperture affect the spectral degree of coherence and positions of correlation vortices. With the optimization algorithm, we obtain the symmetric distributing coherent vortex.     

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.     

Full-field and single-shot quantitative phase microscopy using dynamic speckle illumination

We developed an off-axis quantitative phase microscopy that works for a light source with an extremely short spatial coherence length in order to reduce the diffraction noise and enhance the spatial resolution. A dynamic speckle wave whose coherence length is 440 nm was used as an illumination source. To implement an off-axis interferometry for a source of low spatial coherence, a diffraction grating was inserted in the reference beam path. In doing so, an oblique illumination was generated without rotation of the wavefront, which leads to a full-field and single-shot phase recording with improved phase sensitivity of more than a factor of 10 in comparison with coherent illumination. The spatial resolution, both laterally and axially, and the depth selectivity are significantly enhanced due to the wide angular spectrum of the speckle wave. We applied our method to image the dynamics of small intracellular particles in live biological cells. With enhanced phase sensitivity and speed, the proposed method will serve as a useful tool to study the dynamics of biological specimens.     

Spatial correlation properties and phase singularity annihilation of Gaussian Schell-model beams in the focal region

By using the generalized Debye diffraction integral, this paper studies the spatial correlation properties and phase singularity annihilation of apertured Gaussian Schell-model （GSM） beams in the focal region. It is shown that the width of the spectral degree of coherence can be larger, less than or equal to the corresponding width of spectral density, which depends not only on the scalar coherence length of the beams, but also on the truncation parameter. With a gradual increase of the truncation parameter, a pair of phase singularities of the spectral degree of coherence in the focal plane approaches each other, resulting in subwavelength structures. Finally, the annihilation of pairs of phase singularities takes place at a certain value of the truncation parameter. With increasing scalar coherence length, the annihilation occurs at the larger truncation parameter. However, the creation process of phase singularities outside the focal plane is not found for GSM beams.     

Investigation on z-scan experiment by use of partially coherent beams

Z-Scan experiment using partially coherent beams is investigated theoretically. We derive the expression for the cross-spectral density of the Gaussian Schell-model (GSM) beam passing through the nonlinear thin sample. Then the influences of the aperture radius and the spatial degree of coherence on the z-scan curves are analyzed. We find that transmittance difference ΔT_p-v between the peak and valley in z-scan curves decreases gradually with the increment of the aperture radius, which is similar to the case of the fully coherent beams. It is also shown that ΔT_p-v is getting bigger with the increment of the spatial degree of coherence α₀, and when α₀ is larger than a certain value, ΔT_p-v becomes almost unchanged. The results show that the z-scan experiment with partially coherent beams may provide a feasible method for measuring the spatial degree of coherence.     

Measurements of complex degree of spatial coherence at the end face of an optical fiber

The phase and modulus of the complex degree of spatial coherence at the exit end face of an optical fiber are measured with the help of a real-time data processing computer. Interference fringes produced by superimposing wavefronts of the image of the end cross-section are scanned by a linear photodiode array to calculate the one dimensional value of spatial coherence. Evolution of phase measured at the different positions in the fringe pattern reveals that the phase is intimately related to modal structures of the propagating field in an optical fiber supporting a small number of guided modes.     

聚焦部分相干涡旋光束的传输和相干特性

根据部分相干光的传输理论,研究了部分相干高斯 贝塞尔涡旋光束通过光阑透镜聚焦后的传输和空间相关性质.数值计算结果表明,涡旋暗核的大小和焦平面上的光谱相干度都取决于入射光的拓扑电荷n、截断参量δ、相对相干长度σg和参量α.当选择适当的参量,在几何焦点附近会出现局域空心光束.研究还发现在焦面上光谱相干度会产生一个或多个的相位奇点（相干涡旋）,而且拓扑电荷和相对相干长度会对相干涡旋的位置和个数产生影响.在相干极限下,相干涡旋可逐渐演变为光学涡旋.     

高斯-谢尔模型光束通过光阑像散透镜传输轴上光谱变化

从部分相干光的传输理论出发,研究了高斯-谢尔模型(GSM)光束通过光阑像散透镜传输轴上的光谱变化规律.结果表明,与光源光谱相比,高斯-谢尔模型(GSM)光束通过光阑像散透镜传输轴上光谱发生了中心频率的移动,这种现象被称为光谱位移.详细分析了透镜的像散、光束的空间相关性和光阑的截断参量对光谱变化的影响.数值计算表明,这些参量会对光谱移动产生比较大的作用.     

伪部分相干高斯-谢尔模型光束在湍流大气中传播的闪烁孔径平滑效应

采用光传播的数值模拟方法, 对伪部分相干高斯-谢尔模型光束大气传播过程进行数值模拟, 统计分析不同接收口径内的光强起伏特性,计算闪烁的孔径平滑因子, 讨论了表征伪部分相干光的调制相位屏的相对变化频率对闪烁指数的影响, 并将其与充分发展的部分相干高斯-谢尔模型光束及完全相干光的闪烁指数对比. 结果表明: 降低光源相干性可大幅度降低闪烁指数, 但同时其闪烁指数的孔径平滑效应减弱, 在相同接收孔径下, 伪部分相干光闪烁指数的孔径平滑效果要比完全相干光差; 增大调制相位屏的相对变化频率可在一定程度上降低闪烁指数, 随着其相对频率的增大, 伪部分相干光的闪烁指数与部分相干光的结果趋于一致. 关键词： 伪部分相干高斯-谢尔模型光束 湍流大气 孔径平滑闪烁指数 数值模拟     

Changes in the spectrum, polarization, and coherence of stochastic spatially and spectrally partially coherent electromagnetic J0-correlated Schell-model pulsed beams propagating in free space

Taking the stochastic electromagnetic J ₀-correlated Schell-model pulsed (JSMP) beam as a typical example of stochastic spatially and spectrally partially coherent electromagnetic pulsed beams, the analytical expressions for the cross-spectral density matrix, spectral density, spectral degree of polarization and spectral degree of coherence of stochastic electromagnetic JSMP beams propagating in free space are derived, and used to study the changes in the spectrum, polarization, and coherence of stochastic spatially and spectrally partially coherent electromagnetic JSMP beams. It is shown that the on-axis spectrum is blue-shifted in free-space propagation and is dependent on the pulse temporal coherence length and spatial correlation parameter. The distribution of the on-axis spectral degree of polarization depends on the frequency and spatial correlation parameter. The spectral degree of coherence increases with increasing pulse temporal coherence length. The results derived are interpreted physically.