Temporal evolution of the optical path difference of a supersonic turbulent boundary layer

The density distribution of a supersonic turbulent boundary layer is measured with the nanoparticle-based planar laser scattering technique, and the temporal evolution of its optical path difference (OPD) in a short time interval is characterized by proper orthogonal decomposition (POD). Based on the advantage of POD in capturing the energy of a signal, a temporal evolution model is suggested for the POD coefficients of the OPD. In this model, the first few coefficients vary linearly with time, and the others are modeled by Gaussian statistics. As an application, this method is used to compute the shortexposure optical transfer function.     

Predictive flow-field estimation

We are considering the problem of real-time prediction of 3D turbulent velocity fields based on a small number of scalar measurements. The method of proper orthogonal decomposition (POD) allows for the decomposition of an ensemble of velocity fields into a set of spatial basis functions and a set of temporal coefficients. The computation of the temporal coefficients is by no means a trivial matter, especially when one is faced with a large number of modes. In this paper we discuss the use of radial basis function (RBF) models to capture the discrete time evolution and nonlinear dynamics of the POD coefficients. Further, we propose the use of regularized regression techniques to generate models that provide mappings between the POD coefficients and scalar measurements. As a final step towards real-time prediction, the state-space RBF models and regression measurement models are combined using unscented Kalman filters to produce optimal solutions such that a balance between the state models and measurement models is achieved.The proposed methods are tested for two specific cases. The classical Lorenz model is chosen to demonstrate the use and effectiveness of RBF models as a potential candidate for state models. Flow around a wall-mounted cube in a channel at Re=20,000 is considered as the second case. The aim for the second case is to be able to accurately predict the POD coefficients outside the ensemble. It is shown that a large number of POD coefficients is required to approximate the velocity fields with sufficient accuracy. The RBF models are created based on only the temporal information available from the initial ensemble, and it is shown that the RBF model is able to correctly approximate the high-dimensional phase space. Combined with the unscented Kalman filter it is indeed possible to track the evolution of the POD coefficients for a long time. The robustness of the filter is demonstrated by considering the presence of noise in measurements and using measurement information at time steps greater than the evolution time step.     

基于多级微镜的傅里叶变换成像光谱仪干涉成像系统分析与设计

为了实现傅里叶变换成像光谱仪的静态化与高通量,提出一种基于多级微镜的时空混合调制成像光谱仪,其干涉系统是利用一个多级微镜代替迈克尔逊干涉仪中的平面镜,其显著特点是无运动部件和限制系统光通量的狭缝,可同时获得目标的干涉图与二维空间图像。该成像光谱仪利用前置成像系统将目标成像到干涉系统的平面镜与多级微镜上,利用多级微镜的结构特点对两成像光束的光程差进行调制,然后通过后置成像系统获得不同干涉级次的目标图像。首先通过对该成像光谱仪干涉系统光谱信噪比的分析,明确了光谱信噪比与图像信噪比之间的关系,确定了多级微镜的特征参数。为了确保每个阶梯面所对应光程差的恒定性,通过对前置成像系统成像过程的分析,确定了前置成像系统像方远心的光路结构;通过对系统视场角与光程差之间关系的分析和计算,确定了前置成像系统的设计指标并完成了光学设计。为了保证后置成像系统不引入额外的光程差,通过对后置成像系统成像特点的分析,确定了后置成像系统双远心的光路结构;通过对系统入射孔径角与阶梯级数之间关系的分析和计算,最终设计出满足系统性能需求的后置成像系统。通过对各单元系统的理论分析与光学设计,为静态化与高通量成像光谱仪的发展提供了一种新的思路。     

新型干涉高光谱成像系统的光束剪切特性分析

提出了一种基于新型双折射横向剪切分束器的高光谱成像方法,采用的横向剪切分束器主要由Wollaston棱镜和角锥反射体组成.在分析双折射分束器的偏光结构和分光机理的基础上,利用光线追迹方法分析了光束在Wollaston棱镜中的传播特性,通过计算光束在双折射分束器中的传播方向及出射位置,推导出调制光程差的理论表达公式.根据理论推导结果,分别仿真分析了系统在不同扫描模式下光程差与入射光视场角以及角锥顶点偏移量的调制关系.基于理论分析结果搭建了实验装置,对光程差分析结果进行验证,实验结果与理论分析结果匹配较好.所提方法可以提高剪切光束的平行性,保证干涉条纹的高调制度,降低了复原光谱准确度对光学装调精度和元件加工精度的依赖性,具有结构稳定、复杂度低的显著特点.     

Universal form of the power spectrum of the aero-optical aberration caused by the supersonic turbulent boundary layer

Based on the measurement of one-dimensional （1D） optical path difference （OPD） of the supersonic turbulent bound- ary layer, an analytical form for the power spectrum of the two-dimensional （2D） OPD is obtained with its structure function and under the locally homogeneous isotropic assumption. The universality of this spectrum is argued, and its validity is checked by the comparison with experimental result. The potential applications of this model in theoretical and numerical studies are emphasized. Another contribution of this work is around the application of correlation function to analyzing the statistics of OPD. Based on our results and other results published elsewhere, we show that the OPD is often not stationary, and one should be cautious about using this tool.     

Modal dispersion due to photon–plasmon coupling in a SNOM tip

The mesoscopic effect of spectral modulation is used to experimentally investigate the possible effect of a metal-coated SNOM tip on the intermodal dispersion of an optical fiber. Highly regular modulation registered in a fixed spectral region of the broadband light transmitted by a 200 nm SNOM tip yields the value of optical path difference (OPD) in the two-mode model. To investigate the origin of this OPD a series of spectral measurements accompanied with a gradual reduction of the multimode fiber tail length has been performed. The results indicate that the observed OPD consists of two clearly distinguishable contributions: the OPD in the non-coated multimode fiber and the OPD in the metal-coated SNOM tip. The first one is a result of the inherent modal dispersion of an optical fiber. A numerical consideration shows that the second one can be attributed to a mode-dependent contribution of surface plasmon polaritons: one of the two modes couples to plasmons stronger than the other one, resulting in a remarkably slower propagation. This leads to a completely different value of intermodal dispersion, which actually changes its sign in the SNOM tip. Proposed is a logical explanation for such kind of a sign-switching behavior.     

Birefringent prism based Fourier transform spectrometer

This paper presents the design of a rugged and compact Fourier transform spectrometer (FTS) utilizing a birefringent prism, a pair of polarizers and a linear CCD array. This design improves on existing FTS by eliminating moving parts and spreading the optical path difference (OPD) spatially (rather than temporal scanning), making the system smaller, more reliable, and dramatically reducing measurement times. Both the theoretical models for the design and experimental results of the prototype are presented. The optical performance is tested using LEDs of known wavelengths, with the fringe counting technique employed during interferogram acquisition to ensure accurate sampling of the interferogram at constant OPD intervals. Reconstructing the spectra showed that the detected wavelengths deviated from the actual wavelengths by less than 1 nm.     

Reduced-order modeling of transonic flows around an airfoil submitted to small deformations

A reduced-order model (ROM) is developed for the prediction of unsteady transonic flows past an airfoil submitted to small deformations, at moderate Reynolds number. Considering a suitable state formulation as well as a consistent inner product, the Galerkin projection of the compressible flow Navier–Stokes equations, the high-fidelity (HF) model, onto a low-dimensional basis determined by Proper Orthogonal Decomposition (POD), leads to a polynomial quadratic ODE system relevant to the prediction of main flow features. A fictitious domain deformation technique is yielded by the Hadamard formulation of HF model and validated at HF level. This approach captures airfoil profile deformation by a modification of the boundary conditions whereas the spatial domain remains unchanged. A mixed POD gathering information from snapshot series associated with several airfoil profiles can be defined. The temporal coefficients in POD expansion are shape-dependent while spatial POD modes are not. In the ROM, airfoil deformation is introduced by a steady forcing term. ROM reliability towards airfoil deformation is demonstrated for the prediction of HF-resolved as well as unknown intermediate configurations.     

Study on the optical path difference of aero-optical window

To study the optical path difference (OPD) of optical widow in which light beams transmit under the aerodynamic thermal environment, a grid model is introduced. Based on it, the aero-optical effect of the side-mounted window is analyzed in detail combining the optical transmission theory and the numerical simulation method. Firstly, the temperature and stress of the window are simulated, and then the OPD is obtained through the refractive index. To demonstrate it, temperature field, deformation field and stress field of the window are calculated and analyzed. The influences of thermal shock and atmosphere pressure on the OPD are discussed.     

液体透镜的透射波前特性研究

液体透镜是一种新型光学元件,通过改变表面曲率而调整光焦度。液体透镜的透射波前质量会影响成像质量,将液体透镜应用于精密光学系统需要探明其透射波前变化特性。通过理论和仿真分析液体透镜通光孔径内不同高度入射光线的光程差随曲率半径的变化,以及光程差对光焦度的敏感性,以此研究光瞳空间内光程差微变的一致性。分别测量液体透镜在零、正、负光焦度下的透射波前,通过分析实验数据验证液体透镜的光程差微变的一致性。实验结果表明:光程差微变的空间最大差异约为0.22λ～0.36λ,空间分布离散程度约为0.01λ～0.02λ,得出液体透镜随电流微变产生的光程差微变一致性较好,为液体透镜在精密光学系统中的应用和像差补偿提供了技术支撑。     

基于准静态波的吸气式高重频脉冲激光推进性能数值研究

 根据高重频脉冲激光产生光学脉冲放电形成准静态波的原理,对自编的流体力学计算程序进行了验证,结果表明该程序可用于吸气式高重频脉冲激光推进性能的数值研究。分别计算了基于移动点火点和喷射气流两种模式下准静态波流场的冲量耦合系数,均高达600 N/MW,比传统的低频脉冲激光推进冲量耦合系数250 N/MW高。比较了两种模式的优缺点,给出了不同模式的适用情况,结果表明,对于机理研究来说,喷气模式更易于实现。     

Temporal analysis of tissue displacement induced by a transient ultrasound radiation force

One of the stress sources that can be used in dynamic elastography imaging methods is the acoustic radiation force. However, displacements of the medium induced by this stress field are generally not fully understood in terms of spatial distribution and temporal evolution. A model has been developed based on the elastodynamic Green's function describing the different acoustic waves generated by focused ultrasound. The function is composed of three terms: two far-field terms, which correspond to a purely longitudinal compression wave and a purely transverse shear wave, and a coupling near-field term which has a longitudinal component and a transverse component. For propagation distances in the shear wavelength range, the predominant term is the near field term. The displacement duration corresponds to the propagation duration of the shear wave between the farthest source point and the observation point. This time therefore depends on the source size and the local shear modulus of the tissue. Evolution of the displacement/time curve profile, which is directly linked to spatial and temporal source profiles, is computed at different radial distances, for different durations of force applications and different shear elastic coefficients. Experimental results performed with an optical interferometric method in a homogeneous tissue-mimicking phantom agreed with the theoretical profiles.     

条纹相机在真空弧离子源等离子体诊断中的应用

针对真空弧离子源,利用条纹相机将时间轴信息转换为空间轴信息的特点,结合光谱仪分光功能,建立了一套高时间分辨与光谱分辨能力的发射光谱诊断装置,其时间分辨率和光谱分辨率分别可达26ps与0.1nm。利用该诊断装置采集获得了单次脉冲内等离子体的时间演化特性;同时,基于局域热力学平衡等离子体的发射光谱理论,建立了一套谱线拟合的等离子体温度与密度计算模型。相比传统的Boltzmann斜率法与Stark展宽法需要寻找孤立的不受附近谱线叠加的干净线状光谱,建立的拟合光谱模型可以直接处理多条谱线因为展宽效应而叠加形成的光谱线型,计算得到等离子体中电子温度与电子密度。结果表明,在脉冲功率源的作用下,真空弧放电等离子体的电子温度与电子密度分别可达1eV与3.5×1024 m-3。     

Study on a neural network model for high speed turbulent boundary layer inducing optical distortions

A neural network (NN) model for high speed turbulent boundary layer inducing aero optical distortions is proposed to solve the spatial frequency problem in sparse measurements. The temperature fluctuation, a measurable flow state, is set as the NN model input, and the optical path difference (OPD) is outputted. The NN structure, its optimal inputting point number and neuron number of hidden layer are analyzed. Numerical simulation results for two flow cases show that the OPDs of simulated positions using only limited points have good agreements with the calculated ones by ray tracing from whole field. Their correlation coefficient is up to 0.95 and the relative error of OPD root mean square is within 7% for both cases, which validates this model. Besides, its accuracy performances for different cases are analyzed, and the results accord with the experimental knowledge. This research provides numerical basis for the practical application of NN in sparse measurements.     

基于POD模态分解的液环泵瞬态气液两相流分析

针对液环泵内气液两相流动的复杂时空规律,采用本征正交分解(POD)方法对其瞬态气液两相流场进行特征分解,分析其相态场、速度场的空间基模态特征及模态系数的时域特征,建立非定常流场降阶模型,并对流场进行预测分析。结果表明POD方法可实现对液环泵内复杂流场的时空解耦分析,相态场及速度场的各阶模态系数在时域内的变化能够反映各阶模态场的能量、频率及相位变化规律,模态场能够反映脉动流场的空间尺度变化规律。POD降阶模型能够对样本空间内的流场进行精确预测,进口压力、相态场及速度场预测结果的最大相对误差分别约为0.2%、4%、8%,在样本空间外POD降阶模型具有一定外延预测精度,当预测目标逐渐远离样本空间时POD预测结果与CFD计算结果之间的误差逐渐增大。     

转镜式傅里叶变换光谱仪光程差非线性的研究

转镜式傅里叶光谱仪中,转镜的转动形成光程差的非线性。光程差非线性是转镜材料和工作角选择时要考虑的重要因素,通过对它的研究,可以为工程实践提供指导,为进一步研究奠定基础。通过输入单色光时的情况对干涉图进行研究,发现光程差非线性使干涉图的周期发生变化;通过和光程差线性系统的仪器函数比较对复原光谱进行研究,发现非线性给复原光谱带来了噪声和波数漂移。由于光程差的变化是已知的,在光谱复原时,用非线性的光程差代替傅里叶变换中的光程差,就可以对光程差非线性进行补偿。计算机仿真实验的结果表明,这种方法效果明显,经补偿后复原光谱中光程差非线性带来的噪声基本消失。     

Chirped Lambert W-kink solitons of the complex cubic-quintic Ginzburg-Landau equation with intrapulse Raman scattering

In this paper, an exact explicit solution for the complex cubic-quintic Ginzburg-Landau equation is obtained, by using Lambert W function or omega function. More pertinently, we term them as Lambert W-kink-type solitons, begotten under the influence of intrapulse Raman scattering. Parameter domains are delineated in which these optical solitons exit in the ensuing model. We report the effect of model coefficients on the amplitude of Lambert W-kink solitons, which enables us to control efficiently the pulse intensity and hence their subsequent evolution. Also, moving fronts or optical shock-type solitons are obtained as a byproduct of this model. We explicate the mechanism to control the intensity of these fronts, by fine tuning the spectral filtering or gain parameter. It is exhibited that the frequency chirp associated with these optical solitons depends on the intensity of the wave and saturates to a constant value as the retarded time approaches its asymptotic value.     

偏心激励聚合物光纤横截面的光功率分布

研究了偏心激励多模聚合物光纤横截面的光功率分布。用光线追迹法计算了不同的激励源偏心距离和光纤长度时,光纤出射端横截面的光功率分布,并用二维CMOS图像探测器阵列进行了测量。数值计算和实验测量的结果均表明随着激励源偏心距的增加,光功率分布由光纤轴心向外偏移并形成环状;光功率分布在圆周方向的均匀性随着光纤长度的增加而趋于均匀。对中心激励的弯曲光纤光功率分布的测量结果表明,当弯曲曲率半径远大于临界曲率半径时,光功率分布无显著展宽,光功率分布随曲率半径的减小而向曲率外侧偏移;当光纤弯曲半径接近于临界曲率半径时,光功率分布显著展宽。     

Spectral Based Estimation of Optical Path Difference of Interference Colors

A spectral intensity distribution of interference colors which is a function of optical path difference (OPD) is represented as a pattern vector on a subspace. A new algorithm to design a color scale on the subspace to estimate OPD values is proposed. In experiments, interference colors generated by a differential interference microscope (DIM) were examined. A subspace spanned by four orthogonal bases was constructed to make a color scale to determine OPD values in the range between 0 nm and 1000 nm. Estimated OPD values almost coincided with these expected. In an experiment on two-dimensional interference colors obtained by a spherical surface of a ballbearing observed by DIM, the resultant OPD distribution coincided well with that expected within a standard deviation of 12.8 nm.     

大孔径静态干涉光谱成像系统(LASIS)中实体Mach-Zehnder干涉仪加工误差容限分析

简要叙述了LASIS光谱成像系统的原理和仪器构成,针对LASIS光谱成像仪像方视场与干涉数据单边过零采样的要求,通过对实体Mach-Zehnder横向剪切干涉仪结构和光路进行分析,并对比Sagnac型横向剪切干涉仪的结构,研究了该干涉仪的附加光程差与加工误差的关系,给出了附加光程差公式和误差容限公式,对探测器阵面上光程差变化的非线性效应影响进行了分析和仿真。结果表明,相比Sagnac型横向剪切干涉仪,因实体Mach-Zehnder干涉仪的非共光路特点产生的附加光程差会导致探测器上的零光程位置的偏移,为保证过零单边采样的要求,需对干涉仪的尺寸误差进行严格约束,其中组成干涉仪的两块非对称五角棱镜非对称量的匹配误差小于0.02 mm;而探测器上光程差变化的非线性效应引起的光谱复原误差小于0.2%,基本可以忽略不计。