Spatial and temporal coherence effects in interference microscopy and full‐field optical coherence tomography

Low‐coherence optical microscopy or optical coherence microscopy uses light with short coherence length. The well‐known case is: “white‐light interferometry”, which became recently more known as: “optical coherence tomography”. However, when lenses and microscope objectives are used to create interferometric images, in what is known classically as “interference microscopy” or today as “full‐field optical coherence tomography” the spatial coherence starts to play a critical role. In this article the coherence effects in low‐coherence optical microscopy are reviewed. As this technology is becoming increasingly publicized due to its importance in three‐dimensional imaging, particularly of scattering biological media and optical metrology, the understanding of the fundamental physics behind it is essential. The interplay between longitudinal spatial coherence and temporal coherence and the effects associated with them are discussed in detail particularly when high numerical apertures are used. An important conclusion of this study is that a high‐contrast, high‐resolution system for imaging of multilayered samples is the one that uses narrowband illumination and high‐NA objectives with an index‐matching fluid. Such a system, when combined with frequency‐domain operation, can reveal nearly real‐time three‐dimensional images, and is thus competitive with confocal microscopy.     

Periodic,quasi‐periodic,and random quadratic nonlinear photonic crystals

Quadratic nonlinear photonic crystals are materials in which the second order susceptibility χ⁽²⁾ is spatially modulated while the linear susceptibility remains constant. These structures are significantly different than the more common photonic crystals, in which the linear susceptibility is modulated. Nonlinear processes in nonlinear photonic crystals are governed by the phase matching requirements, which are determined by the reciprocal lattice of these crystals. Therefore, the modulation of the nonlinear susceptibility enables to engineer the spatial and spectral response in various three‐wave mixing processes. It enables to support the efficient generation of new optical frequencies at multiple directions. We analyze three wave mixing processes in nonlinear photonic crystals in which the modulation is either periodic, quasi‐periodic, radially symmetric or even random. We discuss both one‐dimensional and two‐dimensional modulations. In addition to harmonic generations, we outline several new possibilities for all‐optical control of the spatial and polarization properties of optical beams in specially designed nonlinear photonic crystals.     

Light transport and correlation length in a random laser

A random laser is a strongly disordered, laser‐active optical medium. The coherent laser feedback, which has been demonstrated experimentally to be present in these systems beyond doubt, requires the existence of spatially localized photonic quasimodes. However, the origin of these quasimodes has remained controversial. We develop an analytical theory for diffusive random lasers by coupling the transport theory of the disordered medium to the semiclassical laser rate equations, accounting for (coherent) stimulated and (incoherent) spontaneous emission. From the causality of wave propagation in an amplifying, diffusive medium we derive a novel length scale which we identify with the average mode radius of the lasing quasi‐modes. We show that truly localized modes do not exist in the system without photon number conservation. However, we find that causality in the amplifying medium implies the existence of a novel, finite intensity correlation length which we identify with the average mode volume of the lasing quasimodes. We show further that the surface of the laser‐active medium is crucial in order to stabilize a stationary lasing state. We solve the laser transport theory with appropriate surface boundary conditions to obtain the spatial distributions of the light intensity and of the occupation inversion. The dependence of the intensity correlation length on the pump rate agrees with experimental findings.     

Demonstration of temporal coherence,spatial coherence,and threshold effects in the molecular xenon laser

Stimulated emission has been observed at 1722 ± 1 Å in high-pressure xenon gas originating from the bound-free continuum of the Xe¹₂ molecule. This emission exhibits strong line narrowing, spatial coherence corresponding to a few times the diffraction limit, a sharp oscillation threshold, and an output time dependence radically different from the spontaneous emission observed without an optical cavity or below threshold. The confluence of all these observations is an explicit and unequivocal demonstration of a coherent stimulated emission process. Specific data detailing the pressure dependence of the stimulated output and results with rare-gas mixtures are given.     

用于实现散射介质中时间反演的数字相位共轭的相干性

抑制散射介质对光的散射,调控光在散射介质中的传输,是光通信、生物光子学、光镊等领域的重要课题.设计并实现了基于宽谱光源和数字相位共轭的可调控光在散射介质中传输的时间反演实验系统.实验获取了不同相干长度下物光和参考光束之间的光程差与干涉图样、相位图及时间反演信号之间的关系,分析了光源相干性对调控光在散射介质中传输的影响.实验结果表明,基于宽谱光源的相干特性和数字相位共轭技术,通过调节光程差能选择性获取同一散射角度及相同传输路径的光束的相对相位,再利用空间光调制器对参考光束进行调控,实现光束的反向传播,从而选择性实现对同一散射角度及相同传输路径的光的时间反演.     

扩展光源的时间和空间相干性效应分析

在干涉仪不同支路臂中分别加入透明光学层,将扩展光源入射到迈克尔逊干涉仪,观察光场的时间和空间相干现象,发现2种情况下出射光的时间和空间相干包络极值位置发生错位现象。论证了不同支路臂中的光学层可破坏干涉场中的光波相干特性,从而导致时间和空间相干性出现超前或滞后的空间位置互易效应。利用该效应,在2个入射光源条件下,可以得到一种测量光学样品的几何厚度和折射率的实验途径,并给出了相关的计算公式。     

Hybrid Rayleigh,Raman and two‐photon excited fluorescence spectral confocal microscopy of living cells

A hybrid fluorescence–Raman confocal microscopy platform is presented, which integrates low‐wavenumber‐resolution Raman imaging, Rayleigh scatter imaging and two‐photon fluorescence (TPE) spectral imaging, fast ‘amplitude‐only’ TPE‐fluorescence imaging and high‐spectral‐resolution Raman imaging. This multi‐dimensional fluorescence–Raman microscopy platform enables rapid imaging along the fluorescence emission and/or Rayleigh scatter dimensions. It is shown that optical contrast in these images can be used to select an area of interest prior to subsequent investigation with high spatially and spectrally resolved Raman imaging. This new microscopy platform combines the strengths of Raman ‘chemical’ imaging with light scattering microscopy and fluorescence microscopy and provides new modes of correlative light microscopy. Simultaneous acquisition of TPE hyperspectral fluorescence imaging and Raman imaging illustrates spatial relationships of fluorophores, water, lipid and protein in cells. The fluorescence–Raman microscope is demonstrated in an application to living human bone marrow stromal stem cells. Copyright © 2009 John Wiley & Sons, Ltd.     

Coherence properties of individual femtosecond pulses of an x-ray free-electron laser

Measurements of the spatial and temporal coherence of single, femtosecond x-ray pulses generated by the first hard x-ray free-electron laser, the Linac Coherent Light Source, are presented. Single-shot measurements were performed at 780?eV x-ray photon energy using apertures containing double pinholes in "diffract-and-destroy" mode. We determined a coherence length of 17 μm in the vertical direction, which is approximately the size of the focused Linac Coherent Light Source beam in the same direction. The analysis of the diffraction patterns produced by the pinholes with the largest separation yields an estimate of the temporal coherence time of 0.55?fs. We find that the total degree of transverse coherence is 56% and that the x-ray pulses are adequately described by two transverse coherent modes in each direction. This leads us to the conclusion that 78% of the total power is contained in the dominant mode.     

Photon statistics of laserlike emission from polymeric scattering gain media

The coherent properties of the temporally and spectrally narrowed emission of laser-induced fluorescence of organic dyes hosted inside artificial scattering matrices (random lasers) were investigated. The excitation source was a frequency-doubled 200-fs pulsed laser emitting at 400 nm. Spectral and temporal features were simultaneously recorded with a spectrograph and a streak camera operating in photon-counting mode. Photon-number distributions were thus created. The temporal coherence of the laserlike emission above and below the excitation energy threshold was investigated from the photon-number distribution that was obtained.     

Fast three‐dimensional chemical imaging by interferometric multiplex coherent anti‐Stokes Raman scattering microscopy

We report significant improvements in both signal sensitivity and imaging speed of Fourier transform spectral interferometry coherent anti‐Stokes Raman scattering (FTSI‐CARS) microscopy. With a help of an apodization function in the signal retrieval process, background due to the spectral change of nonresonant signals is eliminated. We experimentally verify that the sensitivity of the improved method is nearly shot‐noise‐limited. The current maximum detection sensitivity is ∼10 mM of aqueous sulfate ions, which correspond to ∼10⁶ oscillators in the microscopy focal volume. Operating the charge‐coupled device (CCD) in the crop mode increases the image acquisition speed by more than ten times. A vibrational hyperspectral image of a polymer sample with 100 × 100 pixel can be obtained within 3 s. With the improved sensitivity and speed, we also perform three‐dimensional volume imaging. Superior chemical selectivity is demonstrated with a mixture of two different oil droplets, which have identical vibrational peak positions but different relative peak ratios. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

Partially coherent optical waves in random gradient fibres

The excitation characteristics and spatial coherence of partially coherent optical waves in gradient fibres are demonstrated for incident light waves radiated from semiconductor lasers and light emitting diodes. Lower modes are efficiently excited in the case of coherent laser beams, while incident waves of low coherence such as lightwaves of LEDs excite higher modes. Pulse propagation of partially coherent optical waves in dispersive gradient fibres is also discussed for random index fluctuations. Mode coupled equations for temporal correlation functions of the electric field that are generalizations of coupled power equations are found. Mode filtering and pulse improvement with a lossy inhomogeneous cladding are described.     

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.     

Experimental generation of a partially coherent Laguerre–Gaussian beam

We report experimental generation of a partially coherent Laguerre–Gaussian beam with mode orders 0 and l (i.e., LG_0l beam) using a rotating ground-glass plate and a spatial light modulator. Focusing properties of the generated beam are studied both theoretically and experimentally. It is found that the focused intensity of the LG_0l beam is shaped through varying the initial spatial coherence, and our experimental results agree well with the theoretical predictions. Our results will be useful in particle trapping and free-space optical communications.     

The effects of longitudinal spatial coherence of light in interference experiments

The physical conditions needed to observe the effects of longitudinal spatial coherence of emission of an extended thermal source are considered. Results of experiments on observation of interference pulses of longitudinal spatial coherence, performed using a scanning longitudinal shearing Michelson interferometer, are presented. Distinctions between the effects of temporal and longitudinal spatial coherence of light are established. It is shown that the presence of a noncompensated optical layer in one of the arms of the interferometer makes the interference pulses of the temporal and spatial coherence of light shift relative to each other (“recession”).     

Spectral-domain optical coherence phase and multiphoton microscopy

We describe simultaneous quantitative phase contrast and multiphoton fluorescence imaging by combined spectral-domain optical coherence phase and multiphoton microscopy. The instrument employs two light sources for efficient optical coherence microscopic and multiphoton imaging and can generate structural and functional images of transparent specimens in the epidirection. Phase contrast imaging exhibits spatial and temporal phase stability in the subnanometer range. We also demonstrate the visualization of actin filaments in a fixed cell specimen, which is confirmed by simultaneous multiphoton fluorescence imaging.     

Apparent transfer function for partially coherent optical information processing

In this paper, the general formulations of the apparent transfer function for the partially coherent optical processor will be derived. Although these formulas show that the apparent transfer function is dependent upon the degree of spatial and temporal coherence, there is actually more variability in the spatial coherence. We note that the obtained formulas may also be used as a criterion in the selection of source size and spectral bandwidth of an incoherent light source. Thus a specific optical information processing operation can be carried out with an incoherent source.     

High‐efficiency coherence‐preserving harmonic rejection with crystal optics

This work reports a harmonic‐rejection scheme based on the combination of Si(111) monochromator and Si(220) harmonic‐rejection crystal optics. This approach is of importance to a wide range of X‐ray applications in all three major branches of modern X‐ray science (scattering, spectroscopy, imaging) based at major facilities, and especially relevant to the capabilities offered by the new diffraction‐limited storage rings. It was demonstrated both theoretically and experimentally that, when used with a synchrotron undulator source over a broad range of X‐ray energies of interest, the harmonic‐rejection crystals transmit the incident harmonic X‐rays on the order of 10^?6. Considering the flux ratio of fundamental and harmonic X‐rays in the incident beam, this scheme achieves a total flux ratio of harmonic radiation to fundamental radiation on the order of 10^?10. The spatial coherence of the undulator beam is preserved in the transmitted fundamental radiation while the harmonic radiation is suppressed, making this scheme suitable not only for current third‐generation synchrotron sources but also for the new diffraction‐limited storage rings where coherence preservation is an even higher priority. Compared with conventional harmonic‐rejection mirrors, where coherence is poorly preserved and harmonic rejection is less effective, this scheme has the added advantage of lower cost and footprint. This approach has been successfully utilized at the ultra‐small‐angle X‐ray scattering instrument at the Advanced Photon Source for scattering, imaging and coherent X‐ray photon correlation spectroscopy experiments. With minor modification, the harmonic rejection can be improved by a further five orders of magnitude, enabling even more performance capabilities.     

非均匀关联径向偏振部分相干光的产生

从理论和实验两方面对非均匀关联径向偏振部分相干光的产生进行了研究.理论上,基于相位关联与相干度的联系,推导出了非均匀关联径向偏振部分相干光的2×2阶交叉谱密度矩阵及相干度分布.实验上,利用一个相位型液晶空间光调制器的不同区域,对入射的完全相干的径向偏振光的两个正交偏振分量分别加载随机相位调制,并实验测量了这种光束的相干度分布及其对光强分布的影响.实验结果验证了光束相干度的非均匀关联结构,并且通过改变随机相位的高斯调制半宽可以改变光束的相干性分布.研究表明,随着随机相位的高斯调制半宽的增加,光束中两点间的相干度逐渐减小,其光强分布由圆环状逐渐变化为类平顶的光强分布.这种非均匀关联的径向偏振部分相干光在激光微操纵和材料加工等领域具有一定的潜在应用价值.     

计数率和分辨时间对光场统计性质测量的影响——单探测器直接测量的实验分析

利用工作在盖革(Geiger)模式下的单光子探测器(single-photon-counting module, SPCM)，采取单个探测器直接对光子计数的方法，对相干光场及热光场的光子数统计性质进行了测量和分析. 通过改变计数率，调整分辨时间，系统地研究了光场二阶相干度测量值受实验条件的影响. 结果表明，在综合考虑系统中的各种因素对测量影响的情况下，通过选择合适的测试条件，可以利用单个单光子探测器直接探测的方法快速确定一个待测光场的二阶相干度. 实验表明在实测计数率为109 kc/s，分辨时间范围为2⁸ns—2¹²ns的条件下，该系统能很好地揭示相干光场和热光场的光子统计性质. 关键词： 光子统计 单光子探测器 二阶相干度