Spatially distributed two-photon excitation fluorescence in scattering media: Experiments and time-resolved Monte Carlo simulations

We report on measurements and Monte Carlo analysis of the spatial distribution of light in two-photon excitation fluorescence (TPEF) microscopy operating through scattering media. The axial profile of TPEF produced by a high numerical aperture microscope objective focusing through a tissue-like optical phantom at depths more than five photon mean-scattering lengths is studied. The measured profile is quantitatively interpreted with time-resolved Monte Carlo simulations that take into account the spatio-temporal distribution of the photons within the turbid medium under a femtosecond excitation regime. It is shown that considering only the ballistic photons leads to an under-estimation of the actual out-of-focus distribution of the fluorescence, whereas it is over-estimated when the ballistic and scattered photons are treated alike. Comparison of the in-focus signal to the overall out-of-focus background clearly pointed out that the signal-to-background ratio of TPEF microscopy images benefits from a shortening of the excitation pulses. Moreover, in homogeneously labeled specimen, the background is shown to overcome the signal at imaging depths of about five to six photon mean-scattering paths.     

Out-of-focus fluorescence collection in two-photon microscopy of scattering media

Imaging depth in two-photon microscopy is ultimately limited by the out-of-focus fluorescence background which is collected indistinctly with the useful in-focus signal in scattering samples. We report on a complete Monte Carlo analysis of the collection process in two-photon imaging of turbid media. Epifluorescence collection efficiency of the microscope is shown to vary significantly from point to point inside the scattering medium, to the detriment of the in-focus signal and in favor to the background, lowering the signal-to-background ratio in the image. Moreover we found that this ratio is almost independent of the collecting path field of view for situations where the background overcomes the signal. Assuming that the out-of-focus background can be subtracted to the image, the signal-to-noise ratio in two-photon microscopy is forecast to benefit from enlarging the collection field of view, with a gain roughly proportional to this enlargement for deep imaging. Asymptotic behaviors of the Monte Carlo simulations are quantitatively interpreted from ballistic and diffusive approximations.     

Alternative Oblique-Incidence Reflectometry for Measuring Tissue Optical Properties

To deduce the optical properties, the absorption coefficient SmU_aand reduced scattering coefficient μ’_s, of turbid medium, Lin et al. (Appl. Opt. 34 (1995) 2362) proposed an oblique incidence reflectometry in which the diffusion approximation was assumed. In this paper we propose an alternative method which does not assume the diffusion approximation but uses a Monte Carlo light propagation model. Two features are extracted from the diffuse reflectance distribution detected on the medium surface, and optical properties are then estimated by looking up the predetermined table generated by Monte Carlo simulations. The validity of the proposed method has been confirmed by computer simulations.     

Relationship between depth of a target in a turbid medium and fluorescence measured by a variable-aperture method

The relationship between the depth of a target in a turbid medium and the fluorescence ratio profile measured by use of illumination and collection apertures with variable diameters and the same optical path is shown. The forward problem was studied by Monte Carlo simulations of the propagation of fluorescent light through a theoretical model of a biologically relevant system for a range of aperture diameters. The curve of the fluorescence ratio as a function of the aperture diameter is characterized by a maximum/minimum point whose position shifts linearly with the depth of the target. Furthermore, the position of the maximum/minimum is observed to be insensitive to variations in the fluorescence efficiency and to the optical properties of the target layer or the entire medium.     

Determination of the Asymmetry Parameter and Scattering Coefficient of Turbid Media from Spatially Resolved Reflectance Measurements

We present a technique for determining the asymmetry parameter and scattering coefficient of turbid media from spatially resolved reflectance measurements. This technique will contribute to the development of medical applications in which it is necessary to predict the distribution and propagation of light in tissue. Based on Monte Carlo simulations, we derived correlations which relate the reduced scattering coefficient and the asymmetry parameter to the relative reflectance curve. Initial estimates of the optical properties are obtained from these correlations. Final values are obtained by adjusting the optical parameters and repeating the Monte Carlo simulations until the simulated reflectance pattern matches the measured reflectance pattern. Preliminary experimental results indicate that this technique can be used to determine the asymmetry parameter to within 10% and the reduced scattering coefficient to within 5%.     

Time-gated optical imaging through turbid media using stimulated Raman scattering: Studies on image contrast

In this paper, we report the development of experimental set-up for time-gated optical imaging through turbid media using stimulated Raman scattering. Our studies on the contrast of time-gated images show that for a given optical thickness, the image contrast is better for sample with lower scattering coefficient and higher physical thickness, and that the contrast improves with decreasing value of anisotropy parameters of the scatterers. These results are consistent with time-resolved Monte Carlo simulations.     

Imaging in turbid media using quasi-ballistic photons

We study by means of experiments and Monte Carlo simulations, the scattering of light in random media, to determine the distance up to which photons travel along almost undeviated paths within a scattering medium, and are therefore capable of casting a shadow of an opaque inclusion embedded within the medium. Such photons are isolated by polarisation discrimination wherein the plane of linear polarisation of the input light is continuously rotated and the polarisation preserving component of the emerging light is extracted by means of a Fourier transform. This technique is a software implementation of lock-in detection. We find that images may be recovered to a depth far in excess of that predicted by the diffusion theory of photon propagation. To understand our experimental results, we perform Monte Carlo simulations to model the random walk behaviour of the multiply scattered photons. We present a new definition of a diffusing photon in terms of the memory of its initial direction of propagation, which we then quantify in terms of an angular correlation function. This redefinition yields the penetration depth of the polarisation preserving photons. Based on these results, we have formulated a model to understand shadow formation in a turbid medium, the predictions of which are in good agreement with our experimental results.     

基于蒙特卡罗模拟的散射介质中后向光散射模型及分析应用

构建了内光源模型探讨散射介质中的光散射现象,利用蒙特卡罗方法研究了逃逸出组织的后向散射光子数随光子在组织内部发生的散射次数的分布关系,探讨了光源照明方式、辐射强度、接收方式、调制等参数的变化对后向散射的影响,结果表明后向散射光子的数量随散射次数的分布并非简单的单调递增或递减,而是一条先增大后减小出现峰值的曲线. 峰值位置、峰值大小及曲线形状与光源、探测方式、组织光学特性参数等有关. 关键词： 医用光学与生物技术 散射介质 后向散射 蒙特卡罗模拟     

Multiple passages of light through an absorption inhomogeneity in optical imaging of turbid media

Multiple passages of light through an absorption inhomogeneity of finite size deep within a turbid medium are analyzed for optical imaging by use of the self-energy diagram. The nonlinear correction becomes more important for an inhomogeneity of a larger size and with greater contrast in absorption with respect to the host background. The nonlinear correction factor agrees well with that from Monte Carlo simulations for cw light. The correction is approximately 50%-75% in the near infrared for an absorption inhomogeneity with the typical optical properties found in tissues and five times the size of the transport mean free path.     

Imaging optically scattering objects with ultrasound-modulated optical tomography

We show the feasibility of imaging objects having different optical scattering coefficients relative to the surrounding scattering medium using ultrasound-modulated optical tomography (UOT). While the spatial resolution depends on ultrasound parameters, the image contrast depends on the difference in scattering coefficient between the object and the surrounding medium. Experimental measurements obtained with a CCD-based speckle contrast detection scheme are in agreement with Monte Carlo simulations and analytical calculations. This study complements previous UOT experiments that demonstrated optical absorption contrast.     

Determination of g and mu using multiply scattered light in turbid media

We propose an inversion scheme to reconstruct the scattering coefficient mu and the anisotropy factor g that characterize the optical properties of a turbid medium. It is based on a theory for the scattering of light inside the medium from an angularly collimated light source. We demonstrate the feasibility of this method using light scattering data obtained from a Monte Carlo simulation.     

Path-length distribution and path-length-resolved Doppler measurements of multiply scattered photons by use of low-coherence interferometry

We report first results of measurements by low-coherence Doppler interferometry of the path-length distribution of photons undergoing multiple scattering in a highly turbid medium. We use a Mach-Zehnder interferometer with multimode graded-index fibers and a superluminescent diode as the light source. The path-length distribution is obtained by recording of the heterodyne fluctuations that arise from the Brownian motion of particles in an Intralipid suspension as a function of the optical path length. The experimental path-length distribution is in good agreement with predictions of Monte Carlo simulations. In the heterodyne spectrum, an increase of the mean Doppler frequency with path length is observed.     

Laser beam widening mechanisms in turbid media

We examine theoretically and experimentally the transverse intensity profile of a laser beam as it traverses through a turbid medium. By increasing the concentrations of milk in an aqueous solution we examine the transition from the weakly scattering to the diffusive regime. The experimental data of the transverse beam profiles for various scattering strengths are obtained in a non-contact geometry from digital images of the exit surface of the medium. The intensity distributions are compared with theoretical data obtained from Monte Carlo simulations.     

Effective point-spread function for fast image modeling and processing in microscopic imaging through turbid media

An effective point-spread function (EPSF) for microscopic imaging through turbid media is proposed and calculated. The EPSF incorporates the property of a microscope system as well as the scattering property of a turbid medium. We prove that the image of a thin object embedded in a turbid medium can be expressed by the convolution of the EPSF with an object function. With the help of the convolution relation, image modeling for 5, 000, 000 incident photons can be approximately 15 times faster than the direct Monte Carlo simulation method for a one-dimensional object and can be at least 2 orders of magnitude faster for a two-dimensional object.     

混浊介质多光子激发显微成像的快速模型

将二维点扩散函数（PSF）和蒙特卡罗方法相结合,引入了一种研究混浊介质显微成像的快速仿真模型,将该模型用于混浊介质的多光子激发（MPE）显微成像研究,极大地提高了模拟效率,与直接蒙特卡罗方法计算结果的比较证实了该方法的正确性和有效性,此外,一个计算实例说明了混混介质的多光子激发显微成像具有比共焦荧光显微成像更优的横向分辨率。     

基于快速蒙特卡罗的散射介质光学参量干涉测量方法研究

提出了一种散射介质光学参量的干涉测量方法. 在蒙特卡罗数值模拟的基础上引入聚焦高斯光源模型和基于比例缩放的压缩算法, 实现了对光子后向散射分布和干涉特性的快速模拟. 利用计算数据训练了前向人工神经网络进行了介质光学参量的反向求解. 实验中以脂肪乳注射剂和生物染色剂印度墨水组成的悬混液为样本, 通过光学干涉系统测量得到了后向散射光依赖于深度的干涉光强分布, 并对其中散射和吸收系数进行了反向计算. 所得结果能够正确反映散射和吸收系数与散射和吸收物质浓度之间的线性关系, 验证了该方法的可行性.     

Angularly resolved backscattering of light from turbid suspensions of dielectric spheres

An analytic expression for the angular dependency of light backscattered from turbid suspensions of dielectric spheres that accounts for multiple-scattering effects is developed. The multiple-scattering model expresses backscattered light as a convolution of the phase function and a kernel representing the effects of forward scattering, multiplied by the optical thickness of the slab. Excellent agreement between Monte Carlo simulations and the analytic expressions is demonstrated for optical thicknesses of 0.1-4. The results are important for goniometric sizing measurements of biological cells and cellular organelles using elastically backscattered light.     

Experimentally validated Raman Monte Carlo simulation for a cuboid object to obtain Raman spectroscopic signatures for hidden material

In conventional Raman spectroscopic measurements of liquids or surfaces the preferred geometry for detection of the Raman signal is the backscattering (or reflection) mode. For non‐transparent layered materials, sub‐surface Raman signals have been retrieved using spatially offset Raman spectroscopy (SORS), usually with light collection in the same plane as the point of excitation. However, as a result of multiple scattering in a turbid medium, Raman photons will be emitted in all directions. In this study, Monte Carlo simulations for a three‐dimensional layered sample with finite geometry have been performed to confirm the detectability of Raman signals at all angles and at all sides of the object. We considered a non‐transparent cuboid container (high density polyethylene) with explosive material (ammonium nitrate) inside. The simulation results were validated with experimental Raman intensities. Monte Carlo simulation results reveal that the ratio of sub‐surface to surface signals improves at geometries other than backscattering. In addition, we demonstrate through simulations the effects of the absorption and scattering coefficients of the layers, and that of the diameter of the excitation beam. The advantage of collecting light from all possible 4π angles, over other collection modes, is that this technique is not geometry specific and molecular identification of layers underneath non‐transparent surfaces can be obtained with minimal interference from the surface layer. To what extent all sides of the object will contribute to the total signal will depend on the absorption and scattering coefficients and the physical dimensions. Copyright © 2015 John Wiley & Sons, Ltd.     

大空间生物组织透射的Monte Carlo模拟方法的加速

乳腺等类型生物组织的透射Monte Carlo模拟(简称MC模拟)耗时很长,这主要是由于被模拟的组织较厚和Monte Carlo模拟自身统计特性引起的所需光子数量多造成的。针对光源与接收面在同一直线上,采用光纤接收透射光的模型进行分析,通过考虑生物组织自身的光学特性,进行了边界约束和有效后向散射次数的限制来缩短仿真时间,经过多次实验验证,以两次散射所到位置为分界,并充分利用组织光学参数计算约束边界,计算相对比较简单,同时考虑到入射与出射的实际情况进行微扩,从而得到的约束边界。对光学参数相同但厚度不同的组织进行仿真,分析进入同一位置光纤的光子数所发生后向散射次数,发现后向散射次数随着组织厚度与散射系数的增大而增大,随着吸收系数与各向异性因子的增大而减小,通过限定后向散射次数来节省时间。仿真结果表明,在传统计算机上,该方法能够显著缩短MC模拟的运算时间50%左右,尤其适用于较厚且边界较为复杂的高散射物质的MC模拟。该提速方法主要应用于光源与接收面处于同一直线,且生物组织较厚,散射系数较大的情况,能够有效节约仿真所需时间,有利于分析组织透射成像。     

基于快速蒙特卡罗的散射介质光学参量干涉测量方法研究

提出了一种散射介质光学参量的干涉测量方法.在蒙特卡罗数值模拟的基础上引入聚焦高斯光源模型和基于比例缩放的压缩算法,实现了对光子后向散射分布和干涉特性的快速模拟.利用计算数据训练了前向人工神经网络进行了介质光学参量的反向求解.实验中以脂肪乳注射剂和生物染色剂印度墨水组成的悬混液为样本,通过光学干涉系统测量得到了后向散射光依赖于深度的干涉光强分布,并对其中散射和吸收系数进行了反向计算.所得结果能够正确反映散射和吸收系数与散射和吸收物质浓度之间的线性关系,验证了该方法的可行性.