Kotlarchyk M, Chen S H, Asano S
Appl Opt. 1979 Jul 15;18(14):2470-9. doi: 10.1364/AO.18.002470.
The quasi-elastic light scattering has become an established technique for a rapid and quantitative characterization of an average motility pattern of motile bacteria in suspensions. Essentially all interpretations of the measured light scattering intensities and spectra so far are based on the Rayleigh-Gans-Debye (RGD) approximation. Since the range of sizes of bacteria of interest is generally larger than the wavelength of light used in the measurement, one is not certain of the justification for the use of the RGD approximation. In this paper we formulate a method by which both the scattering intensity and the quasi-elastic light scattering spectra can be calculated from a rigorous scattering theory. For a specific application we study the case of bacteria Escherichia coli (about 1 microm in size) by using numerical solutions of the scattering field amplitudes from a prolate spheroid, which is known to simulate optical properties of the bacteria well. We have computed (1) polarized scattered light intensity vs scattering angle for a randomly oriented bacteria population; (2) polarized scattered field correlation functions for both a freely diffusing bacterium and for a bacterium undergoing a straight line motion in random directions and with a Maxwellian speed distribution; and (3) the corresponding depolarized scattered intensity and field correlation functions. In each case sensitivity of the result to variations of the index of refraction and size of the bacterium is investigated. The conclusion is that within a reasonable range of parameters applicable to E. coli, the accuracy of the RGD is good to within 10% at all angles for the properties (1) and (2), and the depolarized contributions in (3) are generally very small.
准弹性光散射已成为一种成熟的技术，用于快速、定量地表征悬浮液中运动细菌的平均运动模式。到目前为止，对所测量的光散射强度和光谱的几乎所有解释都是基于瑞利 - 甘斯 - 德拜（RGD）近似。由于感兴趣的细菌大小范围通常大于测量中使用的光波长，因此人们不确定使用RGD近似的合理性。在本文中，我们制定了一种方法，通过该方法可以从严格的散射理论计算散射强度和准弹性光散射光谱。对于一个特定的应用，我们通过使用长椭球体散射场振幅的数值解来研究大肠杆菌（大小约为1微米）的情况，已知该长椭球体能很好地模拟细菌的光学特性。我们计算了：（1）随机取向细菌群体的偏振散射光强度与散射角的关系；（2）自由扩散细菌以及在随机方向上以麦克斯韦速度分布做直线运动的细菌的偏振散射场相关函数；（3）相应的去偏振散射强度和场相关函数。在每种情况下，都研究了结果对细菌折射率和大小变化的敏感性。结论是，在适用于大肠杆菌的合理参数范围内，对于特性（1）和（2），RGD在所有角度的精度在10%以内，并且（3）中的去偏振贡献通常非常小。
