McKinnon A John
Canesis Network Ltd, Private Bag 4749, Christchurch, New Zealand.
J Cosmet Sci. 2004;55 Suppl:S37-51.
In a recent prize-winning study (1), Nagase et al. presented an analysis, using geometrical optics, of the perception of luster of hair based on the different directions of light reflection from the front and internal rear surfaces of the fiber. These two reflections, from cuticle cells inclined to the fiber axis, lead to a specular peak and an associated bright zone, displaced in reflection angle, which is associated with luster perception. This work built upon the experimental observations of Bustard and Smith (2). Both these papers employed a model of the fiber which may be described as a linear stack of cone frusta, defined by the exposed axial length and angle of inclination to the fiber axis of the cuticle scales. This fiber model is readily amenable to an alternative treatment, in which the model is recognized as a convolution of a cone frustum with a one-dimensional lattice. The scattering properties are then given in reciprocal (scattering) space as the product of the scattering function of a single frustum and that of the one-dimensional lattice. This problem was addressed, in principle, long ago by Bear and Bolduan (3,4) in work on the scattering of periodically distorted collagen fibrils. The author presents a related theory based on conical shells. It is demonstrated that the scattering from such a model extends over a number of non-equatorial reciprocal lattice planes and is able to reproduce, in a crudely quantitative fashion, several of the features of the experimentally observed scattering. A major benefit of this approach is that it gives a three-dimensional appreciation of light scattering by fibers.
在最近一项获奖研究中（1），长濑等人基于纤维前后表面不同的光反射方向，运用几何光学对头发光泽的感知进行了分析。角质形成细胞相对于纤维轴倾斜，这两种反射导致了一个镜面反射峰和一个相关的亮区，反射角发生了位移，这与光泽感知相关。这项工作建立在巴斯特德和史密斯（2）的实验观察基础之上。这两篇论文都采用了一种纤维模型，该模型可描述为由角质鳞片的暴露轴向长度和相对于纤维轴的倾斜角度所定义的一系列截头圆锥体的线性堆叠。这种纤维模型很容易采用另一种处理方式，即该模型被视为一个截头圆锥体与一维晶格的卷积。散射特性随后在倒易（散射）空间中表示为单个截头圆锥体的散射函数与一维晶格的散射函数的乘积。这个问题在原则上早在很久以前就由贝尔和博尔端（3,4）在关于周期性扭曲胶原纤维散射的研究中解决了。作者提出了一种基于圆锥壳的相关理论。结果表明，这种模型的散射扩展到多个非赤道倒易晶格平面，并且能够以粗略定量的方式重现实验观察到的散射的一些特征。这种方法的一个主要优点是它能对纤维的光散射进行三维理解。
