Chapter 9 317 assemblies since it defines the geometric arrangement of the fibers. For example, one may wish to quantify hair that has undergone permanent waving treatment in order to monitor changes in hair shape. Likewise, hair relaxer treatments are employed to eliminate the curl of hair. Thus, one may seek to quantify the degree of straightening induced by relaxer treatment. We may also wish to measure the de-frizzing or de-volumizing capacity of a treatment. These fiber assembly properties may be quantified using image analysis techniques and two-dimensional Fourier transform. In image processing, Fourier transform is used to remove repeating patterns from images, such as halftones from scanned images or periodic noise that can present itself in images obtained with certain instruments—these include transmission electron microscopy and scanning probe microscopies.1 Fourier transform may also be used to perform fractal analysis and examine texture in images. Finally, it is also used to measure orientation and alignment in images. Specifically, image transform techniques have found particular use in the quantification of fiber alignment of textiles.49 Fourier transform decomposes an image from its spatial domain of intensities into a frequency domain with appropriate magnitude and phase values. In the frequency form of the image, gray scale intensities represent the magnitude of the various frequency components. Analysis is typically performed by using discrete Fourier transform: Eq. 9 where N is the number of sampled points along the function f(x), i is -1, and F(u) the transform function. It determines the rate at which an intensity transition occurs in a given direction in the image. In the case of hair, if fibers are predominantly oriented in one direction the spatial intensities in the perpendicular direction will be high. As an example of fiber straightening, Figure 10 contains images of African hair in its native state (a) and at increasing levels of