Fluctuation electron microscopy (FEM) has been used to study the nanoscale order in various amorphous materials. The method is explicitly sensitive to 3- and 4-body atomic correlation functions in amorphous materials; this is sufficient to establish the existence of structural order on the nanoscale, even when the radial distribution function extracted from diffraction data appears entirely amorphous. The variable resolution form of the technique can reveal the characteristic decay length over which topological order persists in amorphous materials. By changing the resolution, a characteristic length is obtained without the need for a priori knowledge of the structure. However, it remains a formidable challenge to invert the FEM data into a quantitative description of the structure that is free from error due to experimental noise and quantitative in both size and volume fraction. Here, we quantify the FEM method by (i) forward simulating the FEM data from a family of high quality atomistic a-Si models, (ii) reexamining the statistical origins of contributions to the variance due to artifacts, and (iii) comparing the measured experimental data with model simulations. From simulations at a fixed resolution, we show that the variance V("k") is a complex function of the size and volume fraction of the ordered regions present in the amorphous matrix. However, the "ratio" of the variance peaks as a function of diffraction vector "k" affords the size of the ordered regions; and the "magnitude" of the variance affords a quantitative measure of the volume fraction. From comparison of measured characteristic length with model simulations, we are able to estimate the size and volume fraction of ordered regions. The use of the STEM mode of FEM offers significant advantages in identifying artifacts in the variances. Artifacts, caused by non-idealities in the sample unrelated to nanoscale order, can easily dominate the measured variance, producing erroneous results. We show that reexamination and correction of the contributions of artifacts to variance is necessary to obtain an accurate and quantitative description of the structure of amorphous materials. Using variable resolution FEM we are able to extract a characteristic length of ordered regions in two different amorphous silicon samples. Having eliminated the noise contribution to the variance, we show here the first demonstration of a consistent characteristic length at all values of "k." The experimental results presented here are the first to be consistent with both FEM theory and simulations. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]