Thin films are ubiquitous, with uses ranging from optoelectronics to antibacterial coatings. Unfortunately, precisely quantifying how the choice of substrate influences epitaxial growth remains an unsolved problem. Here, a novel thin film of holmium oxide with record-high paramagnetic saturation was grown on a variety of substrates. Conventional attempts to extract epitaxial information to characterize the growth mechanism were ineffective, due to the unique size regime of the product. Instead, a signal-processing inspired Fourier method was used to elucidate information on epitaxial ordering from purely topographical data, avoiding the pitfalls of atomic-level diffraction. Further, we define and utilize an inner product-based metric termed a q-score that can quantify the relative degree of ordering of epitaxial crystallites. The q-score provides a direct measure of epitaxy, enabling more quantitative future studies of thin film growth.