Dihedral Fourier Analysis introduces the theory and applications necessary to study experimental data indexed by, or associated with, the points in a dihedral symmetry orbit.

This book looks at experimental data and analytical models indexed by certain dihedral rotations and reversals realized as vector fields. Its particular relevance as a research tool in areas such as optical and molecular biology statistics appears when formulated within the context of symmetry studies, which formally connects algebraic and statistical reasoning together in one methodology for data summary...

This advanced text introduces the foundations, interpretations, and data-analytic applications of symmetry studies in optical sciences. It discusses the underlying theory that supports symmetry studies by explaining the background of the symmetry studies in physics. It also demonstrates the usefulness of a unified view of algebra and symmetry studies to address data-analytic questions in optics. Computational tools and various examples from diverse areas of optical science are included, as is a brief review of finite group theory and distribution, quadratic forms, and elements of...