Mathematical Theory of Optics by Dr. Rudolf K. Luneburg stands as a monumental work in the field of optical theory, offering a rigorous and innovative approach to understanding instrumental optics through the lens of Maxwell's electromagnetic equations. First presented as a lecture series at Brown University in 1944, and later refined into these notes, Luneburg’s work connects geometrical optics and scalar diffraction optics as systematic extensions of electromagnetic theory. This unification was groundbreaking, as these disciplines were previously treated as distinct fields. Luneburg’s formulation of geometrical optics as exact solutions to Maxwell's equations, rather than simply as asymptotic approximations, redefined the theoretical landscape and laid the groundwork for future developments in optics.

The volume meticulously explores topics such as Hamilton's theory of geometrical optics, the mathematical treatment of optical aberrations, and the now-famous Luneburg lens, which has become a key component in microwave antenna technology. Later chapters delve into diffraction theory, introducing Luneburg diffraction integrals that extend classical results and address complex problems such as resolution improvements. With additional appendices and notes by prominent scholars, the book not only consolidates Luneburg's profound insights but also enriches the field with practical applications and theoretical advancements. Recognized as one of the most significant contributions to optical theory, this volume remains a foundational text for physicists and engineers engaged in advanced optical research.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1964.