This course provides a crucial introduction to linear operators and Fourier analysis with an emphasis on applications in imaging, diffraction, and optical sciences and engineering. The assumptions of linear systems, definition of an impulse response function, and eigenanalysis are introduced. Discrete representation of continuous functions and linear decompositions using basis sets are explained in the framework of linear operator theory. Relevant properties and theorems of Fourier transforms are covered in depth. Diffraction integrals and linear image formation are quantified using relevant wavefront approximations and Fourier transforms.
