To solve the problems in the third edition, you must be fluent in several foundational mathematical operations. Most student errors stem from calculus mistakes rather than a misunderstanding of the physics. 1. Two-Dimensional Fourier Transforms Optical fields exist in two dimensions (
Deriving the boundary conditions for a wave passing through an aperture.
Understanding MRI data reconstruction and optical coherence tomography (OCT).
). Holography problems test your ability to calculate the reconstruction of images from interference patterns recorded on film. 3. Recommended Approach to Difficult Problems To solve the problems in the third edition,
f(x) = exp(-x^2)
Applying the scaling theorem, shift theorem, and Parseval’s theorem in two dimensions. Common Functions: Shifting between spatial coordinates and spatial frequencies functions. 2. Scalar Diffraction Theory
According to commentary from the author and educational reviews, the following problems are considered particularly instructive for mastering Fourier optics: Holography problems test your ability to calculate the
$M = -\fracd_id_o$
Many problems feature circular or square symmetry. If a problem has circular symmetry, instantly convert your Cartesian coordinates to polar coordinates and utilize the Fourier-Bessel (Hankel) transform instead.
Solution: The Fourier transform of $f(x)$ is given by: If a problem has circular symmetry
You will encounter a recurring cast of functions across all problem sets. Ensure you know their exact definitions and transform pairs:
When stuck on a problem from the 3rd edition, use this engineering workflow:
Master Fourier Optics: A Guide to Intro to Fourier Optics 3rd Edition Solutions