Use properties like circular symmetry to convert 2D integrals into 1D Hankel Transforms (using Bessel functions). This is often the "shortcut" intended by the author.

Most early problems focus on the and its application to light propagation.

Joseph W. Goodman’s is the gold standard for understanding how light behaves as a mathematical system. While the third edition is celebrated for its clarity, the problems at the end of each chapter are notoriously challenging. They require a deep synthesis of linear systems theory, diffraction physics, and complex analysis.

Remember that film or sensors record intensity (

You’ll often be asked to find the field distribution at a distance from an aperture.

To find the OTF, you usually need to perform an autocorrelation of the pupil function. 5. Holography and Wavefront Reconstruction (Chapter 9)

4. Frequency Analysis of Optical Imaging Systems (Chapter 6)

is very large, the field is simply the Fourier transform of the input scaled by

Are you working on a or a particular problem number from Goodman's text that I can help clarify?