Bessel beams. Read through Chapter 40 of Nelson. Focus specifically on Section 40.4 on
Bessel beams, and work through the derivation of the Bessel beam solution in Section 40.4.1,
taking notes and filling in any gaps. Then continue onto Section 40.4.2 and through the end
of the chapter. There isn't a particular problem to solve; rather, I want you to understand
why Bessel beams are interesting and why they might be useful in high resolution microscopy.
This Wikipedia article has some good figures and references.