  We revise the symmetries of the Zernike polynomials that determine the Lie
algebra su(1,1) + su(1,1). We show how they induce discrete as well continuous
bases that coexist in the framework of rigged Hilbert spaces. We also discuss
some other interesting properties of Zernike polynomials and Zernike functions.
One of the interests of Zernike functions has been their applications in
optics. Here, we suggest that operators on the spaces of Zernike functions may
play a role in optical image processing.
