The duality between the well-known Zernike polynomial basis set and the Fourier-Bessel expansion of suitable functions on the radial unit interval is exploited to calculate Hankel transforms. In particular, the Hankel transform of simple truncated radial functions is observed to be exact, whereas more complicated functions may be evaluated with high numerical accuracy. The formulation also provides some general insight into the limitations of the Fourier-Bessel representation, especially for infinite-range Hankel transform pairs.