Realistic transverse images of the proton charge and magnetization densities

We develop a technique, denoted as the finite radius approximation (FRA), that uses a two-dimensional version of the Nyquist-Shannon sampling theorem to determine transverse densities and their uncertainties from experimental quantities. Uncertainties arising from experimental uncertainties on the form factors and lack of measured data at high Q(2) are treated. A key feature of the FRA is that a form factor measured at a given value of Q(2) is related to a definite region in coordinate space. An exact relation between the FRA and the use of a Bessel series is derived. The proton Dirac form factor is sufficiently well known such that the transverse charge density is very accurately known except for transverse separations b less than about 0.1 fm. The Pauli form factor is well known to Q(2) of about 10 GeV2, and this allows a reasonable, but improvable, determination of the anomalous magnetic moment density.