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This paper describes the quantitative force mapping of micron-sized particles held in an optical vortex trap. We present a simple and efficient model, which accounts for the diffraction of the strongly localized optical field of the tightly focused laser beam, the spherical aberration introduced by the dielectric glass-to-water interface, employs the multidipole approximation for force calculations, and is able to reproduce, with quantitative agreement, the experimentally measured force map.