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A method to reconstruct full three-dimensional photofragment distributions from their two-dimensional (2D) projection onto a detection plane is presented, for processes in which the expanding Newton sphere has cylindrical symmetry around an axis parallel to the projection plane. The method is based on: (1) onion-peeling in polar coordinates [Zhao etal, Rev. Sci. Instrum. 73, 3044 (2002)] in which the contribution to the 2D projection from events outside the plane bisecting the Newton sphere are subtracted in polar coordinates at incrementally decreasing radii; and (2) ideas borrowed from the basis set expansion (pBASEX) method in polar coordinates [Garcia etal, Rev. Sci. Instrum. 75, 4989 (2004)], which we use to generate 2D projections at each incremental radius for the subtraction. Our method is as good as the pBASEX method in terms of accuracy, is devoid of centerline noise common to reconstruction methods employing Cartesian coordinates; and it is computationally cheap allowing images to be reconstructed as they are being acquired in a typical imaging experiment.