We describe a two-dimensional (2D) imaging technique for recording state-specific photofragment angle-velocity (theta,upsilon) distributions. In these experiments the photofragment images are recorded as 2D sections of the 3D angular distributions using state-specific ionization in a time-of-flight mass spectrometer. We compare this method to previous methods that record 2D projections of the 3D distribution. The 2D sections represent cartesian flux-velocity maps in the center of mass and are related to angle-velocity differential cross sections by a simple geometric factor. Two studies are highlighted. In the first, new results are presented for the A state photodissociation of CH3I to CH3+I. (theta,upsilon) images are presented for I atom in the P-2(3/2) and P-2(1/2) spin-orbit states following photodissociation at 266 and 304 nm. The principal result is detection of the weak perpendicular transitions to the (3)Q(1) state (at 304 nm) and the le state (at 266 nm) that underlie the strong parallel transition to the (3)Q(0) state. We also report the ratio of cross sections sigma(perpendicular to)/sigma(parallel to), the anisotropy and branching ratio for I(P-2(3/2)) and I(P-2(1/2)), and the (3)Q(0)-(1)Q surface crossing probability. In a second study the photodissociation of O-3 to O-2(upsilon)+O(P-3(j=2,1,0)) was measured. A bimodal anisotropic velocity distribution was measured for O(P-3) corresponding to maximum in the O-2(upsilon) vibrational distribution of upsilon=15 and 27, in general agreement with a previous measurement. The anisotropies of the high- and low-velocity components were measured to be beta approximate to 1.1 and 0.4, respectively.