An absorption tomography instrument that is capable of acquiring 100 projections of 100 elements each in less than 200 ns is described. The instrument uses time-multiplexed, fiber-optic fan-beam sources that are sequentially activated in groups to reduce greatly the total number of detectors required for achieving a given resolution. The quantitative details required to tailor this instrument to a particular application are presented. A single-fiber prototype was used to verify the design and establish its sensitivity. The sensitivity is limited by laser-speckle noise. The fiber-optic fan-beam generator can produce an interdetector correlation of the projection noise, reducing the effect of this noise on the reconstruction. The noise is measured as a function of optic-fiber stability and size, laser bandwidth and mode stability, and detector size.