A lattice consisting of arrays of stationary turbulent liquid sheets has been proposed for the HYLIFE-II inertial fusion energy reactor design to allow target injection and driver-beam propagation while protecting the first walls from damaging radiation. Interference between these sheets and the driver beams must be avoided, placing strict requirements on sheet free-surface fluctuations. Experiments were performed on nearly prototypical liquid sheets to determine the surface ripple and the absolute position of the free surface with respect to the nozzle exit. Planar laser-induced fluorescence was used to directly image the free surface at downstream distances up to 25 times the jet thickness (i.e., short dimension) at the nozzle exit for Reynolds numbers up to 130 000. Surface ripple, calculated using two different methods, was compared for two nozzle and two flow straightener designs. The surface ripple was found to be <0.05 (versus the current HYLIFE-II requirement of 0.07). The mean thickness of the sheet was found to decrease with increasing x. This work should be useful in establishing the minimum distance between neighboring jets to avoid interference with the driver beams and to provide quantitative geometric data for shielding and neutronics analyses of such systems.