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A crystal of BaTiO_3 illuminated by a spatially periodic light intensity pattern will exhibit both uniform and spatially periodic photogalvanic currents. The modulated part of the intensity produces a spatially period photo-galvanic current, which creates a spatially periodic electric field in the crystal. This field, measured by two-beam coupling, is spatially in phase with the light pattern and increases monotonically with intensity, saturating at ∼450 V/cm. The spatially uniform photogalvanic current produced by the average light intensity creates a spatially uniform electric field, which is surprisingly small (≈10 V/cm) across a nominally open-circuited BaTiO_3 crystal at high optical intensity. We explain the observed intensity dependence of two-beam coupling by proposing that photogalvanic currents arise with different strengths from at least two trap levels in the crystal.