We report a mathematical formulation that successfully describes the holographic photocurrent that is produced, in strongly absorbing photorefractive materials, by the action of a pattern of interference fringes of light vibrating sinusoidally with large amplitude. The large vibrating amplitude produces a sensible enhancement of the photocurrent signal and in this way facilitates measurements. We also show that taking account of the bulk light absorption of the sample is essential for adequately describing the experiment. We measure the first temporal harmonic of the photocurrent, without an externally applied field, as a function of the amplitude and the temporal frequency of the vibrating pattern of fringes and show that these data fit our theoretical model well. From this fit we are able to determine some material parameters for pure and doped photorefractive Bi12TiO20 crystals. © 2002 Optical Society of America.