The recording and read-out of a volume speckle pattern is investigated for transmission geometry. The modulation of the 3D speckle grains appears when the image of a coherently illuminated random diffusor is formed onto the crystal by an optical system whose pupil consists of two identical holes. The intensity distribution of the speckle pattern imaged onto the BSO crystal leads to a space-charge field by drift of photocarriers, resulting in a refractive index modulation. The main features of diffracted read-out light at the Fourier plane are discussed.