Spatial transfer functions of a volume reflection grating written in photorefractive lithium niobate have been derived and simulated. The Helmholtz equation has been solved analytically under the assumptions that the formed grating is lossless, only two waves exist in the solution, and the wave envelopes are slowly varying functions of space. The grating is assumed to be un-slanted, and the writing and reading wavelengths are equal to 514.5 nm in vacuum. Upon being probed in the reflection geometry, the reflected field experiences low pass spatial filtering, and the transmitted field experiences high-pass spatial filtering. The respective strength of this filtering is determined by the index modulation depth of the reflection grating. Simulation results show this 2D image processing capability of volume reflection gratings in photorefractive materials. In addition, a system has been constructed to test these results experimentally, with initial experimental evidence of spatial filtering.
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