Volume gratings holographically written in a photorefractive material can be used for lensless image processing. This is because plane wave spectral components of an input image that are not at Bragg incidence are reflected with lower diffraction efficiency, so that higher spatial frequencies are transmitted. The dependence of edge enhancement on the spatial distribution of the grating, grating period, and angle of incidence of the incident optical field are investigated.
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.
A method for writing programmable volume phase gratings into photorefractive materials using visible wavelengths in a transmission geometry, and then subsequently probing these gratings in a reflection geometry using infrared (IR) wavelengths to achieve specific angles of reflection of the probe beam is analyzed. The programmable features of these gratings include grating spacing and tilt, or K-vector magnitude and orientation. Relationships have been derived between the incidence angles of the writing beams and the corresponding reflection angles of the IR probe beam. More specifically, for a fixed angle of incidence of the probe beam, two unique writing beam angles can be found which generate a grating with the correct spacing and tilt to reflect and steer the probe beam through a wide field of desired angles.
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