Analysis of the phase conjugation reflectivity for volume speckle patterns in a BSO crystal

When a diffusing surface is illuminated by a coherent light beam, speckles are formed in the space in front of the surface. These speckles have a three-dimensional structure. However, in spite of this three-dimensional nature, two-dimensional recording media are usually used for applications in optical metrology. Since 80's, the photorefractive crystals were widely employed for optical processing and metrology in particular concerning speckle applications. Furthermore, we have taken advantage of the three-dimensional photorefractive medium to store three-dimensional speckle distributions. In our case, the phase conjugation theory, within the transmission grating approximation, is applied to study the phase conjugation reflectivity when speckle patterns are stored in a BSO photorefractive crystal. It is numerically shown that the beam coupling theory is adequate to explain the reflectivity behavior in terms of the average modulation of the registered speckles and the average speckle length. The knowledge of the reflectivity behavior when speckle patterns are considered, allows to optimize interferometric system based on real-time speckle pattern correlation and to improve speckle applications in optical signal processing.