Iterative processing using a cavity with a phase conjugate error

Abstract

Iterative algorithms have become increasingly important for solving signal recovery/restoration as well as for solving recognition/selection problems. The optical implementation of iterative algorithms using a conventional feedback system is limited by the losses and by the accumulation of phase error at each round trip. A cavity that utilizes a phase conjugate mirror (PCM) offers a means to overcome these limitations. A PCM with gain can compensate for the cavity losses and restore the phase of the wave-front after each pair of round trips. It thus provides a regenerative feedback without accumulation of phase errors. Many image recovery schemes are equivalent to an equalization of the eigenvalues distribution. This process requires either a negative feedback, which is generally not possible to achieve in a cavity with a PCM, or a positive feedback with complementary operators in the feedback loop. A typical example of the latter is the Gerchberg algorithm. An optical system was built to implement the Gerchberg algorithm using an externally pumped BaTiO3 crystal as a PCM, and using complementary masks in the feedback loop. The recovery of simple band-limited images is demonstrated, and some of the limitations of the system are discussed.