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The interference theory is developed for of the phase conjugate Michelson interferometer in which its ordinary mirrors are replaced by a single externally pumped phase conjugate mirror. According to the theory, it was found that for an interferometer with two equal arms, the path length difference depends solely on the initial alignment of the two input beams, and the vertical alignment readout. Small vertical misalignments in the readout beam by mrad causes a huge change in the phase difference in the phase between the two interferometer arms beam. The phase difference is proportional to the interferometer arm lengths. The overlap between the phase conjugate beams is not affected by the interferometer beam alignment. The interferometer is proposed for nondestructive testing and the design all optical logic and associated fuzzy logic for ultrafast optical pattern recognition.
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