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.