In this article, it has been pointed out that the pattern recognition is the representation transformation in pattern space. As it is well known, in Hilbert space, the representation transformation is realized by the unitary operator, so it is more suitable to use the optical method for pattern recognition. Further more, we have discussed the method with which one can construct the optical system only from the characteristic patterns, In reality, this problem is to realize the projector by optical method. We also have advanced the optimization method in 3.