This paper is the brief summary of a series of papers published in China, in Acta Physica Sinica. The main question discussed here is the relation between the holographic optical system, the pattern transformation, and the pattern recognition. We have analyzed the following problems: (1) What kind of pattern transformation can be realized by the holographic optical system. (2) How to design a hologaphic optical system to realize an arbitrarily given unitary transformation by the usual optimization methods. (3) How to realize a projection operator by the holographic system in a practical way. The possibility of optical pattern recognition also has been discussed.