Abstract: The synthetic discriminant function (SDF) algorithm based on binary joint transform correlation is introduced. The iterative algorithm was further optimized with SDF obtained by the equally related peaks and the GramSchmidt expansion to acquire the SDF suitable for binary joint transform correlator. The synthetic discriminant filter made up of the algorithm has the advantages of high relevant peak value, sharp relevant peak, and can recognize the rotating images. The computer simulation shows that the signal-to-noise ratio, light efficiency, relevant peak sharpness and recognition ability of this correlator are increased, and the rotational invariant optical mode recognition with high recognizability is realized.