A synthetic discriminant function (SDF) fringe-adjusted joint transform correlator is proposed that is able to provide a high degree of image distortion invariance and classify different objects in the input scene. The SDF reference function, which is displayed alongside the input scene, is a linear combination of the training image set. An iterative algorithm is presented and utilized to obtain the linear combination coefficients from the nonlinear equations of the fringe-adjusted joint transform correlation (JTC) system. When compared with the SDF-based classical JTC and binary JTC, the SDF fringe-adjusted JTC delivers a better capability to give localized equal correlation peak heights for the same class of objects. Furthermore, when the input scene contains the different objects from the different classes of images, the SDF fringe-adjusted JTC is shown to efficiently classify the different target objects and reject the nontarget object in the input scene, whereas the SDF-based classical JTC and binary JTC fail to achieve this.