Joint Extended Fractional Fourier Transform Correlator

Optical correlation systems have been successfully developed for character recognition and target detection. Two common correlation systems, matched filtering correlator (MFC) and joint transform correlator (JTC), have been extensively investigated. Both of these systems can be implemented for real-time operation by incorporating a sensor, spatial light modulators, and a computer. But the joint transform correlation is more easily operated in the real-time mode by using the spatial light modulators as the input device and the Fourier plane converter, because it is necessary to fabricate a filter beforehand and to require extremely precise alignment. As an important real-time image processing system, it is applied to the remote sensing, the medicine, the military, and the industrial automatic check and so on. Some people proposed many methods to improve the performance of the JTC. In recent years, the fractional Fourier transform (FRT) was presented and has attracted a lot of attention for the optical information processing. Based on the FRT, some people proposed a fractional correlation and a joint fractional Fourier transform correlator (JFRTC). The JFRTC has some advantages. First it has sharper fractional correlation peak. Second the fractional order can adjust the position and the maximum value of the cross-correlation peaks. Third the size of required lenses is small. Forth it has high light efficiency. In addition, the extended fractional Fourier transform (EFRT) is a generalization of the FRT, and has more parameters and wider fractional domain. It was used in the field of optical information processing. Based on the EFRT and the JFRTC, we propose a joint extended fractional Fourier transform correlator (JEFRTC). Owing to more parameters, it is freer to adjust the position and intensity of cross-correlation peak. So we can obtain the better cross-correlation peak. We have mainly investigated three aspects of the JEFRTC as follows:...