Image displacement based on phase-encoded reference joint fractional transform correlator

Abstract

In order to utilize the space of an input plane efficiently and make the optical structure more flexible, an image displacement measurement based on phase-encoded reference joint fractional transform correlator (PER-JFrTC) is proposed. We use a random phase mask to encode the reference image and overlay it with the target image forming the input image. Joint power spectrum (JPS) of the input image is obtained by Fourier transform and the resultant is encoded by the same phase mask. Then a fractional Fourier transform with an order p is applied to the phase-encoded JPS (PJPS), resulting in a correlation output with a sharp cross-correlation peak, which includes the displacement information between the reference and the target image. Contrast to displacement measurement based on traditional joint transform correlator (JTC), PER-JFrTC can use the space of the input plane efficiently and reduces the influence of the auto-correlation. Also the position of cross-correlation peak can be fixed arbitrarily according to the fractional order p as well as the optical set-up can be more flexible and easier to implement. Results based on digital computation show that PER-JFrTC could detect the displacement accurately and verify our proposal. A possible optical set-up is suggested.