Joint transform correlator optical encryption system: Extensions of the recorded encrypted signal and its inverse Fourier transform

• Analytical expressions for the extensions of the JTC intensity output were found.
• Numerical analysis of the JTC encryption system.
• Limiting factors of signal decryption were reported.

In this work we study the joint transform correlator setup, finding two analytical expressions for the extensions of the joint power spectrum and its inverse Fourier transform. We found that an optimum efficiency is reached, when the bandwidth of the key code is equal to the sum of the bandwidths of the image plus the random phase mask (RPM). The quality of the decryption is also affected by the ratio between the bandwidths of the RPM and the input image, being better as this ratio increases. In addition, the effect on the decrypted image when the detection area is lower than the encrypted signal extension was analyzed. We illustrate these results through several numerical examples.