A fully phase image encryption technique that uses the double random-phase
encoding method is presented. The performance of this fully phase encryptio
n is compared with that of amplitude-based encryption in the presence of no
ise. Analytic bounds on the mean squared error for the decrypted images are
obtained. The accuracy of the theoretical error bounds is confirmed by com
paring them with the mean squared errors obtained by using numerical and st
atistical methods for actual images. Fully phase-based encryption shows bet
ter performance than amplitude-based encryption with respect to the mean-sq
uared-error metric. (C) 1999 Optical Society of America [S0740-3232(99)0070
8-5].