【正文】 or defined by where FT and IFT denote the Fourier transform and the inverse Fourier transform, fk(x,y)satisfies the convergent criterion, the iteration process stops, and and are the optimized distributions. Otherwise, the fk(x,y) is modified to satisfy the target image constraint as follows Then the modified function is transformed backward to generate both of the phasedistributions as follows where ang{ } denotes the phase extraction function. Then k is replaced by k+1 for the next iteration. It is shown in Eqs. 3(a) and 3(b) that both of the phasedistributions are modified in every iteration, accorded to the estimation of the target image in the present iteration. It ensures he algorithm converges with much faster speed and more consistent for the phasemasks. In general, the convergent criterion can be the MSE or the correlation coefficient between the iterated and the target image, which are defined by where M*N is the size of the image, and E[ ] denotes the mean of the image. The convergent behavior of this algorithm is similar to that of the conventional POCS. That is, the MSE reduces rapidly in the foremost few iterations, then it keeps reducing slowly till it reaches the minimum. Correspondingly, the correlation coefficient is expected to increase rapidly at first and keep increasing slowly till the stopping criterion is satisfied. In decryption, the determined phasemasks and (the keys or essentially, the encrypted images) are placed in the input and the Fourier plane, respectively, and then transformed into the output plane through the correlation defined by Eq. (1). The modulus of the output is the decrypted image. The CIFT algorithm retains the property of the conventional iteration algorithm, that is, the final phasedistributions of the masks are determined by the initializations of them. Therefore different initializations will result in different distributions of and . The target image cannot be decrypted if the keys mismatch (that is, the keys were generated from the different iteration process). In practical system, the phases of the masks are quantized to finite levels, which might reduce the solution space and introduce noise to the recovered image. To pensate the loss of the quality, the target image can be encoded into more phasemasks to provide additional freedom for solutions searching, which means to encrypt the image with a multistages (cascaded) correlator. From the point of view of security, this strategy significantly enlarges the key space (because more keys were generated), and makes the intrusion more difficult. Generally, the tstages correlation is defined asfor t is even, or for t is odd, where the matrix I(x, y) represents the input plane wave, and the superscript i (i=1, 2, …, t) denotes the serial number of the masks in the system. The phasedistributions of these masks may be deduced by analogous analysis for Eq. 3. 3. Computer simulation In this section we numerically demonstrate our general jet plane image of the size 128 180。 128 with 256 grayscale is used as the target image as shown in Fig. 2. The sizes of both phasemasks are same as the target image. And we suppose the optical system is illuminated by a plane wave with the amplitude equating to 1. The algorithm starts with the random initialization of the two phasemasks. Then the phase functions are transformed forward and backward alternatively through the correlation defined by Eqs. (1)(3). The algorithm converges very fast. The correlation coefficient reaches after about 3 iterations, then it keeps increasing slowly and finally reaches 1 within 20 iterations, correspondingly, the intensity distribution of the retrieved image is extremely close to that of the target image. Rigorously, the correlation coefficient does converge but not equate to 1 no matter how many iterations the algorithm runs because no analytic solutions for Eq. (1) can be found. Here we say it REACHES 1 just because the difference between the two images is beyond the limitation of the representational precision of the digital puter. Actually, the CIFT algorithm retains the errorreducing property of the conventional POCS algorithm. The MSE keeps reducing till the local (but not global) minimum is reached. One interesting character of the CIFT algorithm is that arbitrary initializations can generate recovered images with almost same quality, and result in different distributions for the masks, as shown in Fig. 3. Therefore the optimized phasemasks can be used as the keys of the security system. Only two phasemasks, which match each other and are located in the appropriate planes of the 4f architecture, respectively, can recover the target image. Otherwise, the output is meaningless. On the other hand, the keys and,are phaseonly functions, and have randomlike distributions as well. These characters may introduce a high level of security because they offer a property of anticounterfeiting. Another secure advantage of the CIFT algorithm arises in the application of authenticity verification. Instead of detecting a single correlation peak, the verification system based on the CIFT algorithm detects a significant output to determine whether or not to verify the input. So it is impossible to cause a false verification by directly illuminating the output plane bypassing the correlator because the intruder cannot generate the same pattern at the output without the knowledge of the correct phasedistributions. This is especially useful in the applications where high security is necessary. For the sake of security, the two masks are expected assigning to two persons, respectively. Therefore, the verification can be performed only under the authorizations of them both. If higher security is required, more phasemasks can be retrieved and assigned to more authorities so as to diminish the risk of being stolen of the keys. To pare with previous methods, the CIFT algorithm and the previous m