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The performance of fully phase- and amplitude-based encryption processors is analyzed. The effects of noise perturbations on the encrypted information are considered. A thresholding method of decryption that further reduces the mean-squared error (MSE) for the fully phase- and amplitude-based encryption processes is provided. The proposed thresholding scheme significantly improves the performance of fully phase- and amplitude-based encryption, as measured by the MSE metric. We obtain analytical MSE bounds when thresholding is used for both decryption methods, and we also present computer-simulation results. These results show that the fully phase-based method is more robust. We also give a formal proof of a conjecture about the decrypted distribution of distorted encrypted information. This allows the analytical bounds of the MSE to be extended to more general non-Gaussian, nonadditive, nonstationary distortions. Computer simulations support this extension.

A technique that combines the high speed and the high security of optical encryption with the advantages of electronic transmission, storage, and decryption is introduced. Digital phase-shifting interferometry is used for efficient recording of phase and amplitude information with an intensity recording device. The encryption is performed by use of two random phase codes, one in the object plane and another in the Fresnel domain, providing high security in the encrypted image and a key with many degrees of freedom. We describe how our technique can be adapted to encrypt either the Fraunhofer or the Fresnel diffraction pattern of the input. Electronic decryption can be performed with a one-step fast Fourier transform reconstruction procedure. Experimental results for both systems including a lensless setup are shown.

The binary joint transform correlator is a good discriminator with good noise tolerance. However, this is offset by its high sensitivity to distortions. Distortion tolerance can be improved by reducing the degree of nonlinearity applied to the joint power spectrum. However, this results in large reductions in noise tolerance and light efficiency. A technique to derive joint power spectrum windows is introduced that will optimally trade-off noise tolerance with distortion tolerance for the binary joint transform correlator. The window functions do not assume knowledge of the input or reference images, can easily be implemented both optically and digitally, and can be used in conjunction with a composite filter or an optical neural network. The feasibility of applying the windowed binary joint transform correlator to the problem of real-time face recognition is demonstrated by using real faces with synthetic distortions and noise. The results show that the windowed binary joint transform correlator is less sensitive to distortions and noise than is the k’th-lawnonlinear joint transform correlator. Encouraged by the insensitivity to signal-like background noise, further experiments treat the upper part of the faces as background noise. A feedback configuration of the windowed binary joint transform correlator is used to detect and segment the lower part of the faces. These experiments demonstrate the feasibility of using this configuration as a real-time facial gesture recognizer. © 1999 Society of Photo-Optical Instrumentation Engineers.

Disk harmonics are defined, and an explanation is given as to why they can be interpreted as the natural generalization of the Fourier basis set onto the unit disk. An existing statistical theory is used to show that a particular set of disk-harmonic coefficients is more suitable for describing images on the unit disk than Zernike or pseudo-Zernike moments are. Zernike moments have been applied to a wide range of problems. However, we concentrate on the problem of invariant pattern recognition and briefly indicate other problems where disk-harmonic coefficients are possibly useful. The effects that different pixel resolutions and discrete white noise have on the three moment or coefficient sets compared in this paper are briefly investigated experimentally.