Optimal key mask design for optical encryption based on joint transform correlator architecture

We examine perfect recovery in the optical encryption system based on joint transform correlator architecture, which requires the key mask to be space-limited and phase-only in the frequency domain. Accordingly, a discrete sinc function interpolation is used to generate a binary phase difference mask for image encryption and decryption. Furthermore, the optimal binary phase difference mask is derived from the interpolation process best approximating the ideal sinc function interpolation. The simulation results confirm better recovery of the decrypted image for applying the proposed key masks to the optical encryption system. Especially, the optimal binary phase difference mask significantly enhances the recovery performance.     

Correlator-aided alignment of phase key in encrypted holographic storage systems

An encrypted holographic scheme with a compact alignment system for a phase key is proposed. Alignment for a phase key is performed by a holographic correlator. A filter in the correlator system contains the phase information used for encryption. Thus, it can be used to check the authorization of the phase key. Owing to the shift-invariant property of the holographic correlator, the location of the correlation peak is highly related to the alignment of the phase key. Therefore, the phase key can be repositioned on the desired location by searching for the specific position of the correlation peak. With the help of the correlator, alignment of the phase key can be done in 1 min. Experimental results using a correlator system in support of our proposed idea are demonstrated as well.     

Fractional Fourier transform for off-axis elliptical Gaussian beams

The fractional Fourier transform (FRT) is applied to off-axis elliptical Gaussian beam (EGB). An analytical formula is derived for the FRT of off-axis EGB in terms of the tensor method. The corresponding tensor ABCD law for performing the FRT of off-axis EGB is also obtained. By using the derived formulae, numerical examples are given. The derived formulae provide a convenient way for analyzing and calculating the FRT of off-axis EGB.     

Transformation of a hollow Gaussian beam into a ring-shaped beam using a phase aperture

Propagation of a hollow Gaussian beam diffracted by a circular phase aperture is studied without making the paraxial approximation. The analytical expression of the intensity of the apertured hollow Gaussian beam is presented in the far field. The influences of the truncation parameter and the order of hollow Gaussian beam on the intensity distributions are discussed. It is shown that a circular ?-phase aperture can be used to transform a hollow Gaussian beam into a ring-shaped beam in the far field with the appropriate parameters.     

Conceptual design of a phase-shifting telescope-interferometer

This paper deals with the theoretical principle and optical design of a phase-shifting telescope-interferometer. What is called a “telescope-interferometer” (T-I) is indeed a novel, recently proposed wavefront error (WFE) sensing technique, whose basic idea consists in combining the main pupil of a telescope with a second, off-axis reference arm. Then a weak modulation of the point spread function (PSF) is generated at the focal plane, allowing for direct phase measurements. We propose a notable improvement of the method, inspired from classical principles of phase-shifting interferometry. Herein are presented the alternative principle and its achievable measurement accuracy. The technique shows high performance excepted on narrow areas located near the pupil boundary. It is applicable to both ground or space telescopes and is suitable for the co-phasing of segmented mirrors, which is of prime importance in view of future giant telescope projects.     

Rotation-invariant pattern recognition using morphological phase-only correlation

We present a rotation-invariant nonlinear correlator based on the circular harmonic filter (CHF) and the previously proposed morphological phase-only correlator (MPC) [Q. Wang, S. Liu, Opt. Commun. 244 (2005) 93]. We refer to this correlator as a rotation-invariant MPC (RIMPC). Through computer simulation, we compare the output results of RIMPC with those of rotation-invariant MC (RIMC) and CHF when input scene is corrupted by salt-and-pepper noise, white additive Gaussian noise and cluttered background. Our results show that RIMPC yields higher discriminability, sharper and higher correlation peaks and displays better stability against the above three kinds of noise than do the RIMC and common CHF.     

First-order optical systems with real eigenvalues

It is shown that a lossless first-order optical system whose real symplectic ray transformation matrix can be diagonalized and has only real eigenvalues, is similar to a separable hyperbolic expander in the sense that the respective ray transformation matrices are related by means of a similarity transformation. Moreover, it is shown how eigenfunctions of such a system can be determined, based on the fact that simple powers are eigenfunctions of a separable magnifier. As an example, a set of eigenfunctions of a hyperbolic expander is determined and the resemblance between these functions and the well-known Hermite-Gauss modes is exploited.     

Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering

We report a method for generation of arbitrary shape and array of optical vortices by use of a superposition of coherent elementary vortices based on helical phase spatial filtering in spatial frequency domain. In this method, a helical phase spatial filter (HPSF) is placed in the spatial frequency plane of a 4-f imaging processing system. We demonstrated that the output field distribution represents the convolution between the input field and an elementary vortex field introduced by the HPSF, which results in a special shape or array of optical vortices determined by the “degenerate” properties of coherent elementary vortices and the distribution formats of the input field.     

Necessity analyses of phase masks in joint fractional Fourier transform correlator

In this paper, the mathematical expressions and the particularities of the joint fractional Fourier transform correlator (JFRTC) are detailedly analyzed. In a JFRTC, the distance between the two fractional correlation peaks can be adjusted flexibly by shifting the fractional orders. However, the intensity of the fractional correlation peaks decreases rapidly as the first fractional order p₁ drops. The former property is very useful in a practical recognition system, but the latter one seriously reduces the recognition sensitivity of a JFRTC. For this reason, phase masks should be added at the input plane of the JFRTC to enhance the intensities of the fractional correlation peaks and effectively overcome the default. Compared with the existing JFRTC with single phase modulation, a JFRTC with double phase modulation is suggested to more flexibly improve the performance of a JFRTC.