A half-blind color image hiding and encryption method in fractional Fourier domains

We have proposed a new technique for digital image encryption and hiding based on fractional Fourier transforms with double random phases. An original hidden image is encrypted two times and the keys are increased to strengthen information protection. Color image hiding and encryption with wavelength multiplexing is proposed by embedding and encryption in R, G and B three channels. The robustness against occlusion attacks and noise attacks are analyzed. And computer simulations are presented with the corresponding results.     

Optical encryption with a reference wave in a joint transform correlator architecture

In this work we introduce a digital holographic configuration in a Joint Transform Correlator (JTC) architecture for encryption purposes. Conceptually, it is a Mach-Zender interferometer, with a JTC in one arm and a reference wave in the other. We describe the practical implementation of this architecture, along with experimental results that support the proposal. We analyze the noise influence caused by intensity saturation during image capture, and this information allows us a filtering process to reduce the information to be handled, with a consequent increase in the speed of the total procedure.     

Multiple-encoding retrieval for optical security

We propose a method for image encryption by multiple-step random phase encoding with an undercover multiplexing operation. The true image is stored in a multiple record we call encodegram; and then we can reconstruct it by the use of the appropriate random phase masks and a retrieval protocol. To increase the security of the true hidden image and confuse unauthorized receivers, we add to the encodegram an encoded fake image with different content. This fake image has only a small effect on the retrieval of the true hidden image, owing to the specific property of this protocol. In the decryption step, we can reveal the true image by applying the inverse protocol to two cyphertexts, one the encodegram containing the true image along with the fake image; and the other helping to get the random phase key to achieve the true image. Computer simulations verify the validity of this method for image encryption. Digital implementation of the method makes it particularly suitable for the remote transmission of information.     

Double-image encryption based on iterative gyrator transform

A novel double-image encryption algorithm is proposed, which can simultaneously encrypt two images into a single one as the amplitude of gyrator transform with two different groups of angles. The two original images can be retrieved independently by gyrator transforms with two different groups of angles, one common phase mask, and two different private phase masks. The proposed approach can enlarge the key space, achieve faster convergence in iterative process, and avoid cross-talk between two images in reconstruction. Numerical simulations are presented to verify its validity and efficiency.     

Color image encoding in dual fractional Fourier-wavelet domain with random phases

A new cryptology in dual fractional Fourier-wavelet domain is proposed in this paper, which is calculated by discrete fractional Fourier transform and wavelet decomposition. Different random phases are used in different wavelet subbands in encryption. A new color image encoding method is also presented with basic color decomposition and encryption respectively. All the keys, including random phases and fractional orders in R, G and B three channels, should be correctly used in decryption, otherwise people cannot obtain the totally correct information. Some numerical simulations are presented to demonstrate the possibility of the method. It would have widely potential applications in digital color image processing and protection.     

A discrete fractional angular transform

A new discrete fractional transform defined by two parameters (angle and fractional order) is presented. All eigenvectors of the transform are obtained by an angle using recursion method. This transform is named as discrete fractional angular transform (DFAT). The computational load of kernel matrix of the DFAT is minimum than all other transforms with fractional order. This characteristics has very important practical applications in signal and image processing. Numerical results and the mathematical properties of this transform are also given. As fractional Fourier transform, this transform can be applied in one and two dimensional signal processing.     

Precision of degree of polarization estimation in the presence of additive Gaussian detector noise

We address the problem of degree of polarization (DOP) estimation in images limited by additive Gaussian detector noise. We derive and analyze the probability density function (PDF) of the pixelwise DOP estimate, which is shown to have significantly different statistical properties than when noise is Gamma distributed (speckle). We then determine the Cramer-Rao Lower Bound and the maximum likelihood estimator of the DOP. We deduce from this study practical solutions for characterizing and reducing the noise in these images.     

Phase-coded aperture for optical imaging

For the optical spectrum region, we describe a novel phase-coded aperture imaging system that can be used in a computational imaging camera. The optical design includes a phase-only screen followed by a detector array. A specific diffraction pattern forms at the detector array when the wavefront from a point source object passes through the phase screen. Since diffraction effects cannot be ignored in the optical regime, an iterative phase retrieval method is used to calculate the phase coded screen. Correlation type processing can be applied for the image recovery. Computer simulation results are presented to illustrate the excellent imaging performance of this camera.     

A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains

Based on 1-D fractional Fourier transform, we proposed an image encryption algorithm in order to hide two images simultaneously. When the fractional order is closed to 1, most energy in frequency domain is centralized in the center part of spectrum. The image can be recovered acceptable by using a half of spectrum, which locates in the middle part at x-direction or y-direction. Cutting operation is employed in order to combine two spectra. Double random phase encoding is employed for image encryption. The corresponding numerical simulations are performed to demonstrate the validity and efficiency of the algorithm.     

Multiple image encryption using an aperture-modulated optical system

A multiple image cryptosystem based on different apertures in an optical set-up under a holographic arrangement is proposed. The system is a security architecture that uses different pupil aperture mask in the encoding lens to encrypt different images. Based on this approach multiple encryption is achieved by changing the pupil aperture arrangement of the optical system among exposures. In addition to the classical speckle phase mask, the geometrical parameters characterizing the apertures are introduced to increase the system security. Even when an illegal user steals the speckle phase mask, the system cannot be broken into without the correct pupil geometrical parameters. The experimental set-up is based on a volume photorefractive BSO crystal as storing device. Information retrieval is done via a phase conjugation operation. We also have to stress that the multiple storage under this scheme, is only possible with the help of the aperture mask. Simulation and experimental results are further introduced to verify the proposed method.     

Optical color image encryption with redefined fractional Hartley transform

We propose a new method for color image encryption by wavelength multiplexing on the basis of two-dimensional (2-D) generalization of 1-D fractional Hartley transform that has been redefined recently in search of its inverse transform. A color image can be considered as three monochromatic images and then divided into three components and each component is encrypted independently with different wavelength corresponding to red, green or blue light. The system parameters of fractional Hartley transform and random phase masks are keys in the color image encryption and decryption. Only when all of these keys are correct, can the image be well decrypted. The optical realization is then proposed and computer simulations are also performed to confirm the possibility of the proposed method.     

Triple image encryption scheme in fractional Fourier transform domains

We proposed a triple image encryption scheme by use of fractional Fourier transform. In this algorithm, an original image is encoded in amplitude part and other two images are encoded into phase information. The key of encryption algorithm is obtained from the difference between the third image and the output phase of transform. In general case, random phase encoding technology is not required in the proposed algorithm. Moreover, all information of images is preserved in theory when image are decrypted with correct key. The optical implementation of the algorithm is presented with an electro-optical hybrid structure. Numerical simulations have demonstrated the efficiency and the security of this algorithm. Based on this scheme a multiple image algorithm is expanded and designed.     

Double image encryption based on iterative fractional Fourier transform

We present an image encryption algorithm to simultaneously encrypt two images into a single one as the amplitudes of fractional Fourier transform with different orders. From the encrypted image we can get two original images independently by fractional Fourier transforms with two different fractional orders. This algorithm can be independent of additional random phases as the encryption/decryption keys. Numerical results are given to analyze the capability of this proposed method. A possible extension to multi-image encryption with a fractional order multiplexing scheme has also been given.     

Applications of gyrator transform for image processing

Gyrator transform is a new tool for manipulation of two-dimensional signals such as images or laser beam profiles. Here we demonstrate various applications of the gyrator transform for image processing. Several aspects such as noise reduction, filtering and encryption in the gyrator domains are discussed. These operations can be performed by numerical calculations or by an appropriate optical set up.     

Multiple-aperture speckle method applied to local displacement measurements

The goal of this work is to analyze the measurement capability of the modified speckle photography technique that uses different multiple aperture pupils in a multiple exposure scheme. In particular, the rotation case is considered. A point-wise analysis procedure is utilized to obtain the fringes required to access to the local displacement measurements. The proposed arrangement allows simultaneous displaying in the Fourier plane several fringes system each one associated with different rotations. We experimentally verified that the local displacement measurements can be determined with a high precision and accuracy.     

The study of the nonlinear absorption in the nonlinear-imaging technique with phase object

The nonlinear absorption can produce a nonlinear image very similar with the one created by the nonlinear refraction when using the nonlinear-imaging technique with phase object to measure the third-order nonlinearity of materials, but the principles of them are different. The formation of the nonlinear absorption image is explained, and the condition that the highest sensitivity of the nonlinear absorption measurement can be reached is deduced. For the materials with both nonlinear absorption and refraction, we find a proper phase shift of the phase object where the effect of the nonlinear refraction to the measured signal can be eliminated. The nonlinear absorption and refraction are numerically simulated when the phase shift of phase object to be π/2 that is normally used. The qualitative tendency of the signal variation is presented.     

Window fringe pattern demodulation by multi-functional fitting using a genetic algorithm

We present a new way to demodulate complicated fringe patterns containing closed fringes using a genetic algorithm (GA). The entire fringe pattern is divided into a set of partially overlapping smaller sub-image windows. Each of these has a lower dimensionality and as a consequence is faster and can be demodulated more reliably. The demodulation process proceeds row-by-row way passing from one sub-image in a neighborhood until the whole interferogram is processed. The modulating phase of each sub-image is modeled as a parametric analytic function whose parameters are optimized using a GA. The technique is demonstrated demodulating some normalized fringe patterns that have two main difficulties: closed fringes within the interferogram and regions of under-sampled fringes. These fringe images cannot be demodulated by techniques such as the regularized phase tracker (RPT).     

Fast algorithm of discrete gyrator transform based on convolution operation

The expression of gyrator transform (GT) is rewritten by using convolution operation, from which GT can be composed of phase-only filtering, Fourier transform and inverse Fourier transform. Therefore, fast Fourier transform (FFT) algorithm can be introduced into the calculation of convolution format of GT in the discrete case. Some simulations are presented in order to demonstrate the validity of the algorithm.     

Real time dynamic domain observation in bulk materials

The paper briefly reviews the development of domain observation techniques used to study basic properties of electrical steels. A new real-time, dynamic, high magnification domain observation technique is presented as an example of a state-of-the-art system, capable of imaging non-repetitive domain wall motion at power frequencies. Advantages of real-time domain observation over stroboscopic magneto-optic studies are presented and the need for real-time observations in developing future loss theories is proposed. Possible relationships between Barkhausen noise, hysteresis and non-repetitive wall motion in electrical steels are suggested and finally examples of non-repetitive wall motion in other magnetic materials are illustrated.     

Unified approach to short optical pulse recording and spatial imaging with subwavelength resolution

We propose and numerically demonstrate a simple method for measuring waveforms of optical pulses that have spectral bandwidths much larger than the passband of the measuring system, thus enabling a kind of temporal superresolution. The technique is based on pulse intensity modulation that contains high-order harmonics. Parts of the pulse intensity spectrum that are shifted as a result of the modulation, are moved over (“umklapped”) to the center of the passband, transmitted and then recorded by an oscilloscope. The pulse intensity spectrum is restored by parts from the Fourier transform of a few oscillograms, measured after performing the temporal shifts between the pulse train and the modulation. A similar approach is applied for achieving subwavelength spatial resolution in far -field microscopy. The spatial modulation is performed by a diffraction grating. The method allows one to restore a subwavelength object in a single measurement.