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.     

Optical Image Encryption with Simplified Fractional Hartley Transform

We present a new method for image encryption on the basis of simplifed fractional Hartley transform （SFRHT）. SFRHT is a real transform as Hartley transform （HT） and furthermore, superior to HT in virtue of the advantage that it can also append fractional orders as additional keys for the purpose of improving the system security to some extent. With this method, one can encrypt an image with an intensity-only medium such as a photographic film or a CCD camera by spatially incoherent or coherent illumination. The optical realization is then proposed and computer simulations are also performed to verify the feasibility of this method.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Methods of Fourier optics in digital holographic microscopy

In this paper, processing methods of Fourier optics implemented in a digital holographic microscopy system are presented. The proposed methodology is based on the possibility of the digital holography in carrying out the whole reconstruction of the recorded wave front and consequently, the determination of the phase and intensity distribution in any arbitrary plane located between the object and the recording plane. In this way, in digital holographic microscopy the field produced by the objective lens can be reconstructed along its propagation, allowing the reconstruction of the back focal plane of the lens, so that the complex amplitudes of the Fraunhofer diffraction, or equivalently the Fourier transform, of the light distribution across the object can be known. The manipulation of Fourier transform plane makes possible the design of digital methods of optical processing and image analysis. The proposed method has a great practical utility and represents a powerful tool in image analysis and data processing. The theoretical aspects of the method are presented, and its validity has been demonstrated using computer generated holograms and images simulations of microscopic objects.     

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.     

Multiplexing encrypted data by using polarized light

We investigate the feasibility of multiplexing, employing polarized light, a set of security encrypted data. The encryption approach is based on the double random pure-phase enciphering method. Phase conjugation operation is conducted in the reconstruction stage with the aid of a photorefractive crystal which stores the encrypted information. When storing each encrypted image, a polarization change is introduced in the system. This induces decorrelation on the speckle patterns inside the storing medium. We apply this approach for multiple image encryption. We show experimental results that confirm our approach.     

Design of Infrared Inverted Telephoto-Optical System with Double-Layer Harmonic Diffractive Element

A double-layer harmonic diffractive element （HDE） structure is investigated and the optimization procedure is given based on the equation of diffraction efficiency of the double-layer diffractive optical element. A new infrared double-layer inverted telephoto-optical system with an HDE is designed, which can work in the mid- and farinfrared wavebands. The diffraction efficiency of the system at each wavelength in the designed two wavebands is larger than 90%, which improves the image contrast and the imaging quality significantly.     

Image watermarking based on an iterative phase retrieval algorithm and sine-cosine modulation in the discrete-cosine-transform domain

A novel digital image watermarking system based on an iterative phase retrieval algorithm and sine-cosine modulation in the discrete-cosine-transform (DCT) domain is proposed. The original hidden image is first encrypted into two phase masks. Then the cosine and sine functions of one of the phase masks are introduced as a watermark to be embedded into an enlarged host image in the DCT domain. By extracting the watermark of the enlarged superposed image and decryption we can retrieve the hidden image. The feasibility of this method and its robustness against some attacks, such as occlusion, noise attacks, quantization have been verified by computer simulations. This approach can avoid the cross-talk noise due to direct information superposition and enhance the imperceptibility of hidden data.     

Multichanneled puzzle-like encryption

In order to increase data security transmission we propose a multichanneled puzzle-like encryption method. The basic principle relies on the input information decomposition, in the same way as the pieces of a puzzle. Each decomposed part of the input object is encrypted separately in a 4f double random phase mask architecture, by setting the optical parameters in a determined status. Each parameter set defines a channel. In order to retrieve the whole information it is necessary to properly decrypt and compose all channels. Computer simulations that confirm our proposal are presented.     

Complex order fractional Fourier transforms and their use in diffraction theory. Application to optical resonators

The electromagnetic field transfer by diffraction from a spherical emitter to a spherical receiver is expressed by a fractional Fourier transform whose order depends on the distance between the emitter and the receiver and their curvature radii. Special attention is paid to complex order transforms: scaled variables and scaled field amplitudes are defined by complying with mathematical consistency. For a given distance of observation, a simple geometrical condition is set up to determine whether the corresponding transform order is a real or a complex number. The result is applied to check the stability of optical resonators.     

The use of a consumer grade photo camera in optical-digital correlator for pattern recognition and input scene restoration

In this work an optical-digital correlator for pattern recognition and input scene restoration is described. Main features of the described correlator are portability and ability of multi-element input scenes processing. The correlator consists of a consumer grade digital photo camera with a diffractive optical element (DOE) inserted as a correlation filter. Correlation of an input scene with a reference image recorded on the DOE are provided optically and registered by the digital photo camera for further processing. Using obtained correlation signals and DOE’s point spread function (PSF), one can restore the image of the input scene from the image of correlation signals by digital deconvolution algorithms.The construction of the correlator based on the consumer grade digital photo camera is presented. The software procedure that is necessary for images linearization of correlation signals is described. Experimental results on optical correlation are compared with numerical simulation. The results of images restoration from conventionally and specially processed correlation signals are reported. Quantitative estimations of accuracy of correlation signals as well as restored images of the input scene are presented.     

Triple Encrypted Holographic Storage and Digital Holographic System

We propose a triple encrypted holographic memory containing a digital holographic system. The original image is encrypted using double random phase encryption and stored in a LiNbO3：Fe crystal with shift-multiplexing. Both the reference beams of the memory and the digital holographic system are random phase encoded. We theoretically and experimentally demonstrate the encryption and decryption of multiple images and the results show high quality and good fault tolerance. The total key length of this system is larger than 4.7×10^33.     

Three Gaussian beam heterodyne interferometer for surface profiling

A novel three Gaussian beam interferometric technique for profiling optical smooth surfaces is presented. The technique is based on the heterodinization of three Gaussian beams, two of them with the same temporal frequency. The first beam is used as a probe beam after being focused and reflected from the surface under test. The second beam is reflected from a reference surface. The third beam is obtained from the first diffraction order of a Bragg cell and thus, it is shifted in its temporal frequency. The three beams are coherently added at the sensitive plane of a photodetector that integrates the overall intensity of the beams. We show analytically that the electrical signal at the output of the photodetector consists of a temporal carrier whose amplitude is a sinusoidal function of the local topography. We include the measurement of the topography of a sample consisting in a blazed-reflecting grating calibrated by means of an atomic force microscope.     

Coherent imaging of extended objects

When used with coherent light, optical imaging systems are inherently unable to reproduce both the amplitude and the phase of a two-dimensional field distribution. This is because their impulse response function varies slowly from point to point, a property known as non-isoplanatism. For sufficiently small objects, this usually results in a phase distortion and has no impact on the measured intensity. Here, we show that the intensity distribution can be dramatically distorted when extended objects are imaged. We illustrate the problem using two simple examples: the pinhole camera and the thin lens. The effects predicted by our theoretical analysis are confirmed by experimental observations.