Phase contrast, phase retrieval and aberration balancing in shift-invariant linear imaging systems

We treat the problems of phase-contrast image formation, deterministic phase retrieval and aberration balancing, in the imaging of weak objects using two-dimensional shift-invariant linear imaging systems. Three classes of model sample are considered: weak phase objects, weak phase-amplitude objects and single-material weak phase-amplitude objects. For each class of sample we show how the various aberration coefficients, which characterise a given imaging system, contribute to the structure of the associated phase-contrast image. The corresponding inverse problem, of obtaining a closed-form expression for the input wave-field given one or more aberrated phase-contrast images of the same, is then examined. Two sample applications are considered: analyser-crystal phase-contrast imaging of weak objects using hard X-rays, and Zernike-type phase-contrast imaging. We close with a discussion of how coherent and incoherent aberrations may be “balanced” against one another, briefly mentioning the applications of this idea to both “deblur by defocus” and proximity-corrected X-ray lithography.     

Phase imaging from a diffraction pattern in the presence of vortices

We investigate phase imaging from a diffraction pattern in the presence of vortices. In particular we demonstrate that a difference map method for phase retrieval which contains a support constraint does not necessarily conserve the net topological charge of the trial wave field. Hence, no a priori information regarding the charges of the vortices is required for a successful phase retrieval.     

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.     

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.     

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.     

Differentiation and subtraction of amplitude and phase images using a photorefractive novelty filter

In this article, we demonstrate the capability of a two-beam coupling photorefractive optical novelty filter of detecting changes in the amplitude or phase of optical images. These changes may either be continuous or discrete in time. The performance of the two-beam coupling novelty filter is investigated and expressions for the output contrast corresponding to phase and amplitude changes based on a novel, simple interference model of two-beam coupling are derived. These expressions are verified by experimental results on the novelty contrast, revealing that the amplitude contrast is not described correctly by the commonly accepted coupled-wave theory. The novelty filter was applied to the detection of temporally continuous phase changes provided by a gas flow and moving microscopic objects. A novel scheme for image subtraction is also demonstrated, showing the novelty filter’s ability to detect temporally discrete changes. Received: 14 November 1998 / Revised version: 18 January 1999 / Published online: 12 April 1999     

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.     

Propagation characteristics of laser beams with amplitude modulations and phase fluctuations in apertured fractional Fourier transforming system

The apertured fractional Fourier transforming system is introduced and applied to treat the propagation of Gaussian beams with amplitude modulations and phase fluctuations. Based on the treatment that a rectangular function can be expanded into an approximate sum of complex Gaussian functions with finite numbers, the analytical expressions for the mutual intensity distribution of laser beams with amplitude modulations and phase fluctuations passing through the apertured fractional Fourier transforming system are obtained. Some numerical simulations are illustrated for their propagation properties.     

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.     

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.     

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.     

Multiple phase-shifted interferograms obtained from a single interferogram with linear carrier

In this paper we propose a new method for phase retrieval in an interferogram with a spatial linear carrier. We demonstrate that from the primary interferogram one can extract multiple interferograms (with lower resolution than the original one) with arbitrary phase-shift amounts between them. Then, by applying well-known phase-shifting algorithms, from these phase-shifted interferograms the phase can be retrieved. The method does not require sophisticated data-processing and is computationally efficient. Numerical simulations and validation experiments are presented.     

Photorefractive multichannel correlator based on stoichiometric LiTaO3

We demonstrate a Vander Lugt type correlator based on photorefractive stoichiometric LiTaO₃ as the volume holographic material. Accurate correlator output was obtained for binary phase-modulated input images. The correlator is tested with binary amplitude- and phase-modulated input images. Phase-modulated images show a high-quality correlation, whereas amplitude-modulated images suffer in part from a photorefractive self-focusing effect. Using 100 previously stored holograms as filters, a rate of 10000 correlations/s are demonstrated. A paraxial theoretical analysis of the correlator, giving analytic expressions for the shift invariance, is also described in detail. Received: 22 November 2000 / Revised version: 9 February 2001 / Published online: 20 April 2001     

On the origins of decoherence and extinction contrast in phase-contrast imaging

A theoretical formalism describing the formation of images in a linear shift invariant X-ray optical system is derived within the wave-optical theory. It is applicable to a non-crystalline object consisting of two types of features, with the characteristic sizes which are respectively not smaller and much smaller than the resolution of the imaging system. This formalism is then applied to two phase-contrast imaging techniques, the propagation-based and analyser-based imaging. The obtained formulae for the intensity distribution in the image well explain the “decoherence effect” which is observed in the former technique and the “extinction contrast” which is a characteristic of the latter technique. This formalism is shown to be in good agreement with the results of the accurate numerical simulations, using rigorous wave-optical theory, of the propagation-based and analyser-based phase-contrast images of the model objects.     

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.     

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.     

Novel Ghost Imaging Method for a Pure Phase Object

We propose a novel ghost imaging scheme which is especially served to a pure phase object. A spatially incoherent beam is mixed with a coherent beam of the same frequency field by a beamsplitter. Then we perform the ghost imaging scheme using the mixed beam. Our theoretical result shows that this approach is capable of reconstructing a pure phase object in joint-intensity measurement. The visibility of the images is also analysed for two pure phase objects, an optical wedge and a phase grating.     

Cross-talk free image encryption and watermarking by digital holography and random composition

In previous image watermarking methods an encoded host image and a watermark image are usually directly added, consequently the two images have cross-talk in the decryption step. To eliminate this effect, we propose a novel method based on digital holography, in which all the image pixels of the two sets of holograms resulted from two hidden images are rearranged and integrated into one set of composite holograms with a random scattering matrix (RSM). In decryption the use of this matrix can ensure the exact retrieval of each hologram, and then the perfect reconstruction of each image without cross-talk noise can be achieved. The feasibility of this method and its robustness against occlusion and additional noise are verified by computer simulations with phase-shifting interferometry and double random-phase encoding technique. This approach is suitable for both two- and three-dimensional images, and the additional RSM as a key provides a much higher level of security.     

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.