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.     

Design and application of three-zone annular filters

We design three-zone annular filters to be applied to optical storage system. The designed filters extend the depth of focus and realize transverse superresolution simultaneously, which will improve the performance of optical storage system greatly. And we propose two feasible schemes to improve imaging resolution of three-dimensional imaging system. One scheme depends on a complex filter formed by cascading of a three-zone phase filter and a three-zone amplitude filter. The complex filter converge the optimized transverse superresolution and the optimized axial superresolution of two different filters onto a single filter. It can improve the three-dimensional imaging performances greatly. Another scheme depends on a single three-zone complex filter. We propose a three-zone complex filter with phase shift 0.8π, which presents bigger design margin, better imaging quality and stronger three-dimensional superresolution capability.     

The focus of light – theoretical calculation and experimental tomographic reconstruction

We present numerical calculations on the field distribution in the focus of an optical system with high numerical aperture. The diffraction integrals which are based on the Debye approximation are derived and evaluated for a radially polarized input field with a doughnut-shaped intensity distribution. It is shown that this mode focusses down to a spot size significantly smaller as compared to the case of linear polarization. An experimental setup to measure the three-dimensional intensity distribution in the focal region is presented, which is based on the knife-edge method and on tomographic reconstruction. Received: 14 July 2000 / Published online: 30 November 2000     

Quantum phase-space description of light polarization

We present a method to characterize the polarization state of a light field in the continuous-variable regime. Instead of using the abstract formalism of SU(2) quasidistributions, we model polarization as the superposition of two harmonic oscillators of the same angular frequency along two orthogonal axes, much in the classical way of dealing with this variable. By describing each oscillator by an s-parametrized quasidistribution, we derive in a consistent way the final function for the polarization. We compare with previous approaches and show how this formalism works in some relevant examples.     

THz wave polarization-controlled spectroscopic imaging for anisotropic materials

We present a polarization-controlled terahertz (THz) wave spectroscopic imaging modality to investigate the anisotropy of the detected materials. The polarization of the emitted THz wave is controlled by changing the relative phase between the fundamental and second-harmonic waves in the two-color laser-induced air plasma THz generation configuration. The THz wave polarization direction is extracted by measuring the two electric field amplitudes when the polarization of the incident wave is controlled to be horizontal and vertical. The anisotropy of the industrial Sprayed-On-Foam-Insulation (SOFI) is characterized by measuring its azimuthal angle dependent THz polarization response. This work demonstrates that THz wave polarization-controlled imaging technique can be used for highly sensitive industrial nondestructive inspection and biological related characterization.     

Matrix-Based Polarization Analysis and Application of Semiconductor Optical Amplifiers

Employing the Mueller matrix method with polar decomposition, we analyse the polarization rotation (PR) effects in semiconductor optical amplifiers (SOAs) and demonstrate that the PR angle is linear to the birefringence dependent gain while the average PR coefficient is about 0.625 for the employed SOA. It is further evident that the current and optical intensity dependent PRs rotate reversely around the same axis. Thus we propose an optical-electric synchronous control scheme to obtain orthogonal polarization states with power-equalization, and implement it by a polarization-sensitive SOA. The polarization duration time is about 10 ns which is applicable to high-speed polarization state generation.     

Focal field computation of an arbitrarily polarized beam using fast Fourier transforms

In this work the vectorial diffraction theory of Richards and Wolf is extended to compute the focal field components of an arbitrarily polarized beam using fast Fourier transform (FFT) operations. Here the arbitrarily polarized pupil function is written as the vector sum of two mutually perpendicularly polarized pupil functions. The FFT based focal field expressions are particularly useful to compute the focal field components of pupil functions without a simple analytical form. We have then applied these expressions to simulate the effects of Zernike mode aberrations on the point spread functions of a number of important cylindrical-vector beam profiles such as radially and azimuthally polarized and helical light beams.     

High depth of focus by combining annular lenses

In some technological applications, optical systems that produce a high depth of focus and superresolving transversal responses are required. In this paper we present a pupil design consisting in a phase pupil with binary amplitude, that added to a conventional optical system, can accomplish these goals. The pupil function is characterized by a complex amplitude that consists basically in combining two annular lenses with different focal length. Meanwhile the central portion of the pupil has an amplitude equal to 0, the external portion is modulated with two quadratic phases each one covering an annular zone. One of the phases corresponds to a convergent lens and the other to a divergent lens. The effect on the incident wavefront is to redirect the light in front of and behind the best image plane (BIP) producing a widened focus. The evolution of the transverse gain for the extended focus is also studied. Experimental results are given, and they confirm the extended focus and the superresolving behavior of the proposed pupil function.     

Transverse energy flows in vectorial fields of paraxial beams with singularities

A general study of transverse energy flows (TEF) as physically meaningful and informative characteristics of paraxial light beams’ spatial structure is presented. The total TEF can be decomposed into the spin and orbital contributions giving rise to the spin and orbital angular momentums, correspondingly. Definitions and properties of these constituents are discussed in relation with the optical field representation through linear and circular orthogonal polarization bases. With the help of model examples, the results are applied to investigation of TEF singularities in connection with the usual polarization morphology characteristics of paraxial optical fields. An analysis of TEFs near singular points has been carried out; in particular, the behavior of TEF and its partial contributions near polarization singularities (C-points) has demonstrated the special role of a boundary flow in the origin of the spin angular momentum. The analytical and experimental applicability of the introduced concepts are discussed.     

The filtering characteristics of simple grating optical low-pass filters

We studied the characteristics of a two-dimensional grating optical low-pass filter (GOLF) theoretically and experimentally. The modulation transfer function (MTF) of an optical system that consists of a lens and a GOLF is theoretically derived by taking all orders of diffracted beams into consideration. The MTFs of a two-phase chess-board-type GOLF and a three-phase GOLF were calculated for various phase differences and compared with that of a birefringent low-pass filter (BLF). The three-phase GOLF with nine center beams of equal strength removes most moiré fringes, but the resolution degradation is severe compared to the BLF. The two-phase GOLF with a phase difference of 180°, which is similar to the BLF in term of beam distribution, has a medium characteristic somewhere between those of the three-phase GOLF and the BLF. Samples of two GOLFs are made and experimented on by attaching them to a digital camera. The experimental result coincides with the theoretical development. Received: 31 October 2001 / Revised version: 4 March 2002 / Published online: 2 May 2002     

Polarization-resolved analysis of the characteristics of a Raman laser made with a polarization maintaining fiber

We derive a simple model describing steady characteristics of Raman fiber lasers made with polarization maintaining fibers. We show both theoretically and experimentally that this kind of laser simply consists of two independent Raman lasers linearly polarized along the fiber birefringence axes. The output power characteristics of the laser are shown not to be influenced by optical Kerr effect. Finally, we use our model to propose answers to questions recently raised about efficiency of Raman lasers made with polarization maintaining fibers.     

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.     

基于偏振模干涉的可变系数微波光子滤波器

基于偏振调制和光的干涉原理,设计了同时具有正系数和负系数特性的微波光子滤波器,并通过搭建实验模型证实了方案的可行性。利用偏振调制及光的偏振特性实现载波和一阶边带的正交偏振,并通过改变偏振调制器的偏置电压分别对载波和一阶边带引入相移。当载波和一阶边带的相位差为0或90时,利用保偏光纤快慢轴上两正交偏振光在同一偏振态上的干涉效应,分别对应实现具有负系数或正系数特性的微波光子滤波器。最后,测量并验证了0~15 GHz频率范围内滤波器的频率响应。     

Phase-Space Analysis of Wavefront Coding Imaging Systems

We explore the use of the Radon-Wigner transform, which is associated with the fractional Fourier transform of the pupil function, for determining the point spread function （PSF） of an incoherent defocused optical system. Then we introduce these phase-space tools to analyse the wavefront coding imaging system. It is shown that the shape of the PSF for such a system is highly invariant to the defocus-related aberrations except for a lateral shift. The optical transfer function of this system is also investigated briefly from a new understanding of ambiguity function.     

Topological and morphological transformations of developing singular paraxial vector light fields

The paper is devoted to establishment of the real-time topological and morphological dynamics of generic developing paraxial elliptic speckle fields generated and driven by the system ‘laser beam + photorefractive crystal LiNbO₃:Fe’. Generic space-time development of full gamut of polarization ellipse parameters (ellipticity, azimuth, morphology of C points, optical diabolos and handedness) and their combination in fixed beam cross-section was measured in details by the elaborated quick-action real-time Stokes-polarimetry. Whole field irreversible evolution is fulfilled through totality of random space/time C point pair nucleation/annihilation. The ‘life-story’ of C point and optical diabolo pairs is realized through ‘local topological/morphological transition’ with fully reversible scenario. It starts from smooth fragment of speckle field by formation of pre-nucleation local structure and finishes by after-annihilation local structure which decays to another smooth structure. Scenarios of star-monstar pair nucleation/annihilation and monstar  ↔  lemon transformation were established. Measured statistics of C point and diabolo morphological forms was in excellent agreement with theory predictions. All allowed scenarios of diabolo pair ‘life-story’ started/finished as star-hyperbolic monstar-hyperbolic pair were measured. Evolution of polarization ellipses handedness is implemented through L contours movement and reconnection with a saddle as the catalyst. Reconnection of L contour peninsula leads to birth of closed L contour delimiting island of fixed handedness ellipses with/without C points. Elaborated approach and presented results start the dynamic singular optics of time-dependent vector light fields.     

Decay and fusion of polarization umbilics in a singular beam passed through a crystal

Evolution of polarized umbilics in a laser beam propagating in an optical system consisting of two anisotropic crystals with crossed optical axes and a Faraday cell is analyzed. It is shown that the phase perturbation caused by the second crystal results in radial shifts of the singularities, whereas the rotation of the plane of polarization when the Faraday cell is placed between the crystals causes angular displacements. When the Faraday cell is placed behind the second crystal, it provides additional fine control of the linear and angular shifts of the optical vortices.     

Elliptically polarized Terahertz emission through four-wave mixing in a two-color filament in air

We diagnosed the polarization characteristics of Terahertz emission from a two-color femtosecond laser filament when the polarizations of ω and 2ω beams are orthogonal. We discovered that the THz pulse is elliptically polarized. The generation mechanism could be through four-wave optical rectification inside the filament zone where the inversion symmetry of air is broken.     

Generation and Modulation of Phase Difference of Output Intensities in a Feedback Nd:YAG Laser with an Extracavity Waveplate Rotated

External anisotropic feedback effects on the phase difference behaviour of output intensities in a microchip Nd：YAG laser are presented. By rotating a quarter wave plate placed in the external cavity, the angle between laser initial polarization direction and o-axis of the wave plate is tuned from -45°to 45°, which results in variable extra-cavity birefringence along two orthogonal detection directions. With only one optical path and one wave plate, laser intensities of the two orthogonal directions, both modulated by the external cavity length, are output with a tunable phase difference, which can be continuously changed from zero to twice as large as that of the waveplate. Experimental results as well as a theoretical analysis based on Fabry-Perot cavity equivalent model and the refractive index ellipsoid, are presented. The potential applications of this phenomenon are also discussed.     

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.     

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.