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.     

Cross spectral purity and its influence on ghost imaging experiments

Pseudo-thermal light has been widely used in ghost imaging experiments. In order to understand the differences between the pseudo-thermal source and thermal source, we propose a method to investigate whether a light source has cross spectral purity (CSP), and experimentally measure the cross spectral properties of the pseudo-thermal light source in near-field and far-field zones. Moreover we present a theoretical analysis of the cross spectral influence on ghost imaging.     

Incoherent recovering of the spatial resolution in digital holography

We report on a technique to recover the spatial resolution of digitally recorded and reconstructed holograms of large objects. Due to the high-contrast speckle noise diminishes the spatial resolution in coherent imaging systems our proposal is based on the reduction of the contrast of it. This aim is achieved through the superposition on an intensity basis of digitally reconstructed holograms of the same static scene. We show a theoretical justification of the procedure and experimentally-obtained results of applying the technique with digitally reconstructed holograms of an object with very poor optical contrast.     

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.     

Depolarization of multiply scattered light in transmission through a turbid medium with large particles

An approximate analytical method for solving the vector radiative transfer equation is proposed. The method is based on the assumption that single scattering of light by large-scale inhomogeneities occurs predominantly through small angles. The method is applied to calculate the polarization state of multiply scattered light. The results obtained are discussed for various turbid media.     

All-Optical RZ-to-NRZ Format Conversion with a Tunable Fibre Based Delay Interferometer

All-optical format conversion from return-to-zero （RZ） to non-return-to-zero （NRZ） is demonstrated with temperaturecontrolled all-fibre delay interferometer （DI） at 20 Gb/s. The operation principle is theoretical analysed with the help of numerical simulation and spectra analysis. Theoretical analysis results are consistent well with the experimental results. The format conversion can be achieved with power penalty of 0.54 dB and with output extinction ratio 20 dB.     

A Novel Method for Enhancing Goos-Hänchen Shift in Total Internal Reflection

Due to the tiny shift in order of optical wavelength for Goos-Hǎnchen （GH） shift, it is very difficult to directly measure and apply the GH shift. We develop a new method for enhancing GH shift of both TE and TM polarized waves. The method is based on a total reflection prism made of BK9 glass combined with a precise measurement of the resulting spatial displacement with a one-dimensional charge coupled device （CCD）. Measurements are performed to examine the validity of the method. Experimental and theoretical results indicate the feasibility of the method with an enhancement in optical wavelenghth shift at millimetre scale. The method is advantageous to application the GH shift in the optical domain, and is also meaningful for measuring even smaller changes in the refractive index of a liquid.     

Wavelet and model-based spectral analysis of color doppler optical coherence tomography

Color doppler optical coherence tomography (CD-OCT) uses time-frequency analysis (TFA) to extract motion-induced Doppler shifted in the interferometric OCT signal. In this paper, the performance of three TFAs are compared in a scattering flow phantom and in in vivo human retina: the short-time Fourier transform, the Morlet-wavelet transform, and the short-time MUSIC transform (STMT). The STMT is a new TFA that incorporates the MUSIC eigenfrequency estimator in a generalized short-time framework. The Morlet transform excels at identifying blood vessels, while the STMT is the most accurate predictor of Doppler shift frequency.     

Polarisation-sensitive optical coherence tomography for material characterisation and strain-field mapping

Optical coherence tomography (OCT) is a relatively new imaging technique capable of recording cross-sectional images of transparent and turbid structures with micrometer-scale resolution. Originally developed for biomedical imaging applications, this technique also has a great potential for non-destructive material characterisation and testing. Polarisation-sensitive (PS) OCT is a recent extension of classical OCT that measures and images birefringence properties of a sample, which, however, has not yet been applied to materials science. We present imaging of glass-fibre-enforced epoxy resin compounds and the detection of dry spots, where the epoxy did not properly penetrate the glass-fibre structure. Furthermore, we demonstrate PS-OCT imaging of the birefringence properties of different materials. The mapping of strain fields of samples under uniaxial and non-uniform external stress and the detection of flow patterns in injection-moulded plastic parts could be demonstrated with this technique for the first time. Received: 21 October 2002 / Accepted: 22 November 2002 / Published online: 29 January 2003 RID="*" ID="*"Corresponding author. Fax: +43-732/9015-5618, E-mail: david.stifter@uar.at     

A Simple Model for Measuring Refractive Index of a Liquid Based upon Fresnel Equations

Due to many experimental data required and a lot of calculations involved, it is very complex and cumbersome to model prism-based liquid-refractive-index-measuring methods. We develop a new method of mathematical modelling for measuring refractive index of a liquid based upon the Fresnel formula and prism internal reflection at an incident angle less than the critical angle. With this method, only two different concentrations measurements for a kind of solution can lead to the determination of computational model. Measurements are performed to examine the validity of the theoretical model. Experimental results indicate the feasibility of the theoretical model with an error of 1%. The method is also capable of measuring even smaller changes in the optical refractive index of the material on a metal surface by the surface plasma resonance sensing techniques.     

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.     

Phase control algorithms for focusing light through turbid media

Light propagation in materials with microscopic inhomogeneities is affected by scattering. In scattering materials, such as powders, disordered metamaterials or biological tissue, multiple scattering on sub-wavelength particles makes light diffuse. Recently, we showed that it is possible to construct a wavefront that focuses through a solid, strongly scattering object. The focusing wavefront uniquely matches a certain configuration of the particles in the medium. To focus light through a turbid liquid or living tissue, it is necessary to dynamically adjust the wavefront as the particles in the medium move. Here we present three algorithms for constructing a wavefront that focuses through a scattering medium. We analyze the dynamic behavior of these algorithms and compare their sensitivity to measurement noise. The algorithms are compared both experimentally and using numerical simulations. The results are in good agreement with an intuitive model, which may be used to develop dynamic diffusion compensators with applications in, for example, light delivery in human tissue.     

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.     

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.     

A simple method to simulate diffraction and speckle patterns with a PC

A simple, intuitive and pedagogical method is proposed in order to simulate the phenomenon of light diffraction in simple cases. A diffracting plane obstacle is simulated by means of a model with a variable transmittance from one point to another. A numerical matrix is built with transmittance values at those points taken as samples. The matrix is handled with the Matlab program, and the Fraunhofer approximation is used. The method is applied to variable module and constant phase transmittance obstacles in single slit, double slit, square window and round window cases. The method is also applied to an obstacle with a constant reflectance module and random variable phase with Gaussian statistics, which gives rise to speckle phenomenon.     

Parametric study of uniformly polarized stochastic electromagnetic beam and its imaging

A parametric study is performed in investigating the stochastic electromagnetic beam generated by a uniformly polarized electromagnetic Gaussian Schell-model source and passing through ABCD optical systems. Through theoretical analysis, the requirement is derived that the uniformly polarized electromagnetic field can be obtained at the output plane of the imaging optical system. Furthermore, the general imaging formula of the stochastic electromagnetic beam is derived. Numerical examples are also presented to illustrate the application.     

High Efficient Tunable Fractal Axicon Based on LCoS

Based on the Cantor function and phase modulation, a tunable fractal axicon is formed on a liquid crystal on silicon （LCoS） with an improved generating method. It has higher focusing efficiency in higher fractal stage and approaches to 100% theoretically. The on-axis intensity keeps its fractal structure unchanged in operation of fractal stages. The tunability of the axicon is demonstrated by tune fractal stage from 1 to 3 and focal length from 0.8 m to 1 m. We also provide details of theoretical analyses and experimental results.     

Speckle noise attenuation in optical coherence tomography by compounding images acquired at different positions of the sample

This study demonstrates a simple method for attenuating the speckle noise generated by coherent multiple-scattered photons in optical-coherence tomography images. The method could be included among the space-diversity techniques used for speckle reduction. It relies on displacing the sample along a weakly focused beam in the sample arm of the interferometer, acquiring a coherent image for each sample position and adding the individual images to form a compounded image. It is proven that the compounded image displays a reduction in the speckle noise generated by multiple scattered photons and an enhancement in the intensity signal caused by single-backscattered photons. To evaluate its potential biomedical applications, the method is used to investigate in vitro a caries lesion affecting the enamel layer of a wisdom tooth. Because of the uncorrelated nature of the speckle noise the compounded image provides a better mapping of the lesion compared to a single (coherent) image.     

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.