X-ray phase imaging: Demonstration of extended conditions for homogeneous objects.

Optics Express (Impact Factor: 3.53). 07/2004; 12(13):2960-5. DOI: 10.1364/OPEX.12.002960
Source: PubMed

ABSTRACT We discuss contrast formation in a propagating x-ray beam. We consider the validity conditions for linear relations based on the transport-of-intensity equation (TIE) and on contrast transfer functions (CTFs). From a single diffracted image, we recover the thickness of a homogeneous object which has substantial absorption and a phase-shift of --0.37 radian.

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    ABSTRACT: We describe the relationship between different forms of linearized expressions for the spatial distribution of intensity of X-ray projection images obtained in the Fresnel region. We prove that under the natural validity conditions some of the previously published expressions can be simplified without a loss of accuracy. We also introduce modified validity conditions which are likely to be fulfilled in many relevant practical cases, and which lead to a further significant simplification of the expression for the image-plane intensity, permitting simple non-iterative linear algorithms for the phase retrieval.
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    ABSTRACT: Promoted by the advent of coherent synchrotron light sources, phase contrast tomography allows to resolve three-dimensional variations of an unknown sample's complex refractive index from scattering intensities recorded at different incident angles of an X-ray beam. By diffractive free-space propagation of the transmitted wave field, this method is sensitive not only to absorption but also to refractive phase shifts induced by the specimen, permitting three-dimensional nanoscale imaging of quasi-transparent samples such as biological cells. However, the reconstruction of the specimen structure from the observed data constitutes an algorithmically challenging nonlinear ill-posed inverse problem, mainly due to the characteristic loss of phase information in the detection of the wave field. In this work, regularized Newton methods are developed for the solution of this tomographic phase retrieval problem, based on a detailed analysis of its mathematical structure. We consider both the near-field- or Fresnel regime characterized by a moderate propagation length between sample and detector and the far-field limit of large detector distances, where propagation is governed by the Fourier transform. In the former setting, excellent numerical reconstructions are obtained via the chosen Newton-type approach, supplemented by novel theoretical results stating that measurements from a single detector distance are sufficient to uniquely recover both refraction and absorption of a sample. The proposed algorithm simultaneously performs tomographic- and phase reconstruction, which is found to stabilize the latter by exploiting correlations between the diffraction patterns recorded under different incident angles.
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    ABSTRACT: We show that an arbitrary spatial distribution of complex refractive index inside an object can be exactly represented as a sum of two "monomorphous" complex distributions, i.e. the distributions with the ratios of the real part to the imaginary part being constant throughout the object. A priori knowledge of constituent materials can be used to estimate the global lower and upper boundaries for this ratio. This approach can be viewed as an extension of the successful phase-retrieval method previously developed for monomorphous (homogeneous) objects, such as e.g. objects consisting of a single material.

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