Linear algorithms for phase retrieval in the Fresnel region. 3. Validity conditions

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.

[1]  Hong Liu,et al.  A comparison of iterative algorithms and a mixed approach for in-line x-ray phase retrieval. , 2009, Optics communications.

[2]  F. Roddier,et al.  Wavefront sensing and the irradiance transport equation. , 1990, Applied optics.

[3]  M. Teague.  Deterministic phase retrieval: a Green’s function solution , 1983 .

[4]  P. Cloetens,et al.  Mixed transfer function and transport of intensity approach for phase retrieval in the Fresnel region. , 2007, Optics letters.

[5]  K. Nugent,et al.  Phase retrieval with the transport-of-intensity equation. II. Orthogonal series solution for nonuniform illumination , 1996 .

[6]  Anna Burvall,et al.  Phase Retrieval in X-ray Phase-contrast Imaging Suitable for Tomography , 2022 .

[7]  D. Van Dyck,et al.  A new procedure for wave function restoration in high resolution electron microscopy , 1987 .

[8]  Xizeng Wu,et al.  A general theoretical formalism for X-ray phase contrast imaging. , 2003, Journal of X-ray science and technology.

[9]  Hong Liu,et al.  Phase-space formulation for phase-contrast x-ray imaging. , 2005, Applied optics.

[10]  S. Wilkins,et al.  Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object , 2002, Journal of microscopy.

[11]  S. Wilkins,et al.  Linear algorithms for phase retrieval in the Fresnel region , 2004 .

[12]  D Paterson,et al.  X-ray phase imaging: Demonstration of extended conditions for homogeneous objects. , 2004, Optics express.

[13]  Hong Liu,et al.  Feasibility study of the iterative x-ray phase retrieval algorithm. , 2009, Applied optics.

[14]  S. Wilkins,et al.  Contrast and resolution in imaging with a microfocus x-ray source , 1997 .

[15]  P. Cloetens,et al.  Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography. , 2008, Medical physics.

[16]  Cheng-Ying Chou,et al.  Image reconstruction in quantitative X-ray phase-contrast imaging employing multiple measurements. , 2007, Optics express.

[17]  T. Gureyev.  Composite techniques for phase retrieval in the Fresnel region , 2003 .

[18]  Stefano Lagomarsino,et al.  In-line phase-contrast imaging for strong absorbing objects. , 2008, Physics in medicine and biology.

[19]  K. Nugent,et al.  Quantitative phase tomography , 2000 .

[20]  S. Wilkins,et al.  Linear algorithms for phase retrieval in the Fresnel region. 2. Partially coherent illumination , 2006 .

[21]  S. Wilkins,et al.  Quantitative in-line phase-contrast imaging with multienergy X rays. , 2001, Physical review letters.

[22]  Aimin Yan,et al.  X-ray phase-attenuation duality and phase retrieval. , 2005, Optics letters.

[23]  Mark A. Anastasio,et al.  Relationships Between Smooth- and Small-Phase Conditions in X-Ray Phase-Contrast Imaging , 2009, IEEE Transactions on Medical Imaging.

[24]  Hong Liu,et al.  A new theory of phase-contrast x-ray imaging based on Wigner distributions. , 2004, Medical physics.

[25]  A. Barty,et al.  Quantitative phase‐amplitude microscopy. III. The effects of noise , 2004, Journal of microscopy.

[26]  Andrew Pogany,et al.  Optical phase retrieval by use of first Born- and Rytov-type approximations. , 2004, Applied optics.