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Fast eikonal phase retrieval for high‐throughput beamlines.

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Title: Fast eikonal phase retrieval for high‐throughput beamlines.
Authors: Mirone, Alessandro1 (AUTHOR) mirone@esrf.fr, Urban, Theresa1,2 (AUTHOR), Brunet, Joseph1,2 (AUTHOR), Walsh, Claire L.2 (AUTHOR), Lee, Peter D.2 (AUTHOR), Tafforeau, Paul1 (AUTHOR)
Source: Journal of Synchrotron Radiation. Jul2026, Vol. 33 Issue 4, p1169-1179. 11p.
Subjects: Fast Fourier transforms, Iterative methods (Mathematics), X-ray computed microtomography, Light propagation
Abstract: A fast eikonal phase retrieval formulation is introduced that accelerates eikonal phase retrieval by more than two orders of magnitude while retaining controlled accuracy. The method is derived from a second‐order asymptotic expansion in the propagation distance L and complemented by the leading Wentzel–Kramers–Brillouin (WKB) wave‐optics correction, yielding an efficient iterative correction scheme preconditioned by fast Fourier transform (FFT)‐diagonal, energy‐dependent inverse operators (Paganin‐type filters). To ensure robustness across practical experimental regimes, we combine two complementary solvers: (i) a local O(L2) closure that is accurate when eikonal shifts remain sub‐pixel, and (ii) a non‐local formulation for multi‐pixel shifts, in which intensity is propagated through an explicit eikonal ray mapping using a mass‐conserving bilinear redistribution on the detector grid, and detector residuals are transferred back to the object grid by the corresponding discrete adjoint (transpose) operator, implemented as bilinear interpolation, before applying an approximate FFT‐diagonal preconditioner to accelerate convergence. The same framework supports polychromatic data through a compact spectral discretization, allowing energy‐dependent transport and inversion while keeping the iteration efficient for graphics processing unit (GPU)/FFT. Overall, this unified approach enables accurate and computationally efficient phase retrieval across propagation conditions relevant to high‐throughput propagation‐based phase‐contrast micro‐tomography experiments. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Synchrotron Radiation is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Fast eikonal phase retrieval for high‐throughput beamlines.
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  Data: <searchLink fieldCode="AR" term="%22Mirone%2C+Alessandro%22">Mirone, Alessandro</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> mirone@esrf.fr</i><br /><searchLink fieldCode="AR" term="%22Urban%2C+Theresa%22">Urban, Theresa</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Brunet%2C+Joseph%22">Brunet, Joseph</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Walsh%2C+Claire+L%2E%22">Walsh, Claire L.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Lee%2C+Peter+D%2E%22">Lee, Peter D.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Tafforeau%2C+Paul%22">Tafforeau, Paul</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Synchrotron+Radiation%22">Journal of Synchrotron Radiation</searchLink>. Jul2026, Vol. 33 Issue 4, p1169-1179. 11p.
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  Data: <searchLink fieldCode="DE" term="%22Fast+Fourier+transforms%22">Fast Fourier transforms</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22X-ray+computed+microtomography%22">X-ray computed microtomography</searchLink><br /><searchLink fieldCode="DE" term="%22Light+propagation%22">Light propagation</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: A fast eikonal phase retrieval formulation is introduced that accelerates eikonal phase retrieval by more than two orders of magnitude while retaining controlled accuracy. The method is derived from a second‐order asymptotic expansion in the propagation distance L and complemented by the leading Wentzel–Kramers–Brillouin (WKB) wave‐optics correction, yielding an efficient iterative correction scheme preconditioned by fast Fourier transform (FFT)‐diagonal, energy‐dependent inverse operators (Paganin‐type filters). To ensure robustness across practical experimental regimes, we combine two complementary solvers: (i) a local O(L2) closure that is accurate when eikonal shifts remain sub‐pixel, and (ii) a non‐local formulation for multi‐pixel shifts, in which intensity is propagated through an explicit eikonal ray mapping using a mass‐conserving bilinear redistribution on the detector grid, and detector residuals are transferred back to the object grid by the corresponding discrete adjoint (transpose) operator, implemented as bilinear interpolation, before applying an approximate FFT‐diagonal preconditioner to accelerate convergence. The same framework supports polychromatic data through a compact spectral discretization, allowing energy‐dependent transport and inversion while keeping the iteration efficient for graphics processing unit (GPU)/FFT. Overall, this unified approach enables accurate and computationally efficient phase retrieval across propagation conditions relevant to high‐throughput propagation‐based phase‐contrast micro‐tomography experiments. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Synchrotron Radiation is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1107/S1600577526004273
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      – Code: eng
        Text: English
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        PageCount: 11
        StartPage: 1169
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      – SubjectFull: Fast Fourier transforms
        Type: general
      – SubjectFull: Iterative methods (Mathematics)
        Type: general
      – SubjectFull: X-ray computed microtomography
        Type: general
      – SubjectFull: Light propagation
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      – TitleFull: Fast eikonal phase retrieval for high‐throughput beamlines.
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            NameFull: Mirone, Alessandro
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            NameFull: Urban, Theresa
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            NameFull: Walsh, Claire L.
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            – D: 01
              M: 07
              Text: Jul2026
              Type: published
              Y: 2026
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