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Biomedical Optics Express

Biomedical Optics Express

  • Editor: Joseph A. Izatt
  • Vol. 5, Iss. 3 — Mar. 1, 2014
  • pp: 907–920

Isotropic scalar image visualization of vector differential image data using the inverse Riesz transform

Kieran G. Larkin and Peter A. Fletcher  »View Author Affiliations

Biomedical Optics Express, Vol. 5, Issue 3, pp. 907-920 (2014)

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X-ray Talbot moiré interferometers can now simultaneously generate two differential phase images of a specimen. The conventional approach to integrating differential phase is unstable and often leads to images with loss of visible detail. We propose a new reconstruction method based on the inverse Riesz transform. The Riesz approach is stable and the final image retains visibility of high resolution detail without directional bias. The outline Riesz theory is developed and an experimentally acquired X-ray differential phase data set is presented for qualitative visual appraisal. The inverse Riesz phase image is compared with two alternatives: the integrated (quantitative) phase and the modulus of the gradient of the phase. The inverse Riesz transform has the computational advantages of a unitary linear operator, and is implemented directly as a complex multiplication in the Fourier domain also known as the spiral phase transform.

© 2014 Optical Society of America

OCIS Codes
(100.3010) Image processing : Image reconstruction techniques
(110.6760) Imaging systems : Talbot and self-imaging effects
(180.3170) Microscopy : Interference microscopy
(340.7450) X-ray optics : X-ray interferometry
(330.4595) Vision, color, and visual optics : Optical effects on vision
(100.4994) Image processing : Pattern recognition, image transforms

ToC Category:
X-Ray Microscopy and Imaging

Original Manuscript: December 13, 2013
Revised Manuscript: February 4, 2014
Manuscript Accepted: February 17, 2014
Published: February 26, 2014

Kieran G. Larkin and Peter A. Fletcher, "Isotropic scalar image visualization of vector differential image data using the inverse Riesz transform," Biomed. Opt. Express 5, 907-920 (2014)

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