title: Isotropic scalar image visualization of vector differential image data using the inverse Riesz transform.
abstract: 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.
authors.affiliation: Canon Information Systems Research Australia, Pty., Ltd, 1 Thomas Holt Drive, North Ryde, NSW 2113, Australia ; Nontrivialzeros Research, 22 Mitchell Street, Putney, NSW 2112, Australia.
authors.forename: Kieran G
authors.initials: KG
authors.lastname: Larkin
authors.affiliation: Canon Information Systems Research Australia, Pty., Ltd, 1 Thomas Holt Drive, North Ryde, NSW 2113, Australia.
authors.forename: Peter A
authors.initials: PA
authors.lastname: Fletcher
keywords: (100.3010) Image reconstruction techniques; (100.4994) Pattern recognition, image transforms; (110.6760) Talbot and self-imaging effects; (180.3170) Interference microscopy; (330.4595) Optical effects on vision; (340.7450) X-ray interferometry