The fractional Fourier transform as a simulation tool for lens-based X-ray microscopy

Anders Filsøe Pedersen, Hugh Simons, Carsten Detlefs, Henning Friis Poulsen*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

690 Downloads (Pure)


The fractional Fourier transform (FrFT) is introduced as a tool for numerical simulations of X-ray wavefront propagation. By removing the strict sampling requirements encountered in typical Fourier optics, simulations using the FrFT can be carried out with much decreased detail, allowing, for example, on-line simulation during experiments. Moreover, the additive index property of the FrFT allows the propagation through multiple optical components to be simulated in a single step, which is particularly useful for compound refractive lenses (CRLs). It is shown that it is possible to model the attenuation from the entire CRL using one or two effective apertures without loss of accuracy, greatly accelerating simulations involving CRLs. To demonstrate the applicability and accuracy of the FrFT, the imaging resolution of a CRL-based imaging system is estimated, and the FrFT approach is shown to be significantly more precise than comparable approaches using geometrical optics. Secondly, it is shown that extensive FrFT simulations of complex systems involving coherence and/or nonmonochromatic sources can be carried out in minutes. Specifically, the chromatic aberrations as a function of source bandwidth are estimated, and it is found that the geometric optics greatly overestimates the aberration for energy bandwidths of around 1%.
Original languageEnglish
JournalJournal of Synchrotron Radiation
Issue number3
Number of pages12
Publication statusPublished - 2018


  • Wavefront propagation
  • Compound refractive lenses
  • X-ray microscopy


Dive into the research topics of 'The fractional Fourier transform as a simulation tool for lens-based X-ray microscopy'. Together they form a unique fingerprint.

Cite this