Polychromatic X-ray effects on fringe phase shifts in grating interferometry

Abstract

Abstract:In order to quantitatively determine the projected electron densities of a sample, one needs to extract the monochromatic fringe phase shifts from the polychromatic fringe phase shifts measured in the grating interferometry with incoherent X-ray sources. In this work the authors propose a novel analytic approach that allows to directly compute the monochromatic fringe shifts from the polychromatic fringe shifts. This approach is validated with numerical simulations of several grating interferometry setups. This work provides a useful tool in quantitative imaging for biomedical and material science applications. T. Den, "Two-dimensional grating-based x-ray phase-contrast imaging using fourier transform phase retrieval," Opt. Express 19, 3339-3346 (2011). 14. J. Rizzi, P. Mercere, M. Idir, P. D. Silva, G. Vincent, and J. Primot, "X-ray phase contrast imaging and noise evaluation using a single phase grating interferometer," Opt. Express 21, 17340-17351 (2013). 15. A. Bravin, P. Coan, and P. Suortti, "X-ray phase-contrast imaging: from pre-clinical applications towards clinics,"Physics in Medicine and Biology 58, R1-R35 (2013). 16. N. Morimoto, S. Fujino, K. Ohshima, J. Harada, T. Hosoi, H. Watanabe, and T. Shimura, "X-ray phase contrast imaging by compact talbot-lau interferometer with a single transmission grating," Opt. Lett. 39, 4297-4300 (2014). 17. N. Morimoto, S. Fujino, A. Yamazaki, Y. Ito, T. Hosoi, H. Watanabe, and T. Shimura, "Two dimensional x-ray phase imaging using single grating interferometer with embedded x-ray targets," Opt. Express 23, 16582-16588 (2015).

Beam hardening correction in polychromatic x-ray grating interferometry

“…Moreover, the effective energy concept is valid only for small fringe shifts of few degrees, otherwise the polychromatic shift is a non-linear function of monochromatic fringe phase shift. Furthermore, as we showed previously [24], sometimes these two fringe shifts may even have opposite signs, thereby no effective energy exists. As for the second concept, the beam hardening refers to that the x-ray exiting from more attenuated ray paths is with a higher fraction of high-energy photons than that with the original spectrum.…”

“…(10) is the key basic equation for the retrieval of monochromatic fringe phase shifts, it is not a convenient formula to use for retrieval of φ m,D (x, y). In a previous work [24], we developed an iterative approach to retrieve φ m,D (x, y) from the polychromatic measurement provided the effective spectrum is uniform and independent of pixel position. In this work, we extended that approach to the cases with pixel position-dependent effective spectrum to account for the uneven beam hardening effects.…”

“…Note that the optical response coefficient is position dependent, since the effective spectrum is positiondependent due to the beam hardening effect. Following the reasoning and derivation in [24], we extended the previous iterative phase retrieval method to the cases with position-dependent X-ray spectra. Assume that φ…”

“…The fringe shift distortion in polychromatic X-ray grating interferometry has two causes. First, the fringe phase shift and fringe visibility are all photon energy dependent, hence polychromatic fringe shift is a nonlinear function of the monochromatic fringe shifts of different energies [24]. The second cause of fringe shift distortion is the beam hardening, which refers to the nonuniform x-ray spectrum shifts caused by the non-uniform attenuation across the sample.…”

“…In order to reconstruct the electron density gradients of the sample, we recently developed an analytic approach that enables retrieving the monochromatic phase shift φ m (x, y; E) from the polychromatic measurement [24]. We validated this approach for a number of interferometry setup geometries by using the wave-propagation based simulations [24]. However, our previous approach doesn't address the X-ray beam hardening effects.…”