It is essential to image the evolution of meso-structures in real time to explore the response properties of materials under extreme conditions. Detecting the meso-structures in bulk materials consisting of heavy element requires high imaging sensitivity at finite brightness of the impulsive sources and thus is challenging. For light materials, it is widely recognized that the absorption of meso-structures is negligible and the contrast enhancement of the in-line x-ray phase contrast imaging (XPCI) is essential. Most of the in-line XPCI experiments are carried out for the diagnosis of light materials. However, only a few researches that apply the in-line XPCI to materials consisting of moderate Z elements are found in the literature[1-3]. In general, the observed phase contrasts of heavier element materials are lower when compared to lighter element materials[3], and obvious phase contrast has not been proven for heavy element materials such as W. 
    We demonstrate that obvious phase contrast of meso-structures in heavy element materials is possible by numerical simulation of the XPCI in the present work. The image contrasts of XPCI (C_XPCI) are several times larger than those of x-ray radiography (C_XR) for micron-scale voids in W and Cu at spatial resolution of a micron. The phase contrast in dominant and the advantageous of high imaging sensitivity of the XPCI method for heavy element materials is well proved. By comparing the image contrast ratio α=C_XPCI /C_XR, lighter material has a larger α，which has been widely recognized by the community. However the absolute C_XPCI of W is larger than that of Cu, indicating the XPCI method is also advantageous to diagnose meso-structures in heavy materials. Typically, the phase contrast relates to Δϕ [4], where ϕ is the phase shift caused by the object and is proportional to δ (the real part of the refractive index). δ of heavy element is much larger than that of light element at the same x-ray energy, so that the phase contrast is more obvious for heavy element samples in principle. 
    It is also found that the dependence of image contrast on different imaging parameters deviates from the widely used contrast transfer function (CTF). The image contrast in the present work remains significant around \(\sqrt{{\lambda}zu}=1\), while the value of the CTF approaches to 0. This deviation indicates that the CTF is not suitable for heavy element materials, even for the weakly absorbing case. Since the phase shift ϕ may change greatly in adjacent area for heavy element materials with larger δ, the approximation of moderate variation of ϕ is invalid, and thus the CTF is not applicable. The obtained dependence of image contrast on \(\sqrt{{\lambda} zu}\) in the present work allows choosing the imaging parameters in a wider range to meet different experimental requirements. Above all, the in-line XPCI method is hopefully to image the evolution of meso-structures in heavy element materials under different laboratory conditions.
[1] F. Seiboth, L. B. Fletcher, D. McGonegle and et. al., Simultaneous 8.2 keV phase-contrast imaging and 24.6 keV x-ray diffraction from shock-compressed matter at the LCLS, Appl. Phys. Lett., 112:221907, 2018.
[2] A. Borbely, K. Dzieciol, and M. Scheel. Influence of phase contrast and detector resolution on the segmentation of tomographic images containing voids. Journal of Physics: Conference Series, 425:192005, 2013.
[3] J. Hoszowska, P. Monnin, S. Bulling, and et al. Quantitative characterization of edge enhancement in phase contrast x-ray imaging. Am. Assoc. Phys. Med., 31:1372–1383, 2004.
[4] T. E. Gureyev S. W. Wilkins, Ya. I. Nesterets and et al. On the evolution and relative merits of hard x-ray phase-contrast imaging methods. Phil. Trans. R. Soc. A, 372:20130021, 2014.

XPCI imaging technology