Numerical study of Bragg CDI on thick polycrystalline specimens

Abstract

Bragg coherent diffraction imaging (BCDI) is a powerful X-ray imaging technique for crystalline materials, providing high resolution maps of structure and strain. The technique is typically used to study a small isolated object, and is in general not compatible with a bulk polycrystalline sample, due to overlap of diffraction signals from various crystalline elements. In this paper, we present an imaging method for bulk samples, based on the use of a coherent source. The diffracted X-ray beam from a grain or domain of choice is magnified by an objective before being monitored by a 2D detector in the far field. The reconstruction principle is similar to the case of BCDI, while taking the magnification and pupil function into account. The concept is demonstrated using numerical simulations and reconstructions. We find that by using an object-lens distance shorter than the focal length, the numerical aperture is larger than in a traditional imaging geometry, and at the same time the setup is insensitive to small phase errors by lens imperfections. According to our simulations, we expect to be able to achieve a spatial resolution smaller than 20 nm when using the objective lens in this configuration.

Confocal Bragg ptychography for bulk specimens: a numerical demonstration

“…However, the working distance from exit plane to entry of the lens is sufficiently long for the CRL entry point to be effectively in the far-field limit (the Fractional Fourier angle is 0.499π, corresponding to a Fresnel number of 9.83×10 −6 ). Similar observations were made in our previous work on objective based BCDI [14,15].…”

“…Using iterative algorithms, the shape and strain field can be reconstructed. We showed by simulations that aberrations in the objective lens has no significant effect on performance in this set up, as long as the lens is placed in the far-field of the diffracting object [14]. Next, we demonstrated the method experimentally on a 500 nm Pt grain [15].…”

“…We use a fractional Fourier transform (FrFT) approach [25,26] to generate the diffraction data. We have previously demonstrated that this approach accurately and efficiently takes into account the thick-lens behavior of a CRL objective lens and its use for both dark field microscopy and Bragg CDI [14]. For each position of the probe (P j ) the exit field is calculated as a sum (projection) of P j •ρ along the exit direction, the z-axis.…”

“…Recently we demonstrated a new implementation of BCDI, which is able to provide highly resolved 3D images of single interior crystals within a thick poly-crystalline sample [14,15]. The experimental set-up is a generalization of the classical BCDI configuration, where -similar to DFXM -we placed an X-ray lens in the diffracted beam from one selected interior crystal (which depending on context may be a grain or a domain).…”

“…The experimental set-up is a generalization of the classical BCDI configuration, where -similar to DFXM -we placed an X-ray lens in the diffracted beam from one selected interior crystal (which depending on context may be a grain or a domain). The small angular acceptance of the lens behaves as a spatial filter [14,15], which drastically reduces the diffracting volume. The 3D coherent diffraction pattern of the chosen crystal therefore is not superposed upon the diffraction patterns of other crystals.…”