Methods for obtaining superresolution images in coherent x-ray diffraction microscopy

Coherent x-ray diffraction microscopy (CXDM) using an x-ray free electron laser (XFEL) is expected to open up a new frontier of structural studies in materials science and biology, while radiation damage of samples under the extremely intense x rays is a matter of considerable concern. Two superresolution methods for CXDM proposed in this paper offer solutions of the problems by numerical data analysis. Promising results for future applications of CXDM with XFEL were obtained in a numerical simulation.

Figure 1

(Color) (a) (Left) SPring-8 logo as a sample image in $2379\times 1163$ pixels. (Right) Magnified image of the letter r in the logo. (b) Oversampled diffraction pattern of (a) in $4096\times 4096$ pixels. (c) The central $2001\times 2001$ pixels of diffraction pattern of (b). The central $5\times 5$ pixels are masked. (d) Image in the central $1163\times 564$ pixels reconstructed from (c) using the iterative normalization algorithm and the magnified image of the letter r. (e) Central $501\times 501$ pixels of diffraction pattern of (c). (f) Image in the central $291\times 142$ pixels reconstructed from (e) using the iterative normalization algorithm and the magnified image of the letter r. (g) Diffraction pattern with a mask outside the central $501\times 501$ pixels of (c). (h) Image in the central $1163\times 564$ pixels reconstructed from (g) using the iterative normalization algorithm and the magnified image of the letter r. The support is $1163\times 564$ pixels for the image reconstructions of (d) and (h), and is $291\times 142$ pixels square for (f).

Figure 2

(Color) (a) SPring-8 logo image reconstructed using the iterative normalization algorithm in combination with the discrete-upper-bound constraint of Eq. (1) and the magnified image of the letter r. (b) Diffraction pattern derived from the reconstructed image of (a). (c) Logo image improved using MEM and the magnified image of the letter r. (d) The diffraction pattern derived from the reconstructed image of (c). The diffraction patterns of (b) and (d) are calculated by applying fast Fourier transformations to the images of (a) and (c), respectively. The pixels outside of the central $501\times 501$ pixels of (b) and (d) are estimated by the respective superresolution methods.