X-ray Bragg magnifier microscope as a linear shift invariant imaging system: image formation and phase retrieval.

We present the theoretical description of the image formation with the in-line germanium Bragg Magnifier Microscope (BMM) and the first successful phase retrieval of X-ray holograms recorded with this imaging system. The conditions under which the BMM acts as a linear shift invariant system are theoretically explained and supported by the experiment. Such an approach simplifies the mathematical treatment of the image formation and reconstruction as complicated propagation of the wavefront onto inclined planes can be avoided. Quantitative phase retrieval is demonstrated using a test sample and a proof of concept phase imaging of a spider leg is also presented.

On the origin of visibility contrast in x-ray Talbot interferometry.

The reduction in visibility in x-ray grating interferometry based on the Talbot effect is formulated by the autocorrelation function of spatial fluctuations of a wavefront due to unresolved micron-size structures in samples. The experimental results for microspheres and melamine sponge were successfully explained by this formula with three parameters characterizing the wavefront fluctuations: variance, correlation length, and the Hurst exponent. The ultra-small-angle x-ray scattering of these samples was measured, and the scattering profiles were consistent with the formulation. Furthermore, we discuss the relation between the three parameters and the features of the micron-sized structures. The visibility-reduction contrast observed by x-ray grating interferometry can thus be understood in relation to the structural parameters of the microstructures.

Hard-X-ray phase-difference microscopy using a fresnel zone plate and a transmission grating.

Novel hard x-ray phase imaging microscopy that simply uses an objective and a transmission grating is described. The microscope generated an image that exhibited twin features of a sample with an opposite phase contrast having a separation of a specific distance. Furthermore, the twin features were processed to generate an image mapping the x-ray phase shift through a simple algorithm. The presence of the grating did not degrade the spatial resolution of the microscope. The sensitivity of our microscope to light elements was about 2 orders of magnitude higher than that of the absorption contrast microscope that was attained by simply removing the grating. Our method is attractive for easily appending a quantitative phase-sensitive mode to normal x-ray microscopies, and it has potentially broad applications in biology and material sciences.

Photon detection efficiency of laboratory-based x-ray phase contrast imaging techniques for mammography: a Monte Carlo study.

An important challenge in real-world biomedical applications of x-ray phase contrast imaging (XPCI) techniques is the efficient use of the photon flux generated by an incoherent and polychromatic x-ray source. This efficiency can directly influence dose and exposure time and ideally should not affect the superior contrast and sensitivity of XPCI. In this paper, we present a quantitative evaluation of the photon detection efficiency of two laboratory-based XPCI methods, grating interferometry (GI) and coded-aperture (CA). We adopt a Monte Carlo approach to simulate existing prototypes of those systems, tailored for mammography applications. Our simulations were validated by means of a simple experiment performed on a CA XPCI system. Our results show that the fraction of detected photons in the standard energy range of mammography are about 1.4% and 10% for the GI and CA techniques, respectively. The simulations indicate that the design of the optical components plays an important role in the higher efficiency of CA compared to the GI method. It is shown that the use of lower absorbing materials as the substrates for GI gratings can improve its flux efficiency by up to four times. Along similar lines, we also show that an optimized and compact configuration of GI could lead to a 3.5 times higher fraction of detected counts compared to a standard and non-optimised GI implementation.

An improved phase shift reconstruction algorithm of fringe scanning technique for X-ray microscopy.

The X-ray phase imaging method has been applied to observe soft biological tissues, and it is possible to image the soft tissues by using the benefit of the so-called "Talbot effect" by an X-ray grating. One type of the X-ray phase imaging method was reported by combining an X-ray imaging microscope equipped by a Fresnel zone plate with a phase grating. Using the fringe scanning technique, a high-precision phase shift image could be obtained by displacing the grating step by step and measuring dozens of sample images. The number of the images was selected to reduce the error caused by the non-sinusoidal component of the Talbot self-image at the imaging plane. A larger number suppressed the error more but increased radiation exposure and required higher mechanical stability of equipment. In this paper, we analyze the approximation error of fringe scanning technique for the X-ray microscopy which uses just one grating and proposes an improved algorithm. We compute the approximation error by iteration and substitute that into the process of reconstruction of phase shift. This procedure will suppress the error even with few sample images. The results of simulation experiments show that the precision of phase shift image reconstructed by the proposed algorithm with 4 sample images is almost the same as that reconstructed by the conventional algorithm with 40 sample images. We also have succeeded in the experiment with real data.

X-ray diffraction from an atomic plane

Reflection and transmission coefficients of X-rays by a single atomic plane are obtained in the general case where the plane consists of any two-dimensional Bravais lattice and the incident and exit X-ray beams take any direction with respect to the plane. A formula obtained for the coefficients is written in a simple form, different from that obtained by Durbin [Acta Cryst. (1995), A51, 258-268]. This makes it possible to extend Darwin's dynamical theory of X-ray diffraction to general geometries which include the cases of asymmetric skew reflection and noncoplanar multibeam diffraction.