A Gaussian extension for Diffraction Enhanced Imaging

Abstract

Unlike conventional x-ray attenuation one of the advantages of phase contrast x-ray imaging is its capability of extracting useful physical properties of the sample. In particular the possibility to obtain information from small angle scattering about unresolvable structures with sub-pixel resolution sensitivity has drawn attention for both medical and material science applications. We report on a novel algorithm for the analyzer based x-ray phase contrast imaging modality, which allows the robust separation of absorption, refraction and scattering effects from three measured x-ray images. This analytical approach is based on a simple Gaussian description of the analyzer transmission function and this method is capable of retrieving refraction and small angle scattering angles in the full angular range typical of biological samples. After a validation of the algorithm with a simulation code, which demonstrated the potential of this highly sensitive method, we have applied this theoretical framework to experimental data on a phantom and biological tissues obtained with synchrotron radiation. Owing to its extended angular acceptance range the algorithm allows precise assessment of local scattering distributions at biocompatible radiation doses, which in turn might yield a quantitative characterization tool with sufficient structural sensitivity on a submicron length scale.

Diffraction Enhanced Imaging Analysis with Pseudo-Voigt Fit Function

“…Since, from a medical point of view it is desirable to minimize the radiation dose, the authors in [ 6 ] acquired just two images (at roughly half the maximum peak intensity on each side of the RC) and used relative changes of intensity and the slope to compute the two parameters. Assuming a Gaussian RC shape, Arfelli et al [ 19 ] introduced the G 2 DEI algorithm to additionally extract the scattering width from three images on the RC. Chen et al [ 20 ] indicated how to retrieve different types of information from the analysis of the moments of RCs, in particular the skewness (3rd moment) and the kurtosis (4th moment), revealing the asymmetry (caused by the local curvature of interfaces) and the strength of the tails relative to the peak, respectively.…”

“…As a reference, we implemented a fitting procedure based on Gaussian functions (Equation (8)), as suggested, e.g., by Arfelli et al [ 19 ]: where I B is the baseline level (offset), θ c is the center, A is the integral, and w the FWHM of the RC for each pixel. The FWHM is linked to the standard deviation σ by the factor (8 ln(2)) ½ .…”

“…The four images (see Table 1 ) of the specimen and the flat field were used to calculate images of: the transmission (peak integral), the apparent transmission (peak height), the refraction angle (peak position) (according to Equations (2)–(5)), the refraction value C m · d , the attenuation µ · d , and the specific surface C m /( µ · d ), according to Equations (6) and (7). It should be noted that the negative logarithm of the apparent transmission image is named the apparent absorption in some studies (e.g., [ 6 , 19 ]).…”

Tomographic reconstruction using tilted Laue analyser-based X-ray phase-contrast imaging

“…RCs can be modelled using a Taylor series, Gaussian distribution or a Pearson VII function (Pearson, 1916), allowing phase retrieval to be performed. Gaussian functions are commonly used to fit the RCs as they are relatively easy to implement and accurately models the bell curve shape (Zhifeng et al, 2007;Hu et al, 2008;Diemoz et al, 2010;Arfelli et al, 2018). However, Gaussian functions can fail at accurately modelling the peak and tails of the RC from the long slit geometry of ABPCI (Oltulu et al, 2003;Nesterets et al, 2006).…”

Technical Design Considerations of a Human-Scale Talbot-Lau Interferometer for Dark-Field CT

“…Another candidate to extend the value of clinical CT is dark-field imaging which allows to simultaneously measure the attenuation, refraction, and small-angle scattering of a transmitted sample [2]- [4]. While this can be achieved with various methods at synchrotrons (e.g., analyzer-based, speckle-based, propagation-based imaging [5]- [7]) only grating-based Talbot-Lau interferometry and edge illumination have successfully been translated to incoherent X-ray sources with a large source spot [8]- [11].…”