The second-order differential phase contrast and its retrieval for imaging with x-ray Talbot interferometry

• Published in: Medical physics (Lancaster) 2012-12, Vol.39 (12), p.7237-7253
• Main Authors: Yang, Yi, Tang, Xiangyang
• Format: Article
• Language: English
• Subjects: 60 APPLIED LIFE SCIENCES; Algorithms; Biosensors; Computed tomography; Computerised tomographs; computerised tomography; COMPUTERIZED SIMULATION; COMPUTERIZED TOMOGRAPHY; diagnostic radiography; Diffraction gratings; Digital computing or data processing equipment or methods, specially adapted for specific applications; FINE STRUCTURE; Image data processing or generation, in general; IMAGE PROCESSING; image retrieval; Image sensors; Information Storage and Retrieval - methods; INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY; Interferometric imaging; INTERFEROMETRY; Interferometry - methods; Medical image contrast; medical image processing; Medical imaging; Medical X‐ray imaging; PHANTOMS; Radiographic Image Enhancement - methods; Radiographic Image Interpretation, Computer-Assisted - methods; Radiography; REFRACTIVE INDEX; Reproducibility of Results; second‐order derivative; second‐order differential phase contrast; Sensitivity and Specificity; SMALL ANGLE SCATTERING; Talbot effect; Tomography, X-Ray Computed - methods; X RADIATION; X-RAY DIFFRACTION; X-Ray Diffraction - methods; X‐ray detectors; x‐ray differential phase contrast CT; x‐ray differential phase contrast imaging; X‐ray imaging; x‐ray phase contrast CT; x‐ray phase contrast imaging; X‐ray scattering; x‐ray Talbot interferometry
• ISSN: 0094-2405; 2473-4209
• DOI: 10.1118/1.4764901

Purpose: The x-ray differential phase contrast imaging implemented with the Talbot interferometry has recently been reported to be capable of providing tomographic images corresponding to attenuation-contrast, phase-contrast, and dark-field contrast, simultaneously, from a single set of projection data. The authors believe that, along with small-angle x-ray scattering, the second-order phase derivativeΦ ″ s (x) plays a role in the generation of dark-field contrast. In this paper, the authors derive the analytic formulae to characterize the contribution made by the second-order phase derivative to the dark-field contrast (namely, second-order differential phase contrast) and validate them via computer simulation study. By proposing a practical retrieval method, the authors investigate the potential of second-order differential phase contrast imaging for extensive applications. Methods: The theoretical derivation starts at assuming that the refractive index decrement of an object can be decomposed into δ = δ s + δ f , where δ f corresponds to the object's fine structures and manifests itself in the dark-field contrast via small-angle scattering. Based on the paraxial Fresnel-Kirchhoff theory, the analytic formulae to characterize the contribution made by δ s , which corresponds to the object's smooth structures, to the dark-field contrast are derived. Through computer simulation with specially designed numerical phantoms, an x-ray differential phase contrast imaging system implemented with the Talbot interferometry is utilized to evaluate and validate the derived formulae. The same imaging system is also utilized to evaluate and verify the capability of the proposed method to retrieve the second-order differential phase contrast for imaging, as well as its robustness over the dimension of detector cell and the number of steps in grating shifting. Results: Both analytic formulae and computer simulations show that, in addition to small-angle scattering, the contrast generated by the second-order derivative is magnified substantially by the ratio of detector cell dimension over grating period, which plays a significant role in dark-field imaging implemented with the Talbot interferometry. Conclusions: The analytic formulae derived in this work to characterize the second-order differential phase contrast in the dark-field imaging implemented with the Talbot interferometry are of significance, which may initiate more activities in the research and development of