Purpose: Differential phase contrast CT has been recognized as an x-ray imaging method with the potential to greatly improve the differentiation of soft tissues. Talbot interferometry has been one of the promising solutions allowing implementation with commercially available x-ray tubes with a polychromatic spectrum. Mainly due to imperfections in grating fabrication and the polychromatic spectrum of x-ray beam, a twin-peaks phenomenon may exist in phase stepping curves (PSCs) and degrade the performance of phase retrieval. The authors have previously proposed a Fourier analysis based method for phase retrieval in the scenario wherein the twin-peaks phenomenon occurs in PSCs. In this work, the authors propose a 5-step algebraic method for phase retrieval and investigate the potential of reducing radiation dose while both the Fourier and algebraic methods are being utilized for phase retrieval.
Methods: The algebraic method to deal with the twin-peaks phenomenon, in which a set of linear equations with five unknown variables is needed for phase retrieval, is an extension of the so-called 3-step method that has been used in the scenario wherein only single-peak exists in the PSCs. In addition to a numerical phantom, two sets of experimental data (a phantom made of organic materials and a small animal) acquired by a prototype differential phase contrast CT system are employed to evaluate the performance of the Fourier and algebraic phase retrieval methods and their potential in radiation dose reduction.
Results: The evaluation by both numerical phantom and experimental data shows that the algebraic method works as well as the Fourier method in phase retrieval if the twin-peaks phenomenon in the PSCs is appropriately dealt with. In addition, while the radiation dose associated with data acquisition is being reduced via fewer phase shifting steps, the algebraic method can maintain a better performance compared to the Fourier method.
Conclusions: Along with the Fourier method, the proposed 5-step algebraic method can cope with the twin-peaks phenomenon in phase retrieval. With decreased phase shifting steps and thus radiation dose, the proposed algebraic method performs better than the Fourier method, providing a practical solution for implementation of grating based differential phase contrast CT.