Xu Ji1, Yongshuai Ge1, Ran Zhang1, Ke Li1,2, Guang-Hong Chen1,2. 1. Department of Medical Physics, University of Wisconsin School of Medicine and Public Health, Madison, WI, USA. 2. Department of Radiology, University of Wisconsin School of Medicine and Public Health, Madison, WI, USA.
Abstract
PURPOSE: In grating-based x-ray multi-contrast imaging, signals of three contrast mechanisms-absorption contrast, differential phase contrast (DPC), and dark-field contrast-can be estimated from the same set of acquired data. The estimated signals, N0 (related to absorption), N1 (related to dark-field), and φ (related to DPC) may be intrinsically biased. However, it is yet unclear how large these biases are and how the data acquisition parameters affect the biases in the extracted signals. The purpose of this paper was to address these questions. METHODS: The biases of the extracted signals (i.e., N0 , N1 and φ) were theoretically studied for a well-known signal estimation method. Experimental data acquired from a grating-based x-ray multi-contrast benchtop imaging system with a photon counting detector were used to validate the theoretical results for the signal biases of the three contrast mechanisms. RESULTS: Both theoretical and experimental studies showed the following results: (1) The bias of signal estimation for the absorption contrast signal is zero; (2) The bias of signal estimation for N1 is inversely proportional to the number of phase steps and to the average fringe visibility of the grating interferometer, but the ratio between the bias and the signal level (i.e., the relative bias) is independent of the number of phase steps; (3) The bias of signal estimation for φ depends on the mean DPC signal level, the total exposure level of the multi-contrast data acquisition, and the mean fringe visibility of the interferometer. CONCLUSIONS: In grating-based x-ray multi-contrast imaging, the estimated absorption contrast signal is unbiased; the estimated dark-field contrast signal is biased, but the relative bias is only dependent on the mean fringe visibility of the interferometer and the exposure level. The estimated DPC signal may be biased, and the bias level depends on the mean signal level, the exposure level, and the interferometer performance.
PURPOSE: In grating-based x-ray multi-contrast imaging, signals of three contrast mechanisms-absorption contrast, differential phase contrast (DPC), and dark-field contrast-can be estimated from the same set of acquired data. The estimated signals, N0 (related to absorption), N1 (related to dark-field), and φ (related to DPC) may be intrinsically biased. However, it is yet unclear how large these biases are and how the data acquisition parameters affect the biases in the extracted signals. The purpose of this paper was to address these questions. METHODS: The biases of the extracted signals (i.e., N0 , N1 and φ) were theoretically studied for a well-known signal estimation method. Experimental data acquired from a grating-based x-ray multi-contrast benchtop imaging system with a photon counting detector were used to validate the theoretical results for the signal biases of the three contrast mechanisms. RESULTS: Both theoretical and experimental studies showed the following results: (1) The bias of signal estimation for the absorption contrast signal is zero; (2) The bias of signal estimation for N1 is inversely proportional to the number of phase steps and to the average fringe visibility of the grating interferometer, but the ratio between the bias and the signal level (i.e., the relative bias) is independent of the number of phase steps; (3) The bias of signal estimation for φ depends on the mean DPC signal level, the total exposure level of the multi-contrast data acquisition, and the mean fringe visibility of the interferometer. CONCLUSIONS: In grating-based x-ray multi-contrast imaging, the estimated absorption contrast signal is unbiased; the estimated dark-field contrast signal is biased, but the relative bias is only dependent on the mean fringe visibility of the interferometer and the exposure level. The estimated DPC signal may be biased, and the bias level depends on the mean signal level, the exposure level, and the interferometer performance.
Authors: Arne Tapfer; Martin Bech; Astrid Velroyen; Jan Meiser; Jürgen Mohr; Marco Walter; Joachim Schulz; Bart Pauwels; Peter Bruyndonckx; Xuan Liu; Alexander Sasov; Franz Pfeiffer Journal: Proc Natl Acad Sci U S A Date: 2012-09-10 Impact factor: 11.205
Authors: Houxun Miao; Andrew A Gomella; Katherine J Harmon; Eric E Bennett; Nicholas Chedid; Sami Znati; Alireza Panna; Barbara A Foster; Priya Bhandarkar; Han Wen Journal: Sci Rep Date: 2015-08-28 Impact factor: 4.379
Authors: Houxun Miao; Alireza Panna; Andrew A Gomella; Eric E Bennett; Sami Znati; Lei Chen; Han Wen Journal: Nat Phys Date: 2016-04-25 Impact factor: 20.034
Authors: Lorenz Birnbacher; Marian Willner; Astrid Velroyen; Mathias Marschner; Alexander Hipp; Jan Meiser; Frieder Koch; Tobias Schröter; Danays Kunka; Jürgen Mohr; Franz Pfeiffer; Julia Herzen Journal: Sci Rep Date: 2016-04-04 Impact factor: 4.379