Studies of signal estimation bias in grating-based x-ray multicontrast imaging

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.

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.

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.

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.