Biases of estimated signals in x-ray analyzer-based imagingProject supported by the National Natural Science Foundation of China (Grant Nos. U1532113, and 11475170) and the Fundamental Research Funds for the Central Universities, China (Grant No. PA2020GDKC0024)

Recently, a novel three-image algorithm has been proposed to retrieve the sample's absorption, refraction, and scattering properties in x-ray analyzer-based imaging. The feasibility of the three-image algorithm was validated by synchrotron radiation experiments. However, it is unclear yet whether the estimated refraction and scattering signals are biased or not and how the analyzer angular position affects the biases in the estimated signals. For this purpose, the biases of the extracted refraction and scattering signals are theoretically derived for the three-image algorithm. The theoretical models are further confirmed by numerical experiments. The results show that both the estimated refraction and scattering signals are biased, and the biases are strongly dependent on the analyzer angular position. Besides, the biases also show dependence on the sample's refraction and scattering properties locally. Those results can be used as general guidelines to optimize experimental parameters for bias reduction and accurate imaging of different features within the sample.