中国物理B ›› 2025, Vol. 34 ›› Issue (3): 38701-038701.doi: 10.1088/1674-1056/ada430

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Signal estimation bias in x-ray dark-field imaging using dual phase grating interferometer

Zhi-Li Wang(王志立)1,†, Zun Zhang(张尊)1, Heng Chen(陈恒)1, and Xin Ge(葛昕)2   

  1. 1 School of Physics, Hefei University of Technology, Hefei 230009, China;
    2 School of Science, Shenzhen Campus of Sun Yat-sen University, Shenzhen 518107, China
  • 收稿日期:2024-10-10 修回日期:2024-12-05 接受日期:2024-12-31 发布日期:2025-03-15
  • 通讯作者: Zhi-Li Wang E-mail:dywangzl@hfut.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. U1532113, 11475170, and 11905041), Anhui Provincial Natural Science Foundation (Grant No. 2208085MA18), and Fundamental Research Funds for the Central Universities (Grant No. JZ2022HGTB0244).

Signal estimation bias in x-ray dark-field imaging using dual phase grating interferometer

Zhi-Li Wang(王志立)1,†, Zun Zhang(张尊)1, Heng Chen(陈恒)1, and Xin Ge(葛昕)2   

  1. 1 School of Physics, Hefei University of Technology, Hefei 230009, China;
    2 School of Science, Shenzhen Campus of Sun Yat-sen University, Shenzhen 518107, China
  • Received:2024-10-10 Revised:2024-12-05 Accepted:2024-12-31 Published:2025-03-15
  • Contact: Zhi-Li Wang E-mail:dywangzl@hfut.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. U1532113, 11475170, and 11905041), Anhui Provincial Natural Science Foundation (Grant No. 2208085MA18), and Fundamental Research Funds for the Central Universities (Grant No. JZ2022HGTB0244).

摘要: In x-ray dark-field imaging using dual phase grating interferometer, multi-contrast signals are extracted from a set of acquired phase-stepping data by using the least-squares fitting algorithm. The extracted mean intensity, amplitude and visibility signals may be intrinsically biased. However, it is still unclear how large these biases are and how the data acquisition parameters influence the biases in the extracted signals. This work set out to address these questions. Analytical expressions of the biases of the extracted signals were theoretically derived by using a second-order Taylor series expansion. Extensive numerical simulations were performed to validate the theoretical results. It is illustrated that while the estimated mean intensity signal is always unbiased, the estimated amplitude and visibility signals are both positively biased. While the biases of the estimated amplitude signals are proportional to the inverse of the total number of phase steps, the biases of the estimated visibility signals are inversely proportional to the product of the total number of phase steps and the mean number of photons counted per phase step. Meanwhile, it is demonstrated that the dependence of the biases on the mean visibility is quite different from that of Talbot-Lau interferometer due to the difference in the intensity model. We expect that these results can be useful for data acquisition optimizations and interpretation of x-ray dark-field images.

关键词: x-ray imaging, dual phase grating interferometer, dark-field imaging, signal bias

Abstract: In x-ray dark-field imaging using dual phase grating interferometer, multi-contrast signals are extracted from a set of acquired phase-stepping data by using the least-squares fitting algorithm. The extracted mean intensity, amplitude and visibility signals may be intrinsically biased. However, it is still unclear how large these biases are and how the data acquisition parameters influence the biases in the extracted signals. This work set out to address these questions. Analytical expressions of the biases of the extracted signals were theoretically derived by using a second-order Taylor series expansion. Extensive numerical simulations were performed to validate the theoretical results. It is illustrated that while the estimated mean intensity signal is always unbiased, the estimated amplitude and visibility signals are both positively biased. While the biases of the estimated amplitude signals are proportional to the inverse of the total number of phase steps, the biases of the estimated visibility signals are inversely proportional to the product of the total number of phase steps and the mean number of photons counted per phase step. Meanwhile, it is demonstrated that the dependence of the biases on the mean visibility is quite different from that of Talbot-Lau interferometer due to the difference in the intensity model. We expect that these results can be useful for data acquisition optimizations and interpretation of x-ray dark-field images.

Key words: x-ray imaging, dual phase grating interferometer, dark-field imaging, signal bias

中图分类号:  (X-ray imaging)

  • 87.59.-e
87.64.mf (Dark field) 07.60.Ly (Interferometers) 43.60.Cg (Statistical properties of signals and noise)