基于光栅干涉仪的暗场成像的Cramér-Rao下界-《中国医学物理学杂志》

文章信息/Info

Title:: Cramér-Rao lower bound of dark-field imaging using a grating interferometer

Author(s):: LIU Bo; CHEN Zihan; GU Yao; CHEN Heng; WANG Zhili; Department of Optical Engineering, School of Physics, Hefei University of Technology, Hefei 230009, China

Keywords:: Keywords: dark-field imaging grating interferometer Cramér-Rao lower bound visibility

摘要:: 在光栅相衬成像中，通常使用相位步进法进行数据采集和信息提取。然而，对于相位步进法在提取暗场信号的算法效率还没有得到充分的评估。本研究引入Cramér-Rao下界对提取暗场信号的算法效率进行评估。基于理论分析和数值计算发现目前完全有效的算法仅适用于三步相位步进法，其他更多步数的相位步进法都是次优的。本研究以Cramér-Rao下界作为依据，定量地分析了相位步进数和可见度对算法效率的影响。结果表明在低可见度的情况下，相位步进法可以接近理论的最佳效率；在高可见度的情况下，当相位步进数大于5时，算法效率仅为77.4%，这可为基于X射线和中子光栅干涉仪的暗场成像的信噪比优化提高、剂量优化提供指导。

Abstract:: Abstract: In grating-based phase contrast imaging, the phase stepping technique is commonly utilized for data acquisition and signal retrieval from acquired intensity data. However, the algorithm efficiency with respect to the dark-field retrieval has yet to be sufficiently evaluated. Herein the algorithm efficiency of dark-field retrieval based on Cramér-Rao lower bound is evaluated. The theoretical analysis and numerical results demonstrates that fully efficient algorithm is currently available only for 3-step phase stepping technique, and other techniques with more phase steps are all sub-optimal. Quantitatively, the dependence of the algorithm efficiency on the phase step number and the visibility is investigated. It is shown that the phase stepping technique can nearly approach its theoretical optimal efficiency in the case of a low visibility. With a phase step greater than 5, the algorithm efficiency is only 77.4% in the case of a high visibility. The study can provide some reference for signal-to-noise ratio improvement and potential dose optimization in X-ray and neutron grating-based dark-field imaging.