Is high sensitivity always desirable for a grating‐based differential phase contrast imaging system?

Abstract

Purpose In grating‐based x‐ray differential phase contrast (DPC) imaging, the measured signal amplitude of the phase shift induced by an image object is proportional to the so‐called system sensitivity. Therefore, to achieve a better signal‐to‐noise (SNR) for improved imaging performance, it is generally believed that one should increase the system sensitivity by reducing the period of the analyzer grating or increasing the distance between the phase grating and analyzer grating. The purpose of this work is to theoretically and experimentally demonstrate that there is an optimal system sensitivity to attain the highest SNR for a given task provided that the standard phase‐stepping acquisition and phase retrieval methods are used. When system sensitivity goes beyond this optimal value, SNR decreases and the imaging performance deteriorates. Methods Due to the fundamental fact that the measured phase signal is a cyclic variable, the phase wrapping effect is inevitable in DPC imaging when the system sensitivity increases. The phase wrapping effect appears in both signal and noise measurements. The effect in the signal measurement is manifested in the so‐called signal statistical bias and such effect often impacts the accuracy of the measurement. The phase wrapping effect also appears in the noise variance measurement and impacts the precision of the measurement. A thorough theoretical analysis was performed in this work to demonstrate the quantitative impacts of phase wrapping on both signal bias and noise variance and thus on the actual system SNR. The joint effect of phase wrapping in both the signal bias and noise variance yields an optimal system sensitivity to achieve the highest SNR. Both extensive numerical simulation studies and experimental studies were performed to validate the theoretical analysis. Results Both theoretical analysis and experimental studies show that the SNR of the DPC signal is not always proportional to the sensitivity due to the cyclic nature of the signal and the phase wrapping effect. For a given refraction angle and exposure level, there exists an optimal sensitivity factor that maximizes the SNR, beyond which, increasing the sensitivity will decrease the SNR. Conclusions Increase of system sensitivity does not always improve x‐ray DPC imaging performance provided that the standard phase‐stepping acquisition and phase retrieval methods are used.

Grating-free quantitative phase retrieval for x-ray phase-contrast imaging with conventional sources

“…However, because the mesh is directly visible, this method produces two-dimensional measurements from a single image and has different resolution and noise limitations than a stepped Talbot-grating measurement. While there is approximately a factor of 20 reduction in angular sensitivity compared to using a grating with a 20X smaller period, angular sensitivity may be less important than signal-to-noise ratio in assessing image performance [26], and high angular sensitivity may come at the expense of dose. Meshbased image SNR values are comparable to grating measurements [19,26].…”

“…While there is approximately a factor of 20 reduction in angular sensitivity compared to using a grating with a 20X smaller period, angular sensitivity may be less important than signal-to-noise ratio in assessing image performance [26], and high angular sensitivity may come at the expense of dose. Meshbased image SNR values are comparable to grating measurements [19,26]. Images are directly analyzed for distortions, rather than creating and analyzing interference fringes, which avoids phase unwrapping issues.…”

Factors Affecting the Spatial Resolution in 2D Grating–Based X-Ray Phase Contrast Imaging

“…Birnbacher et al developed a laboratory X-ray grating-based phase contrast imaging system with 5 nrad sensitivity [19]. Xu et al discovered that high sensitivity is not always related to high image quality, while the best image quality is achieved at proper sensitivity [20]. As for the signal-to-noise ratio, Fraiz et al compared SNRs of the retrieved images between two information retrieval methods and found that the angular signal radiography method had a better SNR in refraction and scattering images than the phase-stepping method [21].…”