  Background: X-ray grating-based dark-field imaging can sense the small angle
scattering caused by an object's micro-structure. This technique is sensitive
to lung's porous alveoli and is able to detect lung disease at an early stage.
Up to now, a human-scale dark-field CT has been built for lung imaging.
Purpose: This study aimed to develop a more thorough optimization method for
dark-field lung CT and summarize principles for system design. Methods: We
proposed a metric in the form of contrast-to-noise ratio (CNR) for system
parameter optimization, and designed a phantom with concentric circle shape to
fit the task of lung disease detection. Finally, we developed the calculation
method of the CNR metric, and analyzed the relation between CNR and system
parameters. Results: We showed that with other parameters held constant, the
CNR first increases and then decreases with the system auto-correlation length
(ACL). The optimal ACL is nearly not influenced by system's visibility, and is
only related to phantom's property, i.e., scattering material's size and
phantom's absorption. For our phantom, the optimal ACL is about 0.21 {\mu}m. As
for system geometry, larger source-detector and isocenter-detector distance can
increase the system's maximal ACL, helping the system meet the optimal ACL more
easily. Conclusions: This study proposed a more reasonable metric and a
task-based process for optimization, and demonstrated that the system optimal
ACL is only related to the phantom's property.
