  We propose a one-shot thickness measurement method for sponge-like structures
using a propagation-based X-ray phase-contrast imaging (P-PCI) method. In
P-PCI, the air-material interface refracts the incident X-ray. Refracted many
times along their paths by such a structure, incident X-rays propagate randomly
within a small divergent angle range, resulting in a speckle pattern in the
captured image. We found structure thickness and contrast of a phase-contrast
projection are directly related in images. This relationship can be described
by a natural logarithm equation. Thus, from the one phase-contrast view, depth
information can be retrieved from its contrast. Our preliminary biological
experiments indicate promise in its application to measurements requiring in
vivo and ongoing assessment of lung tumor progression.
