X-ray phase contrast tomography potentially offers several advantages over tomography based on absorption contrast, such as greatly improved sensitivity and lower dose. If the coherence of the X-ray beam is sufficient, a simple mode of phase contrast imaging, based on free space propagation, becomes possible. Phase contrast is achieved by moving the detector downstream of the object and a tomographic scan is then recorded at several sample-to-detector distances (Fig. 1). The reconstruction is usually divided into two steps. The phase shift induced by the object is retrieved for each projection angle from the radiographs taken at different distances. This is then used as input to a standard tomographic reconstruction algorithm such as filtered backprojection (FBP). This yields a reconstruction of the 3D refractive index distribution in the sample. Several theoretical approaches for phase retrieval have been proposed, but few works address the quantitative evaluation of such methods.
Figure 1: Schematic of the experimental setup. Phase contrast is achieved by moving the detector a distance D from the sample. A tomographic scan is then recorded for each distance. Moving the detector to D=0 yields absorption contrast only.
Three phase retrieval algorithms were evaluated: one based on the Transport of Intensity Equation (TIE), one based on the Contrast Transfer Function (CTF) and one based on a mixed approach between the previous two, recently developed at the ESRF [Guigay et al., in preparation].
A phantom of known composition was imaged at the ESRF, using the long beamline ID19 micro-CT setup. Tomographic scans were acquired at four distances (0.012, 0.1, 0.3 and 0.99 m) and 1000 angular positions using 24 keV X-rays. A 2048x2048 CCD detector was used at a pixel size of 7.5 µm. A computer simulation was also performed, using an analytically defined phantom. The same experimental parameters and theoretical absorption- and refractive index constants as above were used.
The two data sets were used as input to the phase retrieval algorithms. The retrieved phase maps were in turn input to a 3D FBP reconstruction (Fig. 2). The reconstructed values were then compared to theoretical values of the refractive index. On the simulated data, mean errors of 10 % for the TIE, 16 % for the CTF and 3.8 % for the Mixed approach were measured. On the experimental data, the measured errors were 42 % for the TIE, 17 % for the CTF and 5.9 % for the Mixed approach. The developed tests are foreseen to be utilized to evaluate further developments of phase retrieval techniques .
Figure 2: Reconstructions. From left to right: absorption, TIE, CTF and Mixed approach. (a) Center slice of simulated phantom. (b) representative slice of constructed phantom.