Eikonal Phase Retrieval: unleashing the potential of fourth-generation sources for enhanced propagation-based tomography on biological samples

Abstract

The evolution of synchrotrons towards higher brilliance beams has increased the possible sample-to-detector propagation distances for which the source confusion circle does not lead to geometrical blurring. This makes it possible to push near-field propagation-driven phase-contrast enhancement to the limit, revealing low-contrast features that would otherwise remain hidden under excessive noise. Until now, this possibility was hindered in many objects of scientific interest by the simultaneous presence of strong phase gradient regions and low contrast features. The strong gradients, when enhanced with the now possible long propagation distances, induce such strong phase effects that the linearization assumptions of current state-of-the-art single-distance phase retrieval filters are broken, and the resulting image quality is jeopardized. Here, we introduce a new iterative phase retrieval algorithm and compare it with the Paganin phase retrieval algorithm, in both the monochromatic and polychromatic cases. In the polychromatic case the comparison was done with an extrapolated Paganin algorithm obtained by reintroducing, into our phase retrieval algorithm, the linearization approximations underlying the Paganin forward model. Our work provides an innovative algorithm that efficiently performs the phase retrieval task over the entire near-field range, producing images of superior quality for mixed attenuation objects. Our tests on data with shorter propagation distances show that the artifacts, which our algorithm effectively addresses, are present already in more standard third-generation synchrotron setups. This highlights the potential broad applicability of the Eikonal Phase Retrieval method.

Keywords: eikonal approximation; iterative phase retrieval; phase-contrast tomography; propagation-based imaging; synchrotron imaging.

Figure 1

Spectral shape used for the different samples. Blue curve: adult human lung experiment. Green curve: sheep head experiment. Magenta curve: Leptodactylus pentadactylus experiment. The vertical lines delimit the intervals used in the discretization of the spectral shape. The spectra used for the rabbit bone is close to the one used for the sheep’s head and has been omitted in the plot.

Figure 2

Sheep head HiP-CT scan at an average detected energy of 109 K eV, 5 K × 5 K pixels images. Left, the Paganin et al. algorithm at the average detected beam energy. Right, the result obtained using the algorithms introduced by the present work. For EPR we have considered five spectral points across the BM18 detected spectrum and we have applied SLD for a tail containing 30% of the total signal and a damping length of 80 pixels. We used the refractive indexes for 75% hydroxyapatite, 25% collagen. The regions marked A, B, C and D are shown in detail in Fig. 3 ▸, highlighting a detailed comparison between EPR and Paganin et al. methods.

Figure 3

A detailed comparison between the EPR and Paganin et al. methods on zoomed regions from Fig. 2 ▸ marked A, B, C and D. Monochromatic case.

Figure 4

A detailed comparison between the EPR and Paganin et al. methods on zoomed regions from Fig. 2 ▸ marked A, B, C and D. Polychromatic case.

Figure 5

Incremental application of SLD and EPR: (left) reconstruction by the standard Paganin et al. algorithm, (center) the result by preprocessing the radiography with SLD, (right) the effect of both the SLD and EPR algorithms. In the first row the gray scale is adapted to the soft matter (the range is marked by yellow ticks in the red histogram); in the second it covers the whole range.

Figure 6

Effect of the polychomatic method for EPR and Paganin. First row: monochromatic approach considering only one photon energy in both the Paganin and EPR forward model. Second row: polychromatic approach considering the discretized spectra, with five photon energies (as in Fig. 1 ▸), in the forward models. The polychromatic version of the Paganin phase retrieval has been implemented replacing the EPR forward model, for each spectral point, by equations (1) and (2), and keeping all the rest of the EPR code unchanged.

Figure 7

Frog head: 900 × 800 view spanning the brain (A), ear (B) and skull muscles (C) subregions. The image has been obtained with SLD + Paganin (left) and EPR (right) algorithms. The acquisition has been performed at BM18 with an average beam energy of 127 keV using the HiP-CT protocol, a voxel size of 23.27 µm and 20 m propagation distance.

Figure 8

Zoomed views of the frog head subregions. Rows: regions A, B and C from Fig. 5 ▸. Columns: the difference between the two methods (left); SLD + Paganin et al. (center); SLD + EPR with five spectral points (right). The used gray scales have a constant minimum to maximum width over a given row, and are centered, for each image, over the soft matter range.

Figure 9

Sheep head HiP-CT scan at 112 keV with a 16.45 µm detector pixel size and 30 m propagation distance. The shown region corresponds to region A of Fig. 4 ▸. Reducing the pixel size (from 28 µm of Fig. 4 ▸), while keeping unchanged the propagation distance, enhances the phase effects but also the linearization artifacts which remains strongly reduced using the EPR algorithm.

Figure 10

Comparison between the Paganin method and EPR. Region A: sheep head’s optic nerve region at 90 keV, 1.5 m propagation distance and 2.25 µm pixel size. Region B: rabbit bone at 103 keV, with 1.4 m propagation distance and 2.0 µm pixel size. Region C: an adult human lung sample region at 90 keV, 4 m propagation distance and 4.26 µm pixel size.

Figure 11

Hybrid scheme results, where only a fraction of each radiography is processed with EPR and the remaining part with Paganin, according to automatic detection of the critical regions. From left to right the results are shown for an overall average of 100%, 37% and 27% of the total projection volume processed with EPR. For an EPR coverage of 37% the difference with the 100% case is barely visible.