Geometric boundaries

Provided that the contrast transfer function lies in the direct phase regime, the Fresnel number from Eq.3.30satisfies the relationshipF≥1. It follows

Z_eff ≤ ∆r²_⊥

λ . (5.11)

Considering that the sample thickness is much smaller than the effective propagation dis-tance i.e.,∆tZ_eff [Weitkamp et al., 2011] Eq.3.21that determines the samples thickness for the Fresnel diffraction to take place is established as well.

Let’s consider a critical effective propagation distance Zeff,c, which is sufficient for the ar-gumentation of the geometric boundaries. Here, the resolution is meant to be two times the effective pixel size of the detector [Weitkamp et al., 2011]

Z_eff,c= (2·ps_eff)²

λ . (5.12)

With the average energy of 13.05 keV obtained from the spectrum measure at 40 kV, a wavelengthλ= 0.91 A^◦ is calculated. Evidently, the graph in Fig.5.17 reflects a quadratic course of the functionZ_eff,c(ps_eff). Within the range of propagation distance accounted in experiment I (see Table 5.3), the spacing z₂ draws close to the geometric boundaries of the setup for Z_eff,c= 34.28 mm². The side length of the field of view that may display the measurable object size by binning 2 is defined as

F OV = 1024

| {z }

Number of pixels

×pseff, (5.13)

which is∼1 mm in this specific case. Reversely, in order to measure entirely an object of thickness ∆t ' 3 mm in the near field regime at the setup, aps_eff ≈ 2.9 µm is required and corresponds to a Z_eff ≈ 396 mm that is far above the geometric boundaries of the setup. Hence, the restricted propagation distanceZ_eff enables the phase-contrast imaging of objects which size remain in a range smaller than a couple of millimeters. However, this is actually the scope of performance of a microscope and proves that the X-ray microscope is accommodated for phase-contrast imaging.

2The definition ofZeff,cis considered as sufficient since its value could even get higher for a true resolution, which might exceed two time thepseffaccording to Fig.5.17

Figure 5.17: variation of the effective propagation distanceZ_eff in accordance with the ef-fective pixel size ps_eff. Depending on the geometric boundaries z₁ and z₂ of the system, theps_eff achievable and the corresponding FOV can be evaluated, where the phase-contrast imaging is executable.

5.4 Summary

Studying the geometry, source and detector resolution of the X-ray imaging device ZEISS Xradia 500 Versa enabled us to find the optimal conditions for phase-contrast imaging with, subsequently, phase reconstruction. With some comparison to previous studies at X-ray mi-croscopes [Pogany et al., 1997], the influence of the magnification (z₂=z₁) and the effective propagation distanceZ_eff (implicitlyz₁) on the quality of the retrieved phase has been exper-imentally verified. While maintaining the magnification, it has been experexper-imentally demon-strated with a simple realistic object (Teflon - C₂F₄) that the phase contrast is optimized at low source-to-object distance (z₁). These results have been clearly observed by using a rep-resentative object (ant), where a net contrast in the reconstructed phase was achieved. This unprecedented experimental study with ZEISS Xradia 500 Versa has the importance to reveal the performance of the machine in terms of phase-contrast imaging. Ultimately, it is shown in practice that fast phase-contrast imaging is optimally applicable on real low absorbing objects, and yields high quality phase images in this laboratory device. Despite the choice of only a mean wavelength value λ from the source spectrum and the one-material non-stringent assumption of the phase retrieval used in this work, it can be agreed that the results obtained quantitatively (thicknesses) worked perfectly. However, the correct quantification could deviate, if λis not chosen properly. Apart from the fact that: (1) the imaging system resolution is limited by the finite source size, and (2) reaching high contrast is limited byz₁ (geometry), this study shows optimal application of phase-contrast imaging in radiography and tomography on low absorbing real objects in this commercial device.

Part III Applications

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Chapter 6

Microscopic computed tomography

In this chapter, some pertinent investigations at medium and microscopic resolution using the X-ray systems outlined in this work are featured. It is shown that the association of µCT with a few techniques can enable the execution of various inquiries. As example,µCT combined with methods to improve the contrast such as the staining of biological tissues and the dual-energy CT are demonstrated.

6.1 Introduction

Recent introduction of micro-computed tomography from medium to high resolution in lab-oratories helped to relieve synchrotron facilities and allowed pertinent solutions in different fields. Not long ago, state of the art and upcoming technologies available on the market for industrial applications of computed tomography were surveyed [De Chiffre et al., 2014], while their aptitude in meteorology was also reported [Kruth et al., 2011]. By means ofµCT, the study of ancient insect species fossilized in amber allowed to report on the global distri-bution of today’s related species [Penney et al., 2012], or facilitated taxonomic equivalence between specimen of different era [Dunlop et al., 2011]. With case studies of sample fos-silized in the sediment such as the Ediacaran specimenCorumbella werneri, µCT enabled the recovery of the morphology of the fossil [Bidola et al., 2015a] and coupled with its skele-tonization the taxonomic ranking was completed [Pacheco et al., 2015].

Imaging of soft tissues at true microscopic resolution employing fixation along with staining have been demonstrated [Shearer et al., 2014] and a periodical overview of the status of the technology could introduce in the developments and applications of µCT in biomedicine [Ritman, 2004, Ritman, 2011]. Compared to high flux facilities, studies elab-orated in X-ray laboratory apparatuses need longer scan times, but they are in return easier to access, they generate less expenses, and experience a substantial development towards higher resolution, as well as imaging techniques (e.g., dual-energy CT). For both devices stated in this work, this chapter illustrates the capabilities ofµCT through outstanding case studies.

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