Processing of projections containing phase contrast in laboratory micro-computerized tomography imaging

Processing of phase-contrast images in laboratory conditions is described.


Introduction
Modern laboratory X-ray imaging systems with a microfocus source and a CCD camera make it possible to move some of the modern imaging techniques from synchrotrons to laboratories (Gundogdu et al., 2007). The main stream of our work is to study and to implement advanced phase-contrast imaging techniques in laboratory conditions. For this purpose, it was necessary to design and to build a convenient X-ray imaging system (Zaprazny et al., 2012). This system is suitable for lightweight objects. Such objects can be biological objects, plastics, wood, paper etc., where the phase contrast helps increase the visibility of the finest structures. Phase contrast is simply achieved by propagation of spatially coherent X-rays through free space (Wilkins et. al., 1996). The most common designation of this technique is propagation-based phasecontrast imaging (Gureyev et al., 2009). Phase-contrast images were obtained using this technique and were applied as the input in an algorithm for recovery of the phase information.

Experimental setup
The design of the X-ray imaging system was based on the key requirements for high-resolution X-ray computerized tomography (CT). The requirements are as follows: a high-resolu-tion X-ray detector, a high-resolution goniometer and a small spot size of the X-ray source. The use of a Newport highresolution rotation stage (with minimal incremental motion of 0.0002 ) for the sample holder allows sequential CT projections to be taken. The CCD X-ray mini FDI camera (Photonic Science) was used as a detector. The basic parameters of the camera are as follows: number of pixels: 1392 Â 1040; input pixel size: 6.4 Â 6.4 mm; active area: 10 Â 8 mm; Gd 2 O 2 S:Tb 3 scintillator of 15 mm thickness with optimal energy response in the range 5-17 keV. A focus size of 8 mm is declared for the transmission tungsten anode of the X-ray source. The source emits a conical X-ray beam of space angle 39 , in a voltage range up to 80 kV and a current range up to 100 mA. The X-ray imaging system allows a magnification factor in the range of 1.1-140 to be obtained, corresponding to an effective pixel size in the range 5.8-0.05 mm. These values do not match the spatial resolution of the X-ray imaging system owing to a blur aberration of the X-ray beam. The real spatial resolution of the X-ray imaging system is down to 3 mm (Zá pražný et al., 2011). The lateral coherence lengths are in the range of 0.3-13.5 mm in the case of a polychromatic X-ray spectrum. This property of X-rays allows the visibility (contrast) of some features of the objects to be increased by means of edge visibility enhancement (phase contrast).
SRCLsim is a forward-imaging simulation program for CT, laminography and tomosynthesis (CT with an inclined axis). The image calculated can be a pure transmission image or a phase-contrast image.
X-TRACT is an image analysis and processing application (Gureyev et al., 2011). It contains tools for pre-processing, phase retrieval and tomographic reconstruction. This software was primarily used for recovery of the optical phase of an X-ray beam from a one intensity image. It currently implements more than 20 algorithms for phase and/or amplitude extraction, e.g. transport-of-intensity-based algorithms, Bornand Rytov-based Fourier optics type methods, and Gerchberg-Saxton-Fienup type algorithms.
The Octopus software is a reconstruction package for the processing of tomography data acquired in almost any geometry (parallel beam, fan beam, cone beam, helical cone beam, laminography). The package was used mainly for processing of X-ray projections to CT slices. It allows a tuning of the reconstruction parameters by evaluating a single CT slice before processing the complete volume.
VGStudio 2.1.5 software was used for stacking of CT slices and for final three-dimensional rendering and visualization. The output of this package is a set of voxel data, providing the additional possibility of qualitative evaluation of the X-ray imaging process and of creating animations. There are even very useful measurement features available for distances, angles etc.

Simulations
The phase-contrast X-ray imaging techniques include radiography (two-dimensional) and tomography (three-dimen-sional). The keynote expression of phase contrast in a twodimensional projection is the edge-enhancement effect. A simulation of this effect is shown in Fig. 1. A Kapton foil sample was used as the phase-contrast object. The sample is identifiable only because of the edge-enhancement effect without considering absorption. The sample X-ray absorption is low and it gives practically no relevant information about the projected density inside the sample. Samples made of polymethylmethacrylate (PMMA) and Kapton were chosen for simulations, because the results are appropriate for comparison with real experimental results.    The next simulation of X-ray projections was made taking account of the absorption phenomenon to come close to the real experiment. A single X-ray simulated projection of Kapton foil in absorption mode is shown in Fig. 2(a). Fig. 2(b) shows the reconstructed CT slice using the Octopus software and Fig. 2(c) shows a visualization using the VGStudio tool. Fig. 3 shows simulated radiographic X-ray images of PMMA samples. They are a sphere and a cylinder with the same diameter of 60 mm. The top row of Fig. 3 shows results using monochromatic X-ray radiation at the following energies: 8, 30, 60 keV. The results of imaging in the case of polychromatic X-rays are depicted in the bottom row of Fig. 3. The visibility of interference fringes increases with decreasing energy. It is possible to observe the same phenomenon using both polychromatic and monochromatic radiation. This confirms that the visibility of phase contrast for this kind of material is better when using lower energies. The visibility of interference fringes and their spatial separation from one another is important for the phase-retrieval method, which is used below in x4.1. Fig. 4 illustrates the results of CT obtained using a free-spacepropagation X-ray imaging technique. The results are compatible with the simulation in Fig. 2, with one difference, that the CT slice in Fig. 4(b) contains more ray aliasing artefacts (Barret & Keat, 2004) and its remains are visible at the edges of the reconstructed object in Fig. 4(c). This kind of artefact may be intensified by stronger phase-contrast expression along the longer edges of the sample.

Processing of phase-contrast data
One of thousands of X-ray projections of a plastic foil with a 3 mm layer of paint on one side with the phase contrast resolved on the edges is depicted in Fig. 5(a). The setting of the geometry for the experiment results in a magnification factor of 3.75 at full power of the X-ray tube, 80 kV and 100 mA. Fig. 5(b) shows a reconstructed CT slice using a standard reconstruction algorithm in Octopus. Dark and white stripes appear close to the three-dimensional reconstructed structure, known as ray aliasing. Fig. 5(c) shows a reconstructed CT slice using the X-TRACT software. It shows a suppression of ray artefacts, but it also gives slightly dark hazing near the object, which can cause problems for voxel segmentation.

Phase-retrieval method
The phase-retrieval algorithm in the ANKAphase application (Weitkamp et al., 2011) was used for phase retrieval in the Kapton foil. The program uses the single-distance non-iterative phase-retrieval algorithm described by Paganin et al. (2002). It was applied to the projections described in Fig. 4(a). The intensity distribution I(x, y) in Fig. 4(a) measured at a single known distance Z between the object and the detector plane can be used to retrieve the projected thickness t(x, y) of the object and thus we get a better contrast in the image, which is equivalent to the projected phase shift of the X-ray wavefront.
The algorithm is strictly valid only if the following experimental conditions are fulfilled. The object imaged consists of a single, homogeneous material. Monochromatic radiation is used. The distance Z between the object and the detector plane fulfils the near-field condition. Although not all conditions of the algorithm have been fulfilled (polychromatic radiation was used), we can see a significant improvement in the visibility of the phase object. On the other hand, there was a significant deterioration in the CT reconstruction (see Fig. 6b). It was difficult to obtain a three-dimensional image by voxel segmentation.
The X-TRACT application was used for the purpose of phase retrieval in the case of the PMMA samples. The       wave from a single near-field image by solving the transport of intensity equation. In the case of a polychromatic incident wave, the result allows us to see more clearly the transverse variations of the projected density of the sample. First, we used this algorithm for the simulated objects depicted in Fig. 7(a) for an X-ray energy of 8 keV. For the algorithm, it is necessary to specify input data concerning the sample material and the X-ray energy used. The chemical formula of PMMA is C 5 H 8 O 2 , and the density is 1.19 g cm À3 . Index of refraction decrements and must be entered. The X-TRACT application requires the ratio of and . For an X-ray energy of 8 keV, = 4.2 Â 10 À6 and = 9.2 Â 10 À9 . The ratio / = 453 (Henke et al., 1993). The result of the phase-retrieval algorithm TIE1 is shown in Fig. 7(b).
The retrieved phase is directly proportional to the projected electron density in the sample and can be used for densitometry and CT. Simulation of 2250 projections was carried out. The plane wave source producing the mono-energetic X-ray beam of 8 keV was used. The source to sample distance (SSD) was 2 m and the detector centre to sample origin distance (SDD) was 0.5 m. Phase maps were retrieved from these projections. These maps were reconstructed using a standard reconstruction algorithm to obtain CT slices. The threedimensional phase map in Fig. 8 has been created by stacking of CT slices and by voxel segmentation. The transition from green to blue shows an increase in the relative electron density towards the inside of the samples.
It is possible to compare the dimensions of the phase map with real input data in the simulation of phase-contrast images using measurement features available for distances in VGStudio quite easily. The height of the cylinder of 65 mm is greater (8%) than was specified (60 mm) for the simulated projection. The diameter of the phase distribution (51 mm) for the sphere sample is nearly 10 mm less (15%) than was specified in the simulation. The measurement of distances was done in the slice depicted in Fig. 9.
The single X-ray projection shown in Fig. 10(a) of PMMA spheres (20 mm diameter) deposited on an Si 3 N 4 (500 nm) membrane was taken in an experiment with a real sample. The exposure time of the X-ray projection and of the flat-field image was 40 s. SSD = 16 mm and SDD = 1043.8 mm, which yields a geometrical magnification of M = SDD/SSD = 65. It is possible to calculate the geometrical blur due to finite source size defined by U F = D F (M À 1), where D F is the focal spot size and M is the geometrical magnification (Salamon et al., 2008). In this case, the blur aberration is equal to 512 mm. However, this value does not have a significant influence on the visibility of samples that have a diameter of the order of 20 mm (see Fig. 10a). It can be concluded that the divergence of X-ray beams propagating behind the sample is smaller than the calculated geometrical blur aberration. Also the intensity of the blur aberration seems to be low. Fig. 10 Three-dimensional visualization of a reconstructed three-dimensional phase map of the PMMA samples. An increase of the relative electron density towards the inside of the samples is seen.

Figure 9
The cross section through the three-dimensional phase map, showing the electron density, which grows towards the inside of the samples.  application. Significant increases in the contrast of spheres and the transverse variations of the projected density are observed.

Conclusion
This contribution shows the results of processing of simulated and real phase-contrast images using a phase-retrieval algorithm in laboratory conditions with a microfocus X-ray source and a high-resolution CCD camera. Phase-contrast objects modify not the amplitude of the X-ray radiation but the phase shift. The X-ray detector is sensitive to the intensity (square of amplitude), so it is not possible to see these variations in phase shifts directly. The ANKAphase application was tested first because it is available as a free plug-in in the ImageJ software (Rasband, 2012). For now, it has been tested only for one type of sample (Kapton foil) and comparisons with other available algorithms will be made in future work. In the case of the PMMA samples, phase-retrieved images were obtained using the TIE1 algorithm in the X-TRACT application. One of the strict conditions is using a homogeneous sample. This condition was fulfilled in simulated as well as in real experiments. The three-dimensional phase map has been created only in the case of simulation. Tomographic reconstruction of the retrieved phase images gave us information about the relative electron density in the object. Comparison of the object dimensions in the phase map with input object data in the simulation of X-ray projections shows differences in the range of 8-15%. The experiment with the real sample (PMMA spheres) shows successful application of the phase-retrieval algorithm for a single radiographic X-ray projection. The phase image obtained is very compatible with the simulated image. The phase image visibility of real objects, similarly to simulated objects, was increased. Tomographic reconstruction was not carried out because of the small size of the samples, which is a challenge for our future work.