Clinical boundary conditions for propagation-based X-ray phase contrast imaging: from bio-sample models targeting to clinical applications

Abstract

BACKGROUND:

Typical propagation-based X-ray phase contrast imaging (PB-PCI) experiments using polyenergetic sources are tested in very ideal conditions: low-energy spectrum (mainly characteristic X-rays), small thickness and homogeneous materials considered weakly absorbing objects, large object-to-detector distance, long exposure times and non-clinical detector.

OBJECTIVE:

Explore PB-PCI features using boundary conditions imposed by a low power polychromatic X-ray source (X-ray spectrum without characteristic X-rays), thick and heterogenous materials and a small area imaging detector with high low-detection radiation threshold, elements commonly found in a clinical scenario.

METHODS:

A PB-PCI setup implemented using a microfocus X-ray source and a dental imaging detector was characterized in terms of different spectra and geometric parameters on the acquired images. Test phantoms containing fibers and homogeneous materials with close attenuation characteristics and animal bone and mixed soft tissues (bio-sample models) were analyzed. Contrast to Noise Ratio (CNR), system spatial resolution and Kerma values were obtained for all images.

RESULTS:

Phase contrast images showed CNR up to 15% higher than conventional contact images. Moreover, it is better seen when large magnifications (>3) and object-to-detector distances (>13 cm) were used. The influence of the spectrum was not appreciable due to the low efficiency of the detector (thin scintillator screen) at high energies.

CONCLUSIONS:

Despite the clinical boundary condition used in this work, regarding the X-ray spectrum, thick samples, and detection system, it was possible to acquire phase contrast images of biological samples.

Keywords

Phase contrast imaging propagation-based edge-enhancement optimization digital dental detector clinical application

1 Introduction

As visible light, X-rays can be treated as an electromagnetic wave which changes its phase and amplitude as it travels through the matter. These wave modifications are governed by the complex refraction index which is given by n = 1 - δ + iβ. Here, 1 - δ is the reduction in the real part of the complex refraction index and it is responsible by the wave phase shifts, $φ (r) = \frac{2 π}{λ} \int δ (r) dr$ , where r is a position coordinate inside the object and λ is the wavelength. The parameter $β = \frac{λ μ}{4 π}$ is responsible by the wave amplitude attenuation and is related with the linear attenuation coefficient, μ, on which the attenuation contrast is based. Even though the attenuation (conventional) contrast is widely applied, it presents limitations regarding X-ray energy and doses delivered to the matter [1–3]. For example, at lower energies there is high contrast, but higher doses delivered. While, at higher energies there are lower doses but low contrast. Low energy photons present high probability of being absorbed by the matter than high energy photons [2].

Because of phase changes, X-rays can be refracted as it travels through the object, deviating angularly the X-ray beam from its original path, in a manner that if an image receptor is placed at some distance from the object, a fringe pattern of high and low intensities can be recorded with improved contrast, even at high energy levels [3–5].

There are several methods that can be used to obtain phase contrast images such as the analyzer-based method [6–9], propagation-based method [10–12], grating interferometer [13, 14, 15–18] edge illumination [19–24] and beam tracking method [25–33]. Even though most of these methods provide phase contrast images with good quality, they use synchrotron radiation and experimental arrangements that need fine angular alignments which turns difficult its applications in clinical routines. However, propagation-based method has a great potential to be implemented for biomedical [34–36] and clinical imaging due to its simplicity [37–50]. In the past, especially for clinical applications, optimization of the propagation-based method has been investigated [10, 11, 37, 41, 47, 51–54]. Basic requirements consist in use a polyenergetic small-source size and large source-to-object distance to ensure coherent X-rays. In general, the laboratory setups using polyenergetic sources are tested in very ideal conditions: low-energy (<30 keV) or high-energy (>80 keV), large source-to-object distance (>500 mm), small (0.1–3 mm) and homogeneous materials considered weakly absorbing objects, large object-to-detector distance (>500 mm), long exposure times (>100 s) and non-clinical detector. Therefore, our goal was to explore propagation-based X-ray phase contrast imaging (PB-PCI) features using boundary conditions (mid-energy, small source-to-object distance, thick and heterogenous materials) imposed by a low power polychromatic X-ray source and a small CsI(Tl)/CMOS imaging detector with higher low-detection radiation threshold commonly found in a clinical scenario. Images of a variety of samples (tissue-equivalent material and biological tissues, bio-sample models) were obtained with a simple experimental setup targeting clinical applications to demonstrate the diagnostic potential of the image system.

2 Materials and methods

2.1 Experimental arrangement

The experimental setup used in this work is presented in Fig. 1. It was composed of a X-ray tube (Thermo Scientific PXS5-927 MicroFocus X-Ray Source 90 kV) with a tungsten target, focal spot size varying from 5μm (4 Watts) to 9μm (8 Watts) and a 127μm Beryllium (Be) window. Figure 1(b) shows the schematic representation of the experimental setup and the principal parameters explored in this work such as, source-to-sample distance (R1) and the sample-to-detector distance (R2).

Fig. 1

(a) Picture of the experimental setup. (b) Schematic draw showing the principal elements and distances explored in this work. The image system is composed by a microfocus X-ray source and a digital dental image detector.

2.1.1 X-ray source and detector characterization

The X-ray source output was characterized by its spectrum. For its determination, we used a complete X-ray spectrometer (model X-123 SDD, Amptek^®) which includes a silicon drift detector (SDD), a pre amplifier, a digital pulse processor and a multichannel analyzer. The spectra were acquired by an SSD with a highly collimated beam (pencil beam geometry) and placed in the center of the radiation field, at 100 cm from the focal spot. Lead collimators with 0.1 mm aperture and 5 mm thickness were used near the detector window to reduce the incident fluence rate, pile up effects and dead time losses (less than 2% during all measurements). In order to obtain the true photon spectra incident on the detector, the measured X-ray spectra were corrected with the stripping method [55], by using the response function of the detector. The response function of the SSD was calculated through Monte Carlo (MC) simulations [56], using the PENELOPE code version 2003 [57]. Figure 2(a) shows the corrected X-ray spectra used in the experiments, consistent with the findings of the others [58, 59]. Both spectra were obtained with additional 1.5 mm aluminum (Al) filter placed just after the X-ray tube Be window. Soft spectra (40 kVp and 50 kVp) were chosen since we are targeting for clinical applications, e.g., mammography, which have permitted to complete the range of applications towards mid energy X-rays [39–41, 46–50, 57].

Fig. 2

(a) Measured X-ray source spectra (40 kVp and 50 kVp) acquired with 1.5 mm Al filter and corrected by the detector response function. (b) Detector line spread function (LSF) obtained with the edge method, as indicated the FWHM.

To acquire the images, a digital dental image detector (Eagle Digital Sensor model T2, Dabi Atlante^®), composed by a Fiber Optic Plate (FOS) with a CsI(Tl) Scintillator and a CMOS area image sensor with active area of 26×36 mm² and pixel size of 20×20μm² (Nyquist frequency of 25 cycles/mm) was used. All the images were acquired in exposure times lower than 0.8 s and in the reverse contrast mode, i.e., the bright pixels are the ones which receive more photons. It was characterized by its line spread function (LSF) which was determined by the edge method [61]. Figure 2(b) shows the detector LSF. Assuming it’s a gaussian like curve, one can determine the detector resolution σ _det from the full width at half maximum (FWHM).

2.1.2 Samples

The samples were composed by tissue-equivalent materials and biological tissues, as presented in Table 1. Three different types of in-house built structured samples (phantoms, Fig. 3) were used to test the phase changes effects in transitions between different materials: i) samples composed of materials with huge differences in density and linear attenuation coefficient [e.g., air-polyamide interfaces – Fig. 3(a)]; ii) samples with similar linear attenuation coefficient but different densities and samples with similar linear attenuation coefficient and density (Fig. 3(b)) and; iii) samples with low attenuation fine structures (Fig. 3(c)). As a final test images of trabecular bone and animal mixed soft tissues were acquired.

Fig. 3

Schematic representation of the in-house built structured samples (phantoms) used to test the phase effects in the X-ray images. (a) Polyamide fiber fixed in an acrylic plate with an aperture. (b) Composed cylinders where the outer shell and the inner cylinder are made of different materials. (c) polyamide fibers within polyethylene cylinder.

Table 1

Tissue-equivalent materials and biological tissues used in the experiment

Name (Composition)	Density (g/cm³)
Polypropylene (C₃H₆)	0.90
Polyacetal (CH₂O)	1.41
Polyethylene (C₂H₄)	0.96
Polyamide (C₆H₁₁NO)	1.15
Bone	1.87
Animal mixed soft tissue (mainly adipose)	0.94

3 Results and discussions

3.1 Set up parameters

3.1.1 Geometric parameters

The geometric parameters were tested in terms of the magnification ( $M = 1 + \frac{R 2}{R 1}$ ), the source to sample distance (R1) and the sample to detector distance (R2). For both spectra (40 kVp and 50 kVp), the phase effects started to be enhanced for M≥3 depending on the sample structures. Figures 4(a) and 4(b) show the images of 500μm polyamide fibers (a weak absorbing object, with an effective X-ray transmission above of 94% in this test) obtained with 40 kVp (with 1.5 mm Al filter), M = 1 (image acquired with the sample in contact with the detector, i.e., conventional image) and M = 8 with R2 = 18 cm (phase contrast image), respectively. The conventional image shows lower contrast when compared with the phase contrast image, especially at the edges [62]. Figure 4(c) shows the cross-sectional images profiles showing up the contrast enhancement at the edges in the phase contrast image. These results are in agreement with the literature [36, 38, 62].

Fig. 4

Images of 500μm polyamide fiber acquired with 40 kVp (with 1.5 mm Al filter). (a) Conventional contact image obtained with M = 1. (b) Phase contrast image obtained with R1 = 2.57 cm, R2 = 18 cm M = 8. (c) Cross sectional images profiles. Phase contrast image shows enhanced contrast at the fiber edges. The surface entrance air kerma was 1.8mGy the finest visible features are approximately 20.4μm in size. The CNR (contrast to noise ratio, as defined by Bidola et al., 2015) was 2.51 and 2.68 respectively.

The influence of the geometric parameters was also tested by changing the R2 from 13 cm to 24 cm with 40 kVp (with 1.5 mm Al filter) spectrum, however, keeping M = 8. Figures 5(a) and 5(b) show the images obtained for both R2 distances (13 cm and 24 cm). In both cases it is observed an enhancement of contrast at the edges of the polyamide fiber edges. Figure 5(c) shows the cross-sectional images profiles. The contrast at the edges is increased by almost two when R2 is increased from 13 cm to 24 cm. This result is expected [34, 36, 37, 41, 43, 63]. For the same magnification, as larger is the R2, as larger is the R1 distance. Then, the lateral transverse coherent length is increased [64] and the phase contrast is more pronounced. However, higher exposure times are demanded since the intensity is reduced by 1/(R1)².

Fig. 5

Images of 150μm polyamide fibers obtained with 40kVp (with 1.5 mm Al filter) with M = 8 for (a) R1 = 1.86 cm, R2 = 13 cm, and (b) R1 = 3.43 cm, R2 = 24 cm. (c) Cross sectional images profiles. Higher sample to detector distance shows higher contrast at the edges. The surface entrance air kerma was 3.43 mGy and 1 mGy respectively and the finest visible features are approximately 20.4μm in size. The CNR was 0.74 and 0.87 respectively.

3.1.2 Spectrum parameters

The influence of the spectrum in the phase contrast X-ray images was also tested. Figures 6(a) and 6(b) show the images of a 150μm polyamide fibers (a weak absorbing object, with an effective X-ray transmission above of 98% in this test) obtained with M = 7, R2 = 24 cm for 40 kVp and 50 kVp spectra, respectively. As can be seen, the image obtained with 40 kVp spectrum presents higher area contrast [65], which was expected, since the photoelectric absorption is higher. Whereas, the contrast at the edges [65, 66] showed to be almost the same, as checked by the cross sectional image profiles shown in Fig. 6(c). These results are in agreement with other works available in the literature [12, 37, 38, 66].

Fig. 6

Images of 150μm polyamide fibers obtained with R1 = 4 cm, R2 = 24 cm, M = 7 and spectrum (a) 40 kVp (with 1.5 mm Al filter) and (b) 50 kVp (with 1.5 mm Al filter). (c) Cross sectional images profiles. The entrance surface air kerma in each case is 0.7 mGy and 0.5 mGy respectively. The finest visible features are approximately 20.8μm in size. The CNR was 0.74 and 0.73 respectively.

3.2 Sample parameters

A variety of samples were tested to simulate challenging clinical situations where conventional radiography (mammography) would present low contrast between the assessed structures.

Figure 7 shows images of composed cylinders (Fig. 3(b)) with an outer cylindrical shell made of polypropylene and an inner cylinder made of polyacetal and other composed cylinder made of polyethylene (outer shell) and polypropylene (inner cylinder) acquired with 50 kVp and M = 1 (conventional images, Fig. 7(a) and 7(d), respectively) and M = 4.5 with R2 = 10.5 cm (phase contrast images, Fig. 7(b) and 7(e), respectively). In both cases, the phase contrast images present better contrast at interfaces between material when compared with conventional image. The transition from a higher density material to a lower density material could be seen even when the density of both materials is similar, as shown by the intensity profile across the interface (Fig. 7(c) and 7(f)), even in lower transmission conditions (around 40%). This result agrees with the literature for weak-absorbing objects [67]. These composed cylinders were built to simulate tumoral masses embedded in normal glandular tissues, both with close attenuation coefficient but with (a) high differences (35%) in its densities (polyacetal – polypropylene) and (b) low differences (6%) in its densities (polypropylene – polyethylene).

Fig. 7

Images at polyacetal – polypropylene interface and polypropylene – polyethylene interface acquired with 50 kVp (with 1.5 mm Al filter), M = 1 (conventional images, a and d) and R1 = 3 cm, R2 = 10.5 cm, M = 4.5 (phase contrast images, b and e). The cross-sectional images profiles (dashed areas in the images) are shown in c) (polyacetal – polypropylene interface) and f) (polypropylene – polyethylene interface). The interfaces are enhanced in the phase contrast images. The entrance surface air kerma was 0.9 mGy and the finest visible features are approximately 24μm in size.

To test the capability of the proposed setup in detecting weak attenuation fine structures inside in a thick object (with an effective X-ray transmission between 65% -70% in this test), images of polyamide fibers of different diameters within a polypropylene cylinder (Fig. 3(c)) were acquired. Figures 8(a) and 8(b) show, respectively, the conventional images (M = 1) and the phase contrast images (M = 5.5 and R2 = 13.5 cm) of these samples at 40 kVp. As can be seen, the phase contrast images showed improved contrast when compared with the conventional images. Figure 8(c) shows the cross-sectional images profiles, where an increase in the intensity (phase jumps) is observed at the interfaces between the thinner polyamide fibers (300μm) and the polypropylene cylinder. In the center of the cylinder such an effect is masked due to the strong photoelectric absorption. These polyamide fibers inside polyethylene cylinder aimed to simulate different sizes of collagen fibers in breast tissues.

Fig. 8

Images of a 6 mm diameter polypropylene cylinder with 500μm (in the cylinder center) and 300μm polyamide fibers (symmetrically set around the cylinder center) inside obtained with 40 kVp (with 1.5 mm Al filter). Phase contrast images (R1 = 3 cm, R2 = 13.5 cm, M = 5.5).) (b) shows improved contrast when compared with the conventional contact image (M = 1) (a) at polyamide-polypropylene interfaces. (c) Images cross sections. The dashed circles show the enhanced contrast between the interfaces of different materials. The entrance surface air kerma at the sample plane was 0.9mGy. The finest visible features are approximately 22.2μm in size.

Fig. 9

Images of trabecular dry bone obtained with 40 kVp (with 1.5 mm Al filter) spectrum. (a) conventional image obtained with M = 1 and (b) phase contrast image obtained with R1 = 7.5 cm, R2 = 15 cm, M = 3. Trabecular structures are better seen in the phase contrast. The entrance surface air kerma at the sample plane was 0.1 mGy. The finest visible features are approximately 30.6μm in size.

At last, images of heterogeneous biological samples (bone and animal soft mixed (unblurred) than the conventional image, i.e., the trabecular structures are better seen in the phase contrast image.

Figures 10(a) and 10(b) show images of animal mixed tissues (mainly adipose) acquired with 40 kVp (with 1.5 mm Al filter) with M = 1 (conventional image) and M = 6 and R2 = 12.5 cm (phase contrast image). It’s possible to observe internal structures, such as fibers, with better contrast (unblurred) in phase contrast images, especially at the interfaces between structures.

Fig. 10

Images of animal mixed soft tissues (mainly adipose). (a) conventional contact image obtained with 40 kVp (with 1.5 mm Al filter) and magnification 1 and (b) phase contrast image obtained with 40 kVp (with 1.5 mm Al filter) and R1 = 2.5 cm, R2 = 12.5 cm, M = 6. The phase contrast image shows internal structures not seen in the conventional image. The entrance surface air kerma was about 1mGy. The finest visible features are approximately 21.6μm in size.

4 Conclusion

In this work the higher threshold limits of the propagation-based X-ray phase contrast imaging (PB-PCI) was explored by using a polychromatic X- ray beam and a dental image detector targeting clinical applications (e.g., by using imaging detectors, with similar specifications as presented here). A variety of parameters were appraised. It was showed that phase contrast is better seen when large magnifications and defocus distances (typically, M≥3 and R2 > 10 cm, depending on the sample structures) are used. Also, it was observed that the influence of the spectrum in the phase contrast was not appreciable due to the low efficiency of the thin scintillator screen high energies. In all studied samples, phase contrast images showed better contrast than conventional contact images, principally at interfaces between materials with similar attenuation and density properties. Finally, in spite of the poor spatial resolution provided by the dental imaging detector which reduces the relative intensities of the fringes due to refraction, it was possible to acquire phase contrast images of biological samples. This means that the target on the clinical applications can be achieved by using the same X-ray source, however larger CsI(Tl)/CMOS imaging detector, with similar dental detector specifications (such as Teledyne Shad-o-Box 6K HS with 49μm pixel size and Varex Imaging 1512-Swith 75μm pixel size) are demanded.

Footnotes

Acknowledgments

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001 and by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) under grant Ndeg 312643/2018-7, 311710/2022-0 and 436858/2018-5. The Authors would like to thank Eldereis de Paula and Carlos Renato da Silva with the Faculdade de Filosofia Ciências e Letras de Ribeirão Preto – FFCLRP for the technical support.

References

Arfelli

Assante

Bonvicini

Bravin

, Low-dose phase contrast x-ray medical imaging. Phys Med Biol 43(10) (1998), 2845–2852.

Keyriläinen

Bravin

Fernndez

Tenhunen

Virkkunen

Suortti

, Phase-contrast X-ray imaging of breast. Acta Radiol 51 (2010), 866–884. https://doi.org/10.3109/02841851.2010.504742.

Bravin

Coan

Suortti

, X-ray phase-contrast imaging: From pre-clinical applications towards clinics. Phys Med Biol 58(1) (2013), R1–R35. https://doi.org/10.1088/0031-9155/58/1/R1.

Snigirev

Snigireva

Kohn

Kuznetsov

Schelokov

, On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation. Rev Sci Instrum 66 (1995), 5486–5492. https://doi.org/10.1063/1.1146073.

Endrizzi

, X-ray phase-contrast imaging. Nucl Inst Methods Phys Res A 878 (2018), 88–98. https://doi.org/10.1016/j.nima.2017.07.036.

Aulakh

Mann

Belev

Wiebe

Kuebler

Singh

et al. Multiple image x-radiography for functional lung imaging. Phys Med Biol 63(1) (2017), 015009. https://doi.org/10.1088/1361-6560/aa9904.

Chapman

Thomlinson

Johnston

R.E.

Washburn

Pisano

Gmür

et al. Diffraction enhanced x-ray imaging. Phys Med Biol 42 (1997), 2015–2025. https://doi.org/10.1088/0031-9155/42/11/001.

Davis

Gao

Gureyev

Stevenson

Wilkins

, Phase-Contrast Imaging of weakly absorbing materials using hard X-rays. Nature 373 (1995), 595–598.

Wermick

M.N.

Wirjadi

Chapman

Zhong

Galatsanos

N.P.

Yang

et al. Multiple-image radiography.. Phys Med Biol 48 (2003), 3875–3895.

10.

Gureyev

T.E.

Mayo

S.C.

Myers

D.E.

Nesterets

Paganin

D.M.

Pogany

et al. Refracting Röntgen’s rays: Propagation-based x-ray phase contrast for biomedical imaging. J Appl Phys 105 (2009), 102005. https://doi.org/10.1063/1.3115402.

11.

Nesterets

Y.I.

Wilkins

S.W.

Gureyev

T.E.

Pogany

Stevenson

A.W.

, On the optimization of experimental parameters for x-ray in-line phase-contrast imaging. Rev Sci Instrum 76 (2005), 093706. https://doi.org/10.1063/1.2038107.

12.

Wilkins

Gureyev

T.E.

Gao

Pogany

Stevenson

A.W.

, Phase-contrast imaging using polychromatic hard X-rays. Nature 384 (1996), 335–338.

13.

Momose

, Phase-sensitive imaging and phase tomography using X-ray interferometers.. Opt Express 11 (2003), 2303–2314.

14.

Momose

Kawamoto

Koyama

Hamaishi

Takai

Suzuki

, Demonstration of x-ray Talbot interferometry. Japanese J Appl Physics Part 2 Lett 42 (2003), L866. https://doi.org/10.1143/JJAP.42.L866.

15.

Pfeiffer

Weitkamp

Bunk

David

, Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources. Nat Phys 2 (2006), 258–261. https://doi.org/10.1038/nphys265.

16.

Pfeiffer

Kottler

Bunk

David

, Hard X-ray phase tomography with low-brilliance sources. Phys Rev Lett 98 (2007), 1–4. https://doi.org/10.1103/PhysRevLett.98.108105.

17.

Pfeiffer

Bech

Bunk

Kraft

Eikenberry

E.F.

Brönnimann

C.H.

et al. Hard-X-ray dark-field imaging using a grating interferometer. Nature Mater 7 (2008), 1–4. https://doi.org/10.1038/nmat2096.

18.

Pfeiffer

, Milestones and basic principles of grating-based x-ray and neutron phase-contrast imaging. AIP Conf Proc 1466 (2012), 2–11. https://doi.org/10.1063/1.4742261.

19.

Munro

P.R.T.

Ignatyev

Speller

R.D.

Olivo

, Source size and temporal coherence requirements of coded aperture type x-ray phase contrast imaging systems. Opt Express 18 (2010), 19681. https://doi.org/10.1364/oe.18.019681.

20.

Olivo

Ignatyev

Munro

P.R.T.

Speller

R.D.

, Noninterferometric phase-contrast images obtained with incoherent x-ray sources. Appl Opt 50 (2011), 1765. https://doi.org/10.1364/ao.50.001765.

21.

Diémoz

P.C.

Vittoria

F.A.

Hagen

C.K.

Endrizzi

Coan

Bravin

et al. A single-image retrieval method for edge illumination X-ray phase-contrast imaging: Application and noise analysis. Phys Medica 32 (2016), 1759–1764. https://doi.org/10.1016/j.ejmp.2016.07.093.

22.

Diemoz

P.C.

Bravin

Sztrókay-Gaul

Ruat

Grandl

Mayr

et al. A method for high-energy, low-dose mammography using edge illumination x-ray phase-contrast imaging. Phys Med Biol 61 (2016), 8750–8761. https://doi.org/10.1088/1361-6560/61/24/8750.

23.

Diemoz

P.C.

Olivo

, On the origin of contrast in edge illumination X-ray phase-contrast imaging. Opt Express 22 (2014), 2819. https://doi.org/10.1364/oe.22.028199.

24.

Zamir

Diemoz

P.C.

Anastasio

M.A.

Zamir

Hagen

Diemoz

P.C.

et al. Recent advances in edge illumination x-ray phase-contrast tomography. J Med Imaging (Bellingham) 4(4) (2017), 040901. https://doi.org/10.1117/1.JMI.4.4.040901.

25.

Wen

Bennett

E.E.

Hegedus

M.M.

Rapacchi

, Fourier X-ray Scattering Radiography Yields Bone Structural Information.. Radiology 251 (2009), 910–918.

26.

Wen

H.H.

Bennett

E.E.

Kopace

Stein

A.F.

Pai

, Single-shot x-ray differential phase-contrast and diffraction imaging using two-dimensional transmission gratings. Opt Lett 35 (2010), 1932. https://doi.org/10.1364/ol.35.001932.

27.

Bennett

E.E.

Kopace

Stein

A.F.

Wen

, A grating-based single-shot x-ray phase contrast and diffraction method for in vivo imaging. Med Phys 37(11) (2010), 6047–6054. https://doi.org/10.1118/1.3501311.

28.

Morgan

K.S.

Paganin

D.M.

Siu

K.K.W.

, X-ray phase imaging with a paper analyzer. Appl Phys Lett 100 (2012), 124102. https://doi.org/10.1063/1.3694918.

29.

Morgan

K.S.

Paganin

D.M.

Siu

K.K.W.

, Quantitative single-exposure x-ray phase contrast imaging using a single attenuation grid. Opt Express 19 (2011), 19781. https://doi.org/10.1364/oe.19.019781.

30.

Vittoria

F.A.

Kallon

G.K.N.

Basta

Diemoz

P.C.

Robinson

I.K.

Olivo

, et al. Beam tracking approach for single-shot retrieval of absorption, refraction, and dark-field signals with laboratory x-ray sources. Appl Phys Lett 106 (2015), 224102. https://doi.org/10.1063/1.4922189.

31.

Vittoria

F.A.

Endrizzi

Diemoz

P.C.

Zamir

Wagner

U.H.

Rau

et al. X-ray absorption, phase and dark-field tomography through a beam tracking approach. Sci Rep 5 (2015), 1–5. https://doi.org/10.1038/srep16318.

32.

Zdora

M.C.

Thibault

Pfeiffer

Zanette

, Simulations of x-ray speckle-based dark-field and phase-contrast imaging with a polychromatic beam. J Appl Phys 118 (2015), 113105. https://doi.org/10.1063/1.4931145.

33.

Zdora

M.-C.

, State of the Art of X-ray Speckle-Based Phase-Contrast and Dark-Field Imaging. J Imaging 4 (2018), 60. https://doi.org/10.3390/jimaging4050060.

34.

Kashyap

Y.S.

Roy

Sarkar

P.S.

Yadav

P.S.

Shukla

Sinha

et al. Characterization of pyrocarbon coated materials using laboratory based x-ray phase contrast imaging technique. Rev Sci Instrum 78 (2007), 083703. https://doi.org/10.1063/1.2772780.

35.

Kashyap

Y.S.

Yadav

P.S.

Roy

Sarkar

P.S.

Shukla

Sinha

, Laboratory-based X-ray phase-contrast imaging technique for material and medical science applications. Appl Radiat Isot 66 (2008), 1083–1090. https://doi.org/10.1016/j.apradiso.2007.12.008.

36.

Gundogdu

Nirgianaki

Che Ismail

Jenneson

P.M.

Bradley

D.A.

, Benchtop phase-contrast X-ray imaging. Appl Radiat Isot 65 (2007), 1337–1344. https://doi.org/10.1016/j.apradiso.2007.07.009.

37.

Kotre

C.J.

Birch

I.P.

, Phase contrast enhancement of x-ray mammography: A design study. Phys Med Biol 44 (1999), 2853–2866.

38.

Matsuo

Katafuchi

Tohyama

Morishita

Yamada

Fujita

, Evaluation of edge effect due to phase contrast imaging for mammography. Med Phys 32 (2005), 2690–2697. https://doi.org/10.1118/1.1992087.

39.

Tanaka

Matsuo

Noma

Nitta

Ota

Tsuchiya

et al. The first trial of phase contrast imaging for digital full-field mammography using a practical molybdenum x-ray tube. Invest Radiol 40 (2005), 385–396. https://doi.org/10.1097/01.rli.0000165575.43381.48.

40.

Williams

I.M.

Siu

K.K.W.

Runxuan

Hart

S.A.

Styles

C.B.

et al. Towards the clinical application of X-ray phase contrast imaging. Eur J Radiol 68 (2008), S73–S77. https://doi.org/10.1016/j.ejrad.2008.04.042.

41.

Liu

, Clarification of aspects in in-line phase-sensitive x-ray imaging. Med Phys 34 (2007), 737–743. https://doi.org/10.1118/1.2431475.

42.

Donnelly

E.F.

Price

R.R.

, Quantification of the effect of kVp on edge-enhancement index in phase-contrast radiography. Med Phys 29 (2002), 999–1002. https://doi.org/10.1118/1.1477416.

43.

Donnelly

E.F.

Price

R.R.

Pickens

D.R.

, Quantification of the effect of system and object parameters on edge enhancement in phase-contrast radiography. Med Phys 30 (2003), 2888–2896. https://doi.org/10.1118/1.1617430.

44.

Gao

Pogany

Stevenson

A.W.

Wilkins

S.W.

, Phase-Contrast Radiography. Radiographics 18 (1998), 1257–1267. https://doi.org/10.1148/radiographics.18.5.9747618.

45.

Zhang

Donovan

Fajardo

L.L.

Archer

Liu

, Preliminary feasibility study of an in-line phase contrast X-ray imaging prototype. IEEE Trans Biomed Eng 55 (2008), 2249–2257. https://doi.org/10.1109/TBME.2008.919136.

46.

Wong

M.D.

Yan

Ghani

Fajardo

et al. Dose and detectability improvements with high energy phase sensitive x-ray imaging in comparison to low energy conventional imaging. Phys Med Biol 59(9) (2014), N37–N48. https://doi.org/10.1088/0031-9155/59/9/N37.

47.

Ghani

M.U.

Yan

Wong

M.D.

Ren

et al. Low dose high energy x-ray in-line phase sensitive imaging prototype: Investigation of optimal geometric conditions and design parameters. J Xray Sci Technol 23 (2015), 667–682. https://doi.org/10.3233/XST-150519.

48.

Ghani

M.U.

Wong

M.D.

Zheng

Fajardo

L.L.

Yan

et al. Detectability comparison between a high energy x-ray phase sensitive and mammography systems in imaging phantoms with varying glandular-adipose ratios. Phys Med Biol 62 (2017), 3523–3538. https://doi.org/10.1088/1361-6560/aa644b.

49.

Wong

M.D.

Fajardo

Zheng

et al. Corrigendum: Quantitative investigation of the edge enhancement in in-line phase contrast projections and tomosynthesis provided by distributing microbubbles on the interface between two tissues: A phantom study (Physics in Medicine and Biology (2017) 62. Phys Med Biol 63 (2018), 239501. https://doi.org/10.1088/1361-6560/aaec47.

50.

Zysk

A.M.

Garson

A.B.

Brey

E.M.

Zhou

Brankov

J.G.

et al. Nondestructive volumetric imaging of tissue microstructure with benchtop x-ray phase-contrast tomography and critical point drying. Biomed Opt Express 3 (2012), 1924. https://doi.org/10.1364/boe.3.001924.

51.

Gureyev

T.E.

Nesterets

Y.I.

Stevenson

A.W.

Miller

P.R.

Pogany

Wilkins

S.W.

, Some simple rules for contrast, signal-to-noise and resolution in in-line x-ray phase-contrast imaging. Opt Express 16 (2008), 3223. https://doi.org/10.1364/oe.16.003223.

52.

Ishisaka

Ohara

Honda

, A new method of analyzing edge effect in phase contrast imaging with incoherent X-rays. Opt Rev 7 (2000), 566–572. https://doi.org/10.1007/s10043-000-0566-z.

53.

Pogany

Gao

Wilkin

S.W.

, Contrast and resolution in imaging with a microfocus x-ray source. Rev Sci Instrum 68 (1997), 2774–2782. https://doi.org/10.1063/1.1148194.

54.

Liu

, Clinical implementation of x-ray phase-contrast imaging: Theoretical foundations and design considerations. Med Phys 30 (2003), 2169–2179. https://doi.org/10.1118/1.1593836.

55.

Tomal

Cunha

D.M.

Poletti

M.E.

, Establishment of the mammographic radiation qualities in industrial equipment: Spectra determination. Nucl. Instruments Methods Phys. Res. Sect. A Accel. Spectrometers, Detect. Assoc. Equip. 652 (2011), 883–887. https://doi.org/10.1016/j.nima.2010.08.055.

56.

Tomal

Cunha

D.M.

Antoniassi

Poletti.

M.E.

, Response functions of Si(Li), SDD and CdTe detectors for mammographic x-ray spectroscopy. Appl Radiat Isot 70 (2012), 1355–1359. https://doi.org/10.1016/j.apradiso.2011.11.044.

57.

Salvat

Fernández-Varea José

Sempau

, PENELOPE: A code system for Monte Carlo simulation of electron and photon transport: Workshop proceedings, Issy-les-Moulineaux, France, 7–10 July 2003. Nuclear Energy Agency, Organisation for Economic Co-operation and Development; 2003.

58.

Ghani

M.U.

Wong

M.D.

Ren

Zheng

Rong

J.X.

et al. Characterization of continuous and pulsed emission modes of a hybrid micro focus x-ray source for medical imaging applications. Nucl Instruments Methods Phys Res Sect A Accel Spectrometers, Detect Assoc Equip 853 (2017), 70–77. https://doi.org/10.1016/j.nima.2017.02.030.

59.

Sisniega

Desco

Vaquero

J.J.

, Modification of the TASMIP x-ray spectral model for the simulation of microfocus x-ray sources. Med Phys 41 (2014), 011902 https://doi.org/10.1118/1.4837220.

60.

Matsuo

Katafuchi

Tohyama

Morishita

Yamada

Fujita

, Evaluation of edge effect due to phase contrast imaging for mammography. Med Phys 32 (2005), 2690–2697. https://doi.org/10.1118/1.1992087.

61.

Anastasiou

Papastamati

Bakas

Michail

Koukou

Martini

et al. Spatial frequency domain analysis of a commercially available digital dental detector. Meas J Int Meas Confed 151 (2020), 107171. https://doi.org/10.1016/j.measurement.2019.107171.

62.

Palma-Alejandro

K.D.

Murrieta

Brandan

M.E.

, Use of oversampling to quantify phase effects in X-ray images of straight fibers. Nucl Instruments Methods Phys Res Sect A Accel Spectrometers. Detect Assoc Equip 701 (2013), 201–207. https://doi.org/10.1016/j.nima.2012.10.082.

63.

Bidola

P.M.

Zanette

Achterhold

Holzner

Pfeiffer

, Optimization of propagation-based phase-contrast imaging at a laboratory setup. Opt Express 23, 30000 (2015), https://doi.org/10.1364/oe.23.030000.

64.

Hönnicke

M.G.

Kakuno

E.M.

Manica

Cusatis

, Propagation-based x-ray phase-contrast imaging with broad focus conventional x-ray sources. 16 (2007), 63–8.

65.

Pagot

Cloetens

Fiedler

Bravin

Coan

Baruchel

et al. A method to extract quantitative information in analyzer-based x-ray phase contrast imaging. Appl Phys Lett 82 (2003), 3421–3423. https://doi.org/10.1063/1.1575508.

66.

Donnelly

E.F.

Lewis

K.G.

Wolske

K.M.

Pickens

D.R.

Price

R.R.

, Characterization of the phase-contrast radiography edge-enhancement effect in a cabinet x-ray system. Phys Med Biol 51 (2006), 21–30. https://doi.org/10.1088/0031-9155/51/1/002.

67.

Monnin

Bulling

Hoszowska

Valley

J.F.

Meuli

Verdun

F.R.

, Quantitative characterization of edge enhancement in phase contrast x-ray imaging. Med Phys 31 (2004), 1372–83. https://doi.org/10.1118/1.1755568.