A system for high-resolution X-ray phase-contrast imaging and tomo-
graphy of biological specimens
Luca Poletto
*
, Matteo Caldon, Giuseppe Tondello
CNR - National Institute for the Physics of Matter (Italy)
Laboratory for UV and X-Ray Optical Research
c/o Department of Information Engineering, Padova, Italy
Aram Megighian
Department of Anatomy and Human Physiology
University of Padova, Padova, Italy
ABSTRACT
A system for high-resolution X-ray diagnostics is presented. It consists of a microfocus X-ray source with spot size of 5
µm that is operated in the 10-90 kV range. The detector is a Ce:YAG crystal coupled to a CCD camera with 5µm pixel
size and 1392x1040 format. The magnification of the optical coupling is chosen in the 1 to 4 range, giving a spatial re-
solving element of 5 to 20 µm. The sample to be acquired is mounted on a motorized rototranslation stage for the auto-
matic acquisition of the X-tay views both for tomography and phase-contrast imaging. The sample is positioned half-way
between the source and the detector. X-ray images show very high contrast due to phase effects in addition to absorption.
Some images of biological specimens are presented to assess the capability of revealing very low differences in density
due to the presence of phase contrast. A complete high-resolution tomography of a drosophila is presented.
Keywords: X-ray tomography, phase-contrast imaging
1. INTRODUCTION
For research in natural sciences X-Ray photons have been used since their discovery at the end of the 19
th
century for
many fundamental analysis and outstanding applications. They have played a crucial role in basic science and medical
diagnostics, as well as in industrial research and development. The main reason for this success is that the wavelength,
which determines the smallest distance one can study with such a probe, is comparable to the molecular and atomic di-
mension [1-3]. In this paper, we refer to two fundamental techniques of X-ray analysis: the tomography and the phase-
contrast imaging, both applied for the acquisition of high-contrast and highly-resolved images.
X-ray tomography refers to the cross-sectional imaging of an object from reflection data collected by illuminating it from
many different directions. The impact of this technique in diagnostic medicine has been revolutionary, since it has en-
abled to view the internal structure of the human body with unprecedented resolution and precision in a non-invasive
way. Fundamentally, tomographic imaging deals with reconstructing an image from its projections, where a projection at
a given angle is the integral X-ray absorption of the image in the direction specified by that angle. Although from a ma-
thematical point of view the problem of how to reconstruct a function from its projections has been solved by Radon at
the beginning of the 20
th
century, the invention of the first X-ray computed tomographic scanner dates back approxi-
mately 40 years. Nowadays, tomography is an essential tool for inspecting the internal structure of an object [4,5].
Recent years have seen a growing interest in X-ray phase-contrast imaging. Conventional X-ray imaging relies on ab-
sorption contrast which is only effective in absorbing samples and poor at revealing low density variations especially of
light elements. Phase-contrast is sensitive to high spatial frequency features and enables the analysis with high contrast
of weakly absorbing samples. Phase-contrast imaging relay on the phase shifts imposed on the X-ray wavefront by the
sample. Nowadays, phase-contrast micro-tomography allows the reconstruction of objects with sub-micrometric preci-
sion [6-8].
*
Correspondence: Dr. Luca Poletto. E-mail: poletto@dei.unipd.it. Tel: +39 (0)49 8277680. Fax: +39 (0)49 8277699
Developments in X-Ray Tomography VI, edited by Stuart R. Stock,
Proc. of SPIE Vol. 7078, 70781P, (2008) · 0277-786X/08/$18 · doi: 10.1117/12.793001
Proc. of SPIE Vol. 7078 70781P-1
2008 SPIE Digital Library -- Subscriber Archive Copy
We describe in this paper the system for high-resolution X-ray diagnostics that has been developed in the LUXOR labo-
ratory in Padova (Italy). It consists of a microfocus X-ray source, a high-resolution detector a a sample manipulator. The
system can be used both for phase-contrast imaging and micro-tomography. The paper is organized as follows. The prin-
ciples of phase-contrast and micro-tomography are presented in Par. 2. The system is described in Par. 3. Some examples
and applications are finally presented in Par. 4.
2. PHASE CONTRAST AND µCT BASIS
2.1. Phase contrast radiography
For high resolution imaging of biological specimens, absorption radiography, in which the simple absorption of the X-
ray radiation is measured, is not suitable because of its limited contrast. Therefore, we oriented our research towards
phase-contrast imaging. The difference between the two methods stands in the origin of the data that are measured: ab-
sorption radiography shows only the quantity of the absorption of X-rays by a sample; phase-contrast imaging, beyond
the absorption, gives also a measurement of the distorted wavefront of X-rays.
It has been demonstrated since a decade [6,9] that phase-contrast imaging is feasible without the requirement of highly
monochromatic X-ray beam and sophisticated X-ray optics, the only requirement being an X-ray source having high spa-
tial coherence and a high-resolution X-ray detector. The method is then compatible with the use of conventional poly-
chromatic microfocus X-ray tubes.
The lateral coherence length is
γ
λ
σ
λ
==
⊥
ld , where l is the source to observation distance, σ is the source size, λ is
the wavelength and γ is the angular width of the source as viewed from the observation point. Thus high spatial coher-
ence may be achieved by using a source of small effective size and observing the beam at a large distance from the
source.
When X-rays travelling across the sample encounter a variation of thickness and refractive index, the wavefront under-
goes a change of its shape. In the geometrical optics approximation, the phase difference
φ
for a ray path through an ob-
ject relative to vacuum is given by
() ( ) ()
∫∫
∞−∞−
−=−=
z
e
z
dzzyx
k
r
dzkzyxkkzyx '',,
2
';',,,;,
ρ
π
δφ
, (1)
where the optical axis is parallel to z, k is defined as k = 2π/λ, r
e
is the electron radius and ρ the electron density of the
object. The X-ray refractive index is n = 1 – δ – iβ, where δ is typically of the order of 10
-6
for light materials and X-rays
energy in the 10 to 20 keV range, so that refraction angles are usually quite small. The phase of the wavefront is taken to
be kz -
φ
. The local propagation vector, s(x,y,z), is dependent on the gradient of the phase in the direction perpendicular
to the local incident wave vector and can be written in the paraxial approximation when |∇
φ
| << k as
()
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
∂
∂
−
∂
∂
−≈ k
yx
zyxs
,,,,
φφ
(2)
so that s(x,y,z) is normal to the wavefront at the point (x,y,z).
The angular deviation of the normal to the wavefront, ∆α, can be expressed as
() ()
∫
∞−
∇=∇≈∆
z
yxyx
dzzyxzyx
k
'',,,,
1
,,
δφα
(3)
and depends on the variation of the projected refractive index perpendicular to the propagation vector k.
We want to show that rapid variations in refractive index (the so-called boundary effect) can lead to strong phase-
contrast even with polychromatic radiation. For simplicity, let us consider the case of a spherical object Ω of refractive
index n
Ω
= 1 – δ
Ω
and radius r embedded in a medium of refractive index n
0
= 1 (i.e. the air). The differences of the
lengths of the X-ray optical path through the sample lead, via equation (1), to a phase difference
φ
(x,y) hence to a phase
gradient ∇
x,y
φ
in the direction transverse to the direction of propagation. The angular deviation of rays through Ω can be
derived from Eq.(3) as
()
222
22
,
2
1
yxr
yx
k
k
yx
−−
+
=∇=∆
Ω
δφα
. (4)
Thus the phase gradient diverges at x
2
+ y
2
= r
2
, where the rays can deviate by large angles from the optical axis even for
small δ
Ω
. This can lead to an observable redistribution in intensity in the corresponding forward direction. More gener-
ally, any rapid variations in refractive index or thickness of a sample may be imaged as sharp variations in intensity at
corresponding points in the image even when a polychromatic source is used.
Proc. of SPIE Vol. 7078 70781P-2
0
W2
B
I
The experimental configuration for obtaining phase-
contrast information in a radiographic image is shown
in Fig. 1. It consists of a source of high spatial coher-
ence and an X-ray imaging detector. By recording the
intensity of the wavefront at sufficient distance from
the sample, intensity variations due to sharp variations
of the refractive index and/or of the thickness in the
sample may be detected in the form of a differential
phase-contrast imaging. The location of the imaging
detector is chosen such that its spatial resolution is suf-
ficient to resolve intensity differences arising from the
wavefront distortions.
A more rigorous approach is based on the use of the
Kirchhoff formula in the Fresnel diffraction case. In
the case of a pure phase object and a point source (that
is, a spherical wave), this leads to the expression for
the intensity of the image
()
(
)
()
⎭
⎬
⎫
⎩
⎨
⎧
∇+=
⎭
⎬
⎫
⎩
⎨
⎧
∇+=+
∫
dzzyx
M
R
k
r
MI
kRyx
kM
R
MIkRRMyMxI
yx
e
yx
),,(21
),;,(1,;,
2
,
2
2
2
0
1
2
,
2
2
021
ρπ
φ
(5)
where M = (R
1
+ R
2
)/R
1
is the magnification of the image and I
0
is the uniform intensity in the object plane.
Two significant conclusions may be drawn from Eq. (5):
1. the contrast initially increases with R
2
;
2. the structure of the image is proportional to the Laplacian of the projected electron density and in first order in-
dependent from the energy, because for a polychromatic source one would simply replace 1/k
2
by a spectral
weighted sum.
Other studies [7] have demonstrated that phase retrieval before tomographic reconstruction leads to an improvement in
noise reduction and artefacts removing in the case of a sample made by a single material.
2.2. Microtomography
Tomography is a non-invasive technique for investigating the internal structure of a sample without cutting it. It gives a
set of images corresponding to slices of the object. With the use of microfocus sources and phase-contrast radiography
one can achieve images with a resolution in the micrometer or sub-micrometer range: this method gets the name of mi-
crotomography.
A tomographic sequence is made by the iterative repetition of acquiring an image and rotating the sample. The result of
these steps is a set of images, the so-called projections, representing the value of the integral along a straight line through
the object. By using a 2D detector, one has for each of the rotation angles the amount of the attenuation of X-rays in each
point of the sample.
The heart of the tomographic process is the reconstruction of the sample’s slices from the projections. The raw data have
to be processed in order to obtain a more precise reconstruction. Some of the steps are listed in the following.
• Dark current and white field normalization. The projections have to be corrected against the dark current, being the
latter the signal that is measured in the absence of X-rays, and the white field, being the latter the image which is
acquired with the X-rays on but without the sample, that represents the non uniformity of the beam on the detector;
• Construction of the sinogram, that is the stack formed by the same row in each of the projections. The sinogram
represents the absorption of a selected slice of the sample as a function of the angle of rotation.
• Centering of the sinogram. It consists in calculating the trend of the center of gravity of the rows and in fitting of it
to a sine wave. The symmetry axis of this sine wave is the centre of rotation.
• Reduction of the ring artefact. It is performed by reducing the contribution to image formation of non-linearity in
the detector which results are the presence of ring artefact in the reconstructed slice.
The geometry of the system we use is the so-called cone beam that gives the possibility to use a 2D detector instead of a
linear detector. The use of a linear detector requires a vertical scanning to acquire the complete 3D structure of the ob-
Fig. 1. Schematic illustration of configuration for phase-contrast
imaging using a microfocus source (S), an object (O) and a two
dimensional detector (D). The spherical wavefront W1 emanat-
ing form the point source S becomes distorted to W2 on passing
through the object O.
Proc. of SPIE Vol. 7078 70781P-3
axis of rotation
rotating sample
£ deteclor
cone beam
'I
I
x-ray tube's
variable magnification
P1
(a) (b) (c)
ject, so the acquisition becomes time-demanding and impracticable for large-size objects. A 2D detector simplifies the
acquisition procedure since it avoids the vertical scanning and reduces the acquisition time. The cone beam geometry
presents some complications with respect to the fan beam geometries because of its intrinsic 3D characteristics, the ma-
jor of which is the fact that a tilted fan of X-rays doesn’t go through a single horizontal slice but it crosses several slices.
This leads to a reconstruction algorithm that is approximated with respect to the so-called Tuy-Smith condition [10,11],
which states that all planes intersecting the object must intersect the source trajectory at least once. Approximate recon-
struction yields good results for small cone angles within reasonable calculation times.
The reconstruction algorithm is based on the filtered backprojection (FBP) method [4,5], that can be divided in two steps.
The first step is the filtering, a simple weighting in the frequency domain used to take each projection and estimate a pie-
shaped wedge of the object’s Fourier transform. The simplest way to do this is to take the value of the Fourier transform
of the projection and multiplying it by the width of the wedge at that frequency. The effect of this weighting is shown in
Fig. 2(c). Comparing Fig. 2(c) to Fig. 2(a), it is easy to see that at each spatial frequency the weighted projection has the
same “mass” as the pie-shaped wedge.
The final reconstruction is achieved by adding together the two-dimensional inverse Fourier transform of each weighted
projection. This step is commonly called backprojection, since it can be perceived as the smearing of each filtered pro-
jection over the image plane. There are many implementations of the FBP algorithm, the most common is the so-called
FDK algorithm [12].
3. DESCRIPTION OF THE SYSTEM
A schematic and a picture of the whole system are shown in Fig. 3. The X-ray source is positioned in front of the detec-
tion system and the samples are positioned on the motorized rototranslation stage half-way between the source and the
detector.
a) b)
Fig. 3. a) Schematic of a system for X-ray tomography in the cone beam geometry (from Ref. 5)
b) Picture of the actual system. The X-ray source is on the right side, the motorized stage for the sample on the central part and
the detector on the left side.
Fig. 2. The filtered backprojection algorithm takes the data in (b) and applies a weighting in the frequency domain
so that the data in (c) are an approximation to those in (a).
Proc. of SPIE Vol. 7078 70781P-4
3.1. The X-ray source
The X-ray source is the Hamamatsu L8601-01 type. It is a microfocus X-ray tube with tungsten anode which focal spot
is typically of 7 µm at the maximum power (10 W) and 5 µm at reduced power (4W). The maximum power is 10 W, this
means that the control system regulates automatically the tube current at the raising of the tube voltage in order to stay
below the maximum power and avoid damages. The operating range is 20-90kV and 0-250µA.
3.2. The detection system
The detector is a Ce:YAG crystal scintillator optically coupled to a low-noise CCD camera. The latter is the CoolSNAP
from Photometrics with a resolution of 1392 × 1040 pixels with 4.65 µm × 4.65 µm pixel size, spanning 6.5 × 4.8 mm
2
.
The dynamic range is 12 bit and the chip is cooled down to 5°C under ambience temperature to reduce electronic noise.
This is especially important in low light-level situations where long exposure times are needed. In order to reduce the
time of data elaboration and the space for storage the data, when possible the latter are binned to a lower spatial resolu-
tion. In this way we achieve also a higher signal-to-noise ratio and reduce the scan time.
The camera is optically coupled to a Ce:YAG scintillator via a couple of objectives to maximize the light throughput to
the camera. The main characteristics of the Ce:YAG scintillator are a light emission peaked in the wavelength range 530-
550 nm and the absence of afterglow due to its 70 ns decay time. Different couples of objectives can be used, leading to a
variable magnification. A 50 mm f/1.2 objective can be coupled with an equal 50 mm f/1.2 one for 4.5 µm spatial sam-
pling on the crystal; with a 100 mm f/2.4 objective for 9 µm sampling; with a 200 mm f/2.4 objective for 18 µm sam-
pling.
3.3. The software
The management of the system is performed through a software which implements the control of the motorized stage and
of the camera. Once acquired the dark image and the white field, the acquisition sequence is the following: 1) acquisition
of the X-ray view; 2) rotation of the motorized stage; 3) repetition of steps 1 and 2 to complete the whole 360° angle.
The software gives the possibility to change the exposure time, the amplitude of the angular step and the total angle of
scan.
The processing steps of the tomographic views are carried out by the software Octopus developed by XRayLAB, a spin-
in initiative of the Ghent University (Belgium). The software includes all the processing steps like filtering, normaliza-
tion and rebinning. The reconstruction module performs parallel beam, fan beam and cone beam reconstruction.
4.
EXPERIMENTAL RESULTS
4.1. Phase-contrast imaging
The advantages of the phase-contrast method are evident in case of light samples, where the absorption is very weak. We
present here two examples to assess the increase in contrast obtained by the phase-contrast method.
The radiography of a mosquito is shown in Fig. 4. The mosquito was initially placed in close contact with the detector to
acquire a pure absorption image that is shown in Fig. 4(a). When the sample is moved half-way between the source and
the detector, the phase-contrast image exhibits a definitely higher contrast as evident from Fig. 4(b).
As a second example, the radiography of a fresh onion skin is shown in Fig. 5. Again, the cells are clearly visible only in
the phase-contrast images. For each of the samples under test, the source voltage, then the X-ray maximum energy, has
to be chosen to achieve the best phase contrast. An example of an image taken at a different energy of the source is
shown in Fig. 6 in the case of the onion:it is clear that the contrast is higher at 20 kV.
It can be concluded that the phase-contrast technique gives an evident increase in the image quality and in the definition
of highly-resolved particulars. Since the X-ray energy to be used is generally below 30 kV and the maximum current of
the microfocus source is 0.25 mA, the power is below 7.5 W. To achieve such a high contrast, the user pays the price of a
longer acquisition time because of the low photon flux.
4.2. Micro-tomography
We present some results of the micro-tomography applied on biological samples to assess the resolution that our system
can achieve. We intend to demonstrate that our set-up is capable of revealing very low differences in density and could
then be useful for non-invasive biological inspection.
The images shown in Fig. 7 and Fig. 8 are the results of a scan sequence on a fly taken over the whole 360° angle with an
angular resolution of 0.5° for a total of 720 views. The total scanning sequence took 6 hours. The total processing time
for a complete tomographic reconstruction is 45 minutes on a laptop PC. The resolution and the contrast on the recon-
structed images are very good.
Proc. of SPIE Vol. 7078 70781P-5
The main parameters that the user has to select to obtain high-quality tomographic images are the source voltage and the
acquisition time. High voltages, typically in the 30-50 kV range, give more counts on the detector, then a better signal-to-
noise ratio even for relatively short acquisition time, but a lower contrast because of the small absorption especially on
light materials. Low voltages, typically in the 10-20 kV range, give a definitely better contrast but a weak signal on the
detector, so the acquisition time to obtain a good signal-to-noise ratio is quite long. Then the user has to find the best
trade-off between contrast and acquisition time.
The capability of resolving micrometric particulars has been finally tested on a specimen of Drosophila melanogaster,
that is the common fruit fly (see Fig. 9), whose internal sizes are well known. The images shown in the following are the
results of a scan sequence on the Drosophila m. taken over the whole 360° angle with an angular resolution of 0.5°. The
total scanning sequence took about 3 hours.
a) b)
Fig. 4. Radiography of a mosquito.
a) Absorption image. The source-to-detector distance is 10 cm, the mosquito is placed closed to the detector, the source volt-
age and current are 15 kV and 0.25 mA, the single-image acquisition time is 10 s, the pixel size projected on the Ce:YAG
crystal is 9 µm, the resolution on the sample is 18 µm (binning 2 × 2). The size of the image is 6.8 mm × 4.4 mm.
b) Phase-contrast image. The source-to-detector distance is 30 cm, the sample-to-detector distance is 15 cm (magnification 2),
the source voltage and current are 15 kV and 0.25 mA, the single-image acquisition time is 120 s, the pixel size projected on
the crystal is 9 µm, the resolution on the sample is 9 µm (binning 2 × 2). The size of the image is 3.4 mm × 2.2 mm.
a) b)
Fig. 5. Radiography of a fresh onion skin.
a) Absorption image. The source-to-detector distance is 5 cm, the onion is placed closed to the detector, the source voltage and
current are 15 kV and 0.25 mA, the single-image acquisition time is 10 s, the pixel size projected on the crystal is 9 µm, the
resolution on the sample is 36 µm (binning 4 × 4). The bright spots on the image are defects of the crystal.
b) Phase-contrast image. The source-to-detector distance is 30 cm, the sample-to-detector distance is 15 cm (magnification 2),
the source voltage and current are 20 kV and 0.25 mA, the single-image acquisition time is 180 s, the pixel size projected on
the crystal is 9 µm, the resolution on the sample is 18 µm (binning 4 × 4). The size of both images is 5 mm × 3 mm.
Proc. of SPIE Vol. 7078 70781P-6
Fig. 6. Phase-contrast image of a fresh onion skin. The source Fig. 7. One of the 720 views taken to perform the tomography of
voltage is 15 kV, the other parameters are as in Fig. 5(b). a fly.
Fig. 8. Tomographic reconstruction of a fly. The angular scan has been taken over 360° with 0.5° step. The source voltage and current
are 30 kV and 0.25 mA, the source-to-detector distance 30 cm, the sample-to-detector distance 15 cm, the single-image acqui-
sition time 30 s, the pixel size on the crystal 4.5 µm, the resolution on the sample 4.5 µm (binning 2 × 2) including a magnifi-
cation factor of 2. The size of both images is 3 mm × 3 mm.
In the case of the Drosophila, the duration of the
whole acquisition procedure plays an essential role,
because we experienced a change in the radiographic
images in time due to the drying of the insect after its
death; this effect is much clear in Drosophila than in
the common fly. Fig. 10 shows the phase-contrast im-
age of the same insect just after its death and 7 hours
later in ambient temperature. The drying process is
evident in terms of lower contrast, indicating that the
presence of water is the mainly responsible of good X-
ray imaging. For such a reason, we have chosen to op-
erate at a voltage of 25 kV with 10 s single-image in-
tegration. These experimental parameters give good
contrast tomography in a scan of 3 hours. We have
verified that the drying process is negligible during the
acquisition.
Fig. 9. Drosophila melanogaster.
Proc. of SPIE Vol. 7078 70781P-7
T
r
'1••
A
a) b)
Fig. 10. Phase-contrast radiography of a Drosophila: a) just after its death and b) 7 hours later in ambient temperature. The size of
both images is 2.5 mm × 2.5 mm.
The volume rendering of the sample is shown in Fig. 11. The structure of the eyes is highly recognizable even though the
diameter of a single element of the eye, the ommatidium, is approximately 40 µm. Fig. 12 shows two slices of the insect
at different positions, the holes on the structure of the thorax are the hosts of the fly muscles, their diameter is about 150-
300 µm and they take the whole length of the thorax (600 µm). Fig. 13 shows the volume rendering of the sample
clipped over a plane: the internal structure of the insect is clearly visible, evidencing its fly muscles.
Fig. 11. Tomographic reconstruction of a Drosophila. The angular scan has been taken over 360° with 0.5° step. The source voltage
and current are 25 kV and 0.25 mA, the source-to-detector distance 22 cm, the sample-to-detector distance 11 cm, the single-
image acquisition time 10 s, the pixel size on the crystal 4.5 µm, the resolution on the sample 4.5 µm (binning 2 × 2). The size
of the images is approximately 1 mm × 1 mm.
Proc. of SPIE Vol. 7078 70781P-8
a) b)
Fig. 12. Tomographic reconstruction of a Drosophila. Slices of the insect: a) head and the top of the thorax; b) centre of the thorax.
The parameters are as in fig. 10.
Fig. 13. Tomographic reconstruction of a Drosophila. Volume rendering clipped over a plane in such a way to make visible the struc-
ture of the fly muscles. The parameters are as in fig. 10. The size of the images is approximately 1 mm × 1 mm.
5. CONCLUSIONS
A system for high-resolution and high-contrast X-ray imaging has been described. The aim of the instrument is perform
tomographic imaging with micrometric resolution. The results here presented on biological samples assess the perform-
ance of the system and of the techniques and confirm that micrometric resolution has been achieved.
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Proc. of SPIE Vol. 7078 70781P-9
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Proc. of SPIE Vol. 7078 70781P-10
