1. INTRODUCTION
The detection of specific elements or compounds in a sample is a task
of a great interest in a wide range of fundamental and applied research
fields. In some circumstances, information on the total concentration
as well as on the spatial distribution of a given compound in a sample
can be obtained by exploiting the self-emission properties of a
specific radioactive tracing element included in the compound (Barbarics et al., 1994). Alternatively,
highly X-ray absorbing contrast agents are used in combination with
radiographic imaging techniques that provide a two-dimensional (2D)
mapping of the X-ray absorption in the sample (Suortti & Thomlinson, 2003). Techniques based
upon these principles are currently used in a number of laboratory as
clinical diagnostic techniques.
The differential absorption imaging technique is an alternative
powerful tool for accomplishing this task that relies solely on the
spectral properties of absorption of X-ray radiation by an atomic
element. In particular, the technique takes advantage of the sharp
change of the photon attenuation length across a chosen absorption edge
of a given element.
The method has already been proposed for the detection of small
concentrations of contrast agents for biological and medical
applications. For instance, it is currently under study for clinical
application in coronary angiography (Dill et
al., 1998). Up to now, such studies have been carried out
using monochromatic radiation emitted from synchrotron sources (Suortti & Thomlinson, 2003). More recently,
laser-plasma Kα sources have also been suggested as
possible compact sources for this application (Tillman et al., 1996; Andersson et al., 2001).
In this paper, we present investigations aimed at scaling the
application of this technique from the hard X-rays typically used for
coronary angiography to the soft X-ray range. This allows to perform a
quantitative elemental analysis of thin samples. In particular, we
investigate the possibility of using a table-top laser-plasma soft
X-ray source combined with the diffractive crystal properties for the
development of a standard arrangement for a dedicated small-scale
equipment.
A short basic introduction to the technique of differential
absorption is first given, followed by the description of a preliminary
experiment carried out using the PLX laser-plasma soft X-ray source
developed (Marzi et al., 2000) at
the Intense Laser Irradiation Laboratory. We then show the results
obtained by applying the differential imaging to a thin sample
containing a solution of bromine.
2. BASIC PRINCIPLES OF THE TECHNIQUE
In principle, the detection of a given element characterized by an
absorption edge at a given wavelength, denoted by λEdge,
requires two images of the sample to be taken using monochromatic
radiation at two different photon wavelengths, one (λ1)
just below the edge wavelength, and another one (λ2)
just above the edge. Therefore the logarithmic subtraction of these two
images gives directly a 2D map of the tracing element inside the
sample.
More quantitatively, the 2D map of the intensity of the X-ray
radiation transmitted by a sample irradiated at a normal incidence at a
photon wavelength λj can be written as:
where z is the coordinate along the direction of the
incident beam, x and y are the coordinates
perpendicular to z,
I0(j)(x,y) is
the incident beam intensity, with the index j = 1,2
identifying the two wavelengths, respectively, above and below the
absorption edge, μi(j) is the
mass absorption coefficient of the i-th element in the sample
at the j-th value of the wavelength,
ρi(x,y,z) is its
density distribution and finally s is the thickness of the
sample. Performing the logarithmic subtraction of the two distributions
of intensity taken at the two photon wavelengths yields a map of the
optical depth:
where R =
I(2)(x,y)I0(1)(x,y)/I0(2)(x,y)I(1)(x,y)
and Δμi =
μi(1) −
μi(2) is the difference of the mass
absorption coefficient of the element at the two wavelengths. For
simplicity, we restrict our analysis to the case in which the two
values of the photon wavelength are close enough to neglect the
variation of the mass absorption coefficient of the other elements
present in the sample, provided these elements do not exhibit an
absorption edge in that wavelength range. This assumption sets a limit
to the minimum detectable surface density of the tracing element in the
sample. In this case, the surface mass density σ of the tracing
element can be written as:
The uncertainty on the detectable surface mass density of the tracing
element is obtained from Eq. (3) considering the uncertainties on
Δμ and R, and can be written as:
From an experimental viewpoint, the uncertainty on Δμ comes
out to be negligible in comparison with the one concerning the measured
intensities since tabulated values of μ are typically very
accurate. Therefore, the uncertainty on the measurement of the surface
mass density of a tracing element becomes:
This corresponds also to the minimum detectable surface mass density,
which will be denoted as σmin, corresponding to the
condition of a 100% relative error on the surface density
(δσ/σ = 1).
3. THE CASE OF BROMINE
We will consider a sample containing a contrast agent consisting of
Br whose L2 edge (ΔμBr = 1,506
± 10 cm2/g) is located at a wavelength of 7.7682
Å (1,596 eV). We will assume that the detection of X-rays is
carried out using a cooled CCD X-ray detector. In these circumstances,
the instrumental uncertainty on the transmitted X-ray beam intensity is
given by the intensity resolution of the detector. In the case of a 14
bits detector, we have δI = 6.2 ×
10−5, which leads to δR/R
≈ 1.24 × 10−4. According to Eq. (5), these
values give a minimum detectable surface mass density of
σmin = 8.32 × 10−8
g/cm2. Assuming a sample thickness of 50 μm, a
reasonable value of the X-ray attenuation length in the soft X-ray
range for biological materials, we find that the minimum detectable
average mass density is ρmin = 17
μg/cm3.
It should be pointed out here that in the case of the investigation
of complex biological systems, the tracing element is usually found in
well-localized (typically micrometer sized) regions with specific
spatial properties (such as, interstitial regions, vessels,
capillaries, etc). In these regions, the local concentration of the
tracing element can be much higher than the average value.
Consequently, provided sufficient spatial resolution is available in
the imaging system, local concentrations of contrast agent can be
detected even when average concentration values are well below the
detectable value calculated above.
The use of Bromine as a test element for differential absorption
studies requires X-ray radiation in the spectral region close to the Br
L2 edge. When using laser-plasma sources, X-ray emission in
a given spectral range can be optimized by selecting the appropriate
target material (Giulietti & Gizzi,
1998). In the case discussed here, K-shell emission from an Al
plasma was selected which provides a number of spectral components in a
range around the Br L2 edge. Figure
1 shows the mass absorption coefficient of Br as a function of
the wavelength. Also shown in the figure (dashed line) is an
experimental spectrum of X-ray emission from an Al laser-plasma
obtained using a slit-less flat crystal spectrometer (Labate et al., 2001). The L2
absorption edge of Br is located just between some of the most intense
K-shell Al lines. The bright line below the edge is the 1s2
1S–1s2p 1P transition line from the He-like Al
(the so-called He-α resonance line) located at 7.757 Å (1,598 eV).
The brightest lines above the edge are the 1s2 1S–1s2p
3P (the so-called intercombination (IC) line) at 7.807 Å
(1,588 eV), and the Li-like 1s22p–1s2p2 at 7.875
Å (1,574 eV). The IC line, while being closer to the edge and therefore
being a better candidate than the Li-like line at λ2 =
7.875 Å, is more sensitive to changes in the physical plasma
conditions and therefore its intensity is subject to larger
shot-to-shot fluctuations. For this reason, the Li-like
1s22p–1s2p2 at λ2 = 7.875
Å (E2 = 1574 eV) is a more reliable emission
line.
Mass absorption coefficient of Br (dashed-dotted line) showing the
L2 absorption edge at 1596.0 eV. An experimental X-ray
spectrum of K-shell Al emission around the absorption edge is also
shown (dashed line). The solid line shows the same plot calculated
assuming a line-width of 1 mÅ (see text).
The width of these two X-ray lines as shown in Figure 1 is mainly due to instrumental and
geometrical factors originating from the finite size of the X-ray
emitting region. From the point of view of our imaging application, one
should consider the actual transition line-width which is essentially
determined by the Doppler effect arising from the thermal motion of the
emitting ions. For an Al plasma at a temperature of the order of 100
eV, the relative width of an emitting line (Δλ/λ) is of
the order of 10−4. Therefore, one should expect an
effective line-width as shown by the solid line in Figure 1. We can therefore conclude that the
He-α and Li lines are sufficiently well-separated and monochromatic
to be considered good candidates for differential absorption
measurements across the L2 edge of Br.
4. EXPERIMENTAL SET-UP
A schematic view of the experimental set up is shown in Figure 2. X-ray radiation emitted from the source
(K-shell emission from an Al target plasma) is collected using a
spherically bent mica crystal set up in such a way that the X-ray
source is located on the Rowland circle (that is, the circle of
diameter equal to the radius of curvature of the crystal). In such a
configuration, the crystal acts as a monochromator and consequently, a
highly monochromatic beam is Bragg-reflected on the CCD detector. The
crystal is placed on a remotely controlled mount that can perform
rotation on the Rowland circle. This enables the X-ray wavelength to be
tuned according to the Shadow Monochromatic Backlighting set up
presented in detail in (Pikuz et al.,
2001; Sanchez del Rio et al.,
2001). A comprehensive description and modeling of the crystal
imaging system is given by Labate et al. (2004). Here we present the main experimental
results concerning the implementation of this system for differential
absorption micro-imaging.
Experimental set-up for monochromatic imaging of thin samples using a
laser-plasma X-ray source. The geometry of the imaging system is based
upon a spherically bent crystal set up according to so-called Shadow
Monochromatic Backlighting configuration (Pikuz
et al., 2001).
Figure 3 shows the beam pattern produced by
the crystal (behaving as a monochromator) tuned on the
1s2-1s2p He-α line mentioned earlier. The IC line and
the Li-like lines are also just visible on the left-side of the main
component. A small rotation of the crystal enables the beam photon
wavelength to be tuned on a different value, while still keeping the
sample on the X-ray beams.
CCD image of the monochromatic X-ray beam as obtained with the
experimental configuration shown in Figure 2.
The crystal was tuned on the 1s2–1s2p (He-α
transition line from the He-like Al). The Li-like transition line and
the intercombination line are also visible.
When a sample is placed between the source and the crystal, as shown
in Figure 2, a micrometer-resolution
radiography of the sample at the selected photon wavelength is
generated. The image of Figure 4 shows a
micro-imaging resolution test carried out on the system using an object
consisting of a Fresnel zone-plate (λf = 0.114
mm2, radius of the first opaque zone equal to 340 μm)
whose total diameter was 7.5 mm. According to this test we can find
that, in our experimental conditions, the spatial resolution in the
horizontal direction is about 15 μm while in the vertical direction
its value is about 40 μm. A comprehensive discussion on the spatial
resolution properties of this imaging system can be found elsewhere
(Labate et al., 2004).
Monochromatic micro-imaging resolution test of the Shadow
Monochromatic Backlighting set-up tuned at 7.757 Å
(1s2–1s2p He-α) using a Fresnel zone-plate
(λf = 0.114 mm2, radius of the first opaque
zone equal to 340 μm, total diameter is 7.5 mm).
5. RESULTS AND DISCUSSION
A sample containing Bromine as a test element was prepared (see Figure 5) using a water solution of LiBr of a known
concentration of 0.265 g/ml. An amount of 0.2 μl of the
solution was deposited on the 30 μm thick paper substrate and the
water was then removed in vacuum. The sample was mounted on a washer
and placed between the source and the crystal as indicated in Figure 2. Taking into account the absorption
properties of Br and considering the parameters of the sample, a simple
calculation gives an average surface mass density of 6 ×
10−4 (±7 × 10−5)
g/cm2 and a corresponding optical depth difference of
Δt = 0.9 ± 0.1.
Schematic view of the sample consisting of a solution of LiBr
deposited on the 30 μm thick paper substrate mounted on a
washer.
The raw experimental results are shown in Figures 6a
and b. The upper images of (a) and (b) show, respectively, the
incident X-ray beam, that is, the beam without the sample, at the two
wavelengths below (λ1 = 7.757 Å) and above
(λ2 = 7.785 Å) the L2 absorption edge of
Br. These images were obtained integrating the CCD image over 10 X-ray
pulses (10 shots of the driving laser) at 10 Hz, corresponding to a total
time of exposure of 1 s. The lower images of (a) and (b) show the X-ray
beam transmitted through our sample for the same two wavelengths obtained
integrating over 300 X-ray pulses (which corresponds to 30 s of
exposure).
a–b. Experimental data of the differential absorption experiment
on the LiBr sample used in our experiments. Images (a) were taken at the
wavelength (7.75 Å) below the L2 absorption edge of Br :
the highest one show the X-ray beam without the sample and the other one
for the transmitted X-ray beam through the sample. The lowest ones (b) are
taken above (7.87 Å) the L2 edge.
The transmitted image of the sample consists of a circular region
(inside the washer) with an inner, irregularly shaped darker (optically
thicker) region due to the LiBr deposit. The parallel darker lines
visible on the images are a consequence of the fiber-like structure of
the paper substrate that results in modulations of the paper thickness,
and consequently, modulations on the transmitted intensity. Finally,
the shadow due to the washer used to hold the sample is also
visible.
A quantitative analysis of these results has been carried out using
Eq. (1) and averaging the result on the area of the sample containing
the LiBr deposit. The measurements give an average optical depth
difference Δt = 1.1 ± 0.8 that corresponds to a
surface mass density σ = 7.3 × 10−4
(±5 × 10−4) g/cm2. Such a
value of optical depth difference is in agreement with the value of
Δt = 0.9 ± 0.1 expected from the presence of Br.
The large uncertainty found in our measurements, compared with the
uncertainty given by Eq. (3) is partly due to the single-photon noise
arising from diffuse X-ray scattering, especially for the measurement
at the photon energy above the edge, where too high absorption from Br
occurs. In view of these considerations, higher signal-to-noise ratios
should be obtained for samples with a much lower surface density, as in
the case of real tracing concentrations.
This result should also be considered in view of the fact that the
other known elements present in the sample with substantial abundances
(e.g., Li, C, H, O) exhibit a smooth change, but no absorption edges,
of the mass absorption coefficient between the two wavelengths
considered here. Consequently, the change of optical depth expected for
the presence of elements other than Br is negligible. Indeed, a simple
estimate shows that, in the presence of a smooth variation of the mass
absorption coefficient, a change of 10 eV in the photon beam energy
corresponds to a typical change of the mass absorption coefficient of
approximately less than 100 cm2/g and, according to Eq.
(2), a corresponding difference in the optical depth smaller than 0.1,
that is, approximately 10 % of the value expected for Bromine.
6. SUMMARY AND CONCLUSIONS
In this paper, we have shown that our technique based on differential
imaging using a laser-plasma soft X-ray source combined with crystal
optics enabled us to detect the presence of Br in a thin sample. In
fact, we were able to detect a significant change in the optical depth
of the sample by changing the imaging X-ray wavelength by less than 100
mÅ. Moreover, our measurement enabled us to measure the surface
density of Br in our test sample.
Important issues need to be addressed in order to make this method a
general purpose technique for the detection of trace-level elements in
thin samples. The main aspect concerns the possibility of extending the
range of applicability to other absorption edge wavelengths, that is,
other elements. To this purpose, suitable emission photon energies
close to the absorption edge under investigation can be identified. On
the other hand, the possibility of using a laser-driven plasma source
may result in an easy access to the technique on the basis of a small
scale dedicated laboratory. This may result in the possibility of
improving the image quality and spatial resolution of widely used
techniques like self-emission radiography. On the other hand, the
possibility of using non-radioactive tracing elements opens new
possibilities for radioactivity-free laboratory diagnostics in medicine
and biology.
ACKNOWLEDGMENTS
We would like to thank A. Barbini, A. Rossi, A. Salvetti, W.
Baldeschi and M. Voliani for their invaluable technical assistance. SL
acknowledges financial support from the European Research Training
Network XPOSE Contract No. HPRN-CT-2000-00160. LL and PT acknowledge
financial support from MIUR (Project “Metodologie e diagnostiche
per materiali ed ambiente”). This work was partially supported by
the MIUR Project “Impianti innovativi multiscopo per la
produzione di radiazione X.”
