Tilted-grating approach for scanning-mode X-ray grating interferometry
Among the existent X-ray phase-contrast modalities, grating interferometry appears as a promising technique for commercial applications, since it is compatible with conventional X-ray tubes. However, since applications such as medical imaging and homeland security demand covering a considerable field of view, the fabrication of challenging and expensive large-area gratings would be needed. A scanning setup is a good solution, because it uses cheaper line detectors instead of large-area 2D detectors and would require smaller gratings. In this setup, the phase-retrieval using the conventional phase-stepping approach would be slow, so having a faster method to record the signals becomes fundamental. To tackle this problem, a scanning-mode grating interferometer configuration is used, in which a grating is tilted to form Moire fringes perpendicular to the grating lines. The sample is then translated along the fringes, so each line detector records a different phase step for each slice of the sample.
1. A grating interferometer system for obtaining absorption, differential phase contrast (DPC) and dark-field data from quantitative X-ray images from a sample, the grating interferometer system comprising:
an X-ray source;
gratings including one of:
a phase grating and an analyzer grating; or
a source grating, said phase grating and said analyzer grating;
a position-sensitive detector;
means for recording images of said position-sensitive detector;
means for evaluating intensities for each pixel in a series of the quantitative X-ray images, in order to identify characteristics of an object for each individual pixel as at least one of an absorption-dominated pixel, a DPC-dominated pixel, and an X-ray dark-field dominated pixel;
means to tilt either said phase grating or said analyzer grating by a predetermined angle; and
means to move the sample, said x-ray source, or said gratings and said position-sensitive detector to perform a scanning of a probe; and
wherein for near-field-regime operation, a distance between said gratings is chosen freely within the near-field-regime, and a Talbot-regime is chosen according to:
D
n
,
sph
=
L
·
D
n
L
-
D
n
=
L
·
n
·
p
1
2
/
2
η
2
λ
L
-
n
·
p
1
2
/
2
η
2
λ
where
n
=
1
,
3
,
5
…
,
and
η
=
{
1
if
the
phase
shift
of
G
1
is
(
2
l
-
1
)
π
2
,
p
2
=
L
+
D
n
,
sph
L
p
1
2
if
the
phase
shift
of
G
1
is
(
2
l
-
1
)
π
2
,
p
2
=
L
+
D
n
,
sph
L
where l=1, 2, 3 . . . , D n is an odd fractional Talbot distance when a parallel X-ray beam is used, G 1 is said phase grating, D n,sph is when a fan or cone X-ray beam is used and L is a distance between said source grating and said phase grating.
2. The system according to claim 1 , wherein said phase grating is a line grating, an absorption grating or a phase grating that is a low-absorption grating but generating a considerable X-ray phase shift and of Π or odd multiples thereof.
3. The system according to claim 1 , wherein said analyzer grating is a line grating having a high X-ray absorption contrast with its period being a same as that of a self-image of said phase grating, wherein said analyzer grating is placed closely in front of said position-sensitive detector with its lines parallel to those of said phase grating, before tilting said phase grating or said analyzer grating.
4. The system according to claim 1 , wherein said position-sensitive detector is a line sensitive detector.
5. A method to retrieve absorption, differential phase contrast (DPC) and dark field signals from a Moire fringe pattern obtained by detuning a grating interferometer system having an X-ray source, a phase grating, an analyzer grating and a line sensitive detector, which comprises the steps of:
producing the Moire fringe pattern of a desired period by tilting one of the phase grating or the analyzer grating by a predetermined angle; and
calculating a tilting angle using:
a period P 2 of the analyzer grating;
a number n of detector lines;
a number m of the periods P 2 that are to be covered;
a separation D between the detector lines of the line sensitive detector;
and employing formulas:
δ
x
=
m
p
2
n
θ
=
arc
tan
(
δ
x
D
)
where θ is the tilting angle; and
scanning either a sample or the grating interferometer system along the Moire fringe pattern.
6. The method according to claim 5 , which further comprises using reference and sample data acquired with the grating interferometer system to retrieve the absorption, the DPC and the dark-field signals by Fourier Component analysis.
7. The method according to claim 5 , wherein:
the grating interferometer system has the phase grating and the analyzer grating, and one of the phase grating and the analyzer grating is tilted; or
the grating interferometer system has a source grating, the phase grating and the analyzer grating, and wherein:
only the phase grating is tilted; or
only the analyzer grating is tilted; or
a pair of the source grating and the phase grating is tilted; or
a pair of the phase grating and the analyzer grating is tilted.
8. The method according to claim 5 , wherein compatible with radiography, tomosynthesis and computed tomography, either the sample or the grating interferometer system is rotated to acquire multiples views.