Phase contrast particle image velocimetry (PIV) using a laboratory x-ray microfocus source is investigated using a numerical model. Phase contrast images of 75 μm air bubbles, embedded within water exhibiting steady-state vortical flow, are generated under the paraxial approximation using a tungsten x-ray spectrum at 30 kVp. Propagation-based x-ray phase-contrast speckle images at a range of source–object and object–detector distances are generated, and used as input into a simulated PIV measurement. The effects of source-size-induced penumbral blurring, together with the finite dynamic range of the detector, are accounted for in the simulation. The PIV measurement procedure involves using the cross-correlation between temporally sequential speckle images to estimate the transverse displacement field for the fluid. The global error in the PIV reconstruction, for the set of simulations that was performed, suggests that geometric magnification is the key parameter for designing a laboratory-based x-ray phase-contrast PIV system. For the modeled system, x-ray phase-contrast PIV data measurement can be optimized to obtain low error (<0.2 effective pixel of the detector) in the system with magnification lying in the range between 1.5 and 3. For large effective pixel size (>15 μm) of the detector, high geometric magnification (>2.5) is desired, while for large source size system (FWHM > 30 μm), low magnification (<1.5) would be suggested instead. The methods developed in this paper can be applied to optimizing phase-contrast velocimetry using a variety of laboratory x-ray sources.

1.
W. C.
Röntgen
,
Nature
53
,
274
(
1896
).
2.
C. A.
Helms
,
Fundamentals of Skeletal Radiology
, 3rd ed. (
Elsevier
,
Philadelphia, USA
,
2003
).
3.
E. D.
Pisano
,
M. J.
Yaffe
, and
C. M.
Kuzmiak
,
Digital Mammography
(
Lippincott Williams & Wilkins
,
Philadelphia, USA
,
2004
).
4.
A.
Momose
,
T.
Takeda
,
Y.
Itai
, and
K.
Hirano
,
Nat. Med.
2
,
473
(
1996
).
5.
R.
Alford
,
H. M.
Simpson
,
J.
Duberman
,
G. C.
Hill
,
M.
Ogawa
,
C.
Regino
,
H.
Kobayashi
, and
P. L.
Choyke
,
Mol. Imaging
8
(
6
),
341
(
2009
).
6.
A.
Snigirev
,
I.
Snigireva
,
V.
Kohn
,
S.
Kuznetsov
, and
I.
Schelokov
,
Rev. Sci. Instrum.
66
(
12
),
5486
(
1995
).
7.
P.
Cloetens
,
R.
Barrett
,
J.
Baruchel
,
J. P.
Guigay
, and
M.
Schlenker
,
J. Phys. D: Appl. Phys.
29
,
133
(
1996
).
8.
K. A.
Nugent
,
T. E.
Gureyev
,
D. F.
Cookson
,
D.
Paganin
, and
Z.
Barnea
,
Phys. Rev. Lett.
77
,
2961
(
1996
).
9.
S. W.
Wilkins
,
T. E.
Gureyev
,
D.
Gao
,
A.
Pogany
, and
A. W.
Stevenson
,
Nature
384
,
335
(
1996
).
10.
T. E.
Gureyev
,
S. C.
Mayo
,
D. E.
Myers
,
Ya.
Nesterets
,
D. M.
Paganin
,
A.
Pogany
,
A. W.
Stevenson
, and
S. W.
Wilkins
,
J. Appl. Phys.
105
,
102005
(
2009
).
11.
R. J.
Adrian
,
Exp. Fluids
39
,
159
(
2005
).
12.
M.
Raffel
,
C.
Willert
,
S. T.
Wereley
, and
J.
Kompenhans
,
Particle Image Velocimetry: A Practical Guide
, 2nd ed. (
Springer
,
Berlin
,
2007
).
13.
A.
Fouras
,
J.
Dusting
,
R.
Lewis
, and
K.
Hourigan
,
J. Appl. Phys.
102
,
064916
(
2007
).
14.
S. J.
Lee
and
G. B.
Kim
,
J. Appl. Phys.
94
,
3620
(
2003
).
15.
A.
Fouras
,
M. J.
Kitchen
,
S.
Dubsky
,
R. A.
Lewis
,
S. B.
Hooper
, and
K.
Hourigan
,
J. Appl. Phys.
105
,
102009
(
2009
).
16.
S. C.
Irvine
,
D. M.
Paganin
,
R. A.
Jamison
,
S.
Dubsky
, and
A.
Fouras
,
Opt. Express
18
,
2368
(
2010
).
17.
A.
Fouras
,
J.
Dusting
,
J.
Sheridan
,
M.
Kawahashi
,
H.
Hirahara
, and
K.
Hourigan
,
Clin. Exp. Pharmacol. Physiol.
36
,
238
(
2009
).
18.
R. A.
Jamison
,
S.
Dubsky
,
K. K. W.
Siu
,
K.
Hourigan
, and
A.
Fouras
,
Ann. Biomed. Eng.
39
,
1643
(
2011
).
19.
A.
Seeger
,
K.
Affeld
,
L.
Goubergrits
,
E.
Wellnhofer
, and
U.
Kertzscher
,
Exp. Fluids
31
,
193
(
2001
).
20.
S.
Dubsky
,
R. A.
Jamison
,
S. C.
Irvine
,
K. K. W.
Siu
,
K.
Hourigan
, and
A.
Fouras
,
Appl. Phys. Lett.
96
,
023702
(
2010
).
21.
A.
Fouras
,
B. J.
Allison
,
M. J.
Kitchen
,
S.
Dubsky
,
J.
Nguyen
,
K.
Hourigan
,
K. K. W.
Siu
,
R. A.
Lewis
,
M. J.
Wallace
, and
S. B.
Hooper
,
Ann. Biomed. Eng.
40
,
1160
(
2012
).
22.
F. E.
Carroll
,
M. H.
Mendenhall
,
R. H.
Traeger
,
C.
Brau
, and
J. W.
Waters
,
Am. J. Roentgenol.
181
,
1197
(
2003
).
23.
U.
Bonse
and
M.
Hart
,
Appl. Phys. Lett.
6
,
155
(
1965
).
24.
F.
Pfeiffer
,
M.
Bech
,
O.
Bunk
,
P.
Kraft
,
E. F.
Eikenberry
,
Ch.
Brönnimann
,
C.
Grünzweig
, and
C.
David
,
Nature Mater.
7
,
134
(
2008
).
25.
C.
Kottler
,
F.
Pfeiffer
,
O.
Bunk
,
C.
Grünzweig
,
J.
Bruder
,
R.
Kaufmann
,
L.
Tlustos
,
H.
Walt
,
I.
Briod
,
T.
Weitkamp
, and
C.
David
,
Phys. Status Solidi
204
,
2728
(
2007
).
26.
S. C.
Mayo
,
P. R.
Miller
,
S. W.
Wilkins
,
T. J.
Davis
,
D.
Gao
,
T. E.
Gureyev
,
D.
Paganin
,
D. J.
Parry
,
A.
Pogany
, and
A. W.
Stevenson
,
J. Microsc.
207
,
79
(
2002
).
27.
B. D.
Arhatari
,
K.
Hannah
,
E.
Balaur
, and
A. G.
Peele
,
Opt. Express
16
,
19950
(
2008
).
28.
Y. S.
Kashyap
,
P. S.
Yadav
,
T.
Roy
,
P. S.
Sarkar
,
M.
Shukla
, and
A.
Sinha
,
Appl. Radiat. Isot.
66
,
1083
(
2008
).
29.
D.
Paganin
,
Coherent X-ray Optics
(
Oxford University Press
,
New York, USA
,
2006
).
30.
A.
Fouras
,
J.
Dusting
, and
K.
Hourigan
,
Exp. Fluids
42
,
799
(
2007
).
31.
A.
Fouras
,
D.
Lo Jacono
, and
K.
Hourigan
,
Exp. Fluids
44
,
317
(
2008
).
32.
M. J.
Kitchen
,
D.
Paganin
,
R. A.
Lewis
,
N.
Yagi
,
K.
Uesugi
, and
S. T.
Mudie
,
Phys. Med. Biol.
49
,
4335
(
2004
).
33.
M.
Sánchez del Río
and
R. J.
Dejus
, “
XOP 2.1: A new version of the X-ray optics software toolkit
” in
Eighth International Conference on Synchrotron Radiation Instrumentation
(
Americal Institute of Physics
,
2004
), p.
784
.
34.
M.
Born
and
E.
Wolf
,
Principles of Optics
(
Cambridge University Press
,
1997
).
35.
H.
Huang
,
D.
Dabiri
, and
M.
Gharib
,
Meas. Sci. Technol.
8
,
1427
(
1997
).
36.
Ya. I.
Nesterets
,
S. W.
Wilkins
,
T. E.
Gureyev
,
A.
Pogany
, and
A. W.
Stevenson
,
Rev. Sci. Instrum.
76
,
093706
(
2005
).
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