ВЫБОР РАДИУСА ИСТОЧНИКА В ФАЗОВОКОНТРАСТНОМ МЕТОДЕ ФОРМИРОВАНИЯ РЕНТГЕНОВСКИХ ИЗОБРАЖЕНИЙ
the Choice method of light source radius in X-ray phase contrast imaging system
ВЫБОР РАДИУСА ИСТОЧНИКА В ФАЗОВОКОНТРАСТНОМ МЕТОДЕ ФОРМИРОВАНИЯ РЕНТГЕНОВСКИХ ИЗОБРАЖЕНИЙ
© 2013 г. Jie Wu
School of Medical Instrument and Food Engineering, University of Shanghai for Science and Technology, Shanghai, China
E-mail: jieusst@163.com
Based on the partially coherent optical theory, a new theoretical model is established about the X-ray light source radius of X-ray phase contrast imaging system. Through the integral phase contrast modulation transfer function, a comprehensive analysis about the light source radius is made. Then the light source radius selection methods are investigated. Finally, an actual imaging experiment is shown to confirm the choice method of light source radius in X-ray phase contrast imaging system.
Ключевые слова: X-ray phase contrast, light source radius, micro focus.
Поступила в редакцию 27.09.2012.
1. INTRODUCTION
From the 1990s, the X-ray phase contrast imaging technology has developed gradually, it relies on the X-ray phase shift degree, for those weak absorption material, the phase shift is often significantly greater than its absorption attenuation, even more than 1000 times higher [1, 2]. Therefore, the X-ray phase contrast imaging technology can effectively detect the internal structure of weak absorption material. This not only makes up for the weakness of traditional absorption imaging, but also extends the X-ray detection range to the weak absorption materials, and the imaging spatial resolution can reach the sub micron level [3, 4, 5].
At present, micro-focus X-ray phase contrast imaging is a research hot spot, because it has these characteristics, simple optical method, low cost, suitable for experiment and easy operation, etc. It records the Laplacian of edge details of the imaging objects, so it has broad application prospects in the clinical and laboratory research.
However, in the former published research literatures, the theoretical model basis can be divided into two categories, one is evolved directly from the hard X-ray synchrotron radiation imaging theory, the X-ray is assumed to be parallel light. Another category assumed microfocus point to be entirely ideal coherent light with ideal spherical wave, which are reported by
“Оптический журнал”, 80, 9, 2013
S. W. Wilkins, A. Pogany, A. Momos etc [4–6]. Lately, Chika Honda , A. Olivo, Xi-zeng Wu, and domestic Chen Min, Yu-hong, have introduced partial coherence theory to phase contrast imaging theoretical model analysis, but the light source radius of micro-focus has not included their theoretical model especially, and lacking of the concrete example data analysis in these literatures [7–9].
Therefore, in this paper, first of all, a new integral phase contrast modulation transfer function model is established considering of the light source radius of X-ray micro-focus , then the theoretical simulation and calculation are analyzed, after that, a micro-source selection principle and a parameter optimization method are proposed, finally, the actual imaging experiments verify the model and method.
2. Materials and methods
The micro-focus X-ray phase contrast imaging system diagram is shown in Fig. 1. X-ray is assumed to spread along the z direction, a experimental object is placed between the X-ray source and the image detector. Suppose that the light source is circular with a radius of R0 , the distance from the light source to the object is D, the distance from the object to image detector is Z, the light source coordinate system is x0o0y0 coordinate, the object
33
R1 ≈ Z +
(x – x1)2 + (y – y1)2 , 2Z
R2 ≈ Z +
(x – x2)2 + (y – y2)2 . 2Z
(5)
Fig. 1. Micro focus X-ray phase contrast imaging system diagram.
coordinate system is x1o1y1 coordinate, the image detector coordinate system is xoy coordinate. To simplify the theoretical model, assume that two unrelated points o1o2 emits the partially coherent X-ray, the thin object is weak absorption, the light path and other symbols are shown in Fig. 1.
The coherence of any two points in light field can be described as the mutual intensity, using Van Cittert-Zernike assumption, any two points on the light source is statistical independent [10, 11], the mutual intensity is:
J(O1, O2) = I(O1)δ(x01 – x02, y01 – y02). (1)
In the spread process from the source to the front surface of the object, according to the mutual intensity propagation theory, the mutual coherence function at the front surface of the object can be expressed as:
J0(P1,
P2)
=
1 — λ2
∫∫Ω I(O1)
exp ik(r1 r1r2
–
r2)
dS .
(2)
Assuming the object projection function with T, the mutual intensity after the object can be expressed as:
J(P1, P2) = T(P1)T*(P2)J0(P1, P2).
(3)
After passing through the object, X-ray continues to spread and overlap in image plane, similarly, according to the mutual intensity propagation theory, get the Eq. (4) :
1
I(Q)
=
— λ2
∫∫
S
∫∫
S
J(P1,
P2)
exp
ik(R1 R1R2
–
R2)
dS1dS2.
(4)
Under the paraxial approximation, using the binomial expansion approximation:
Substitute the denominator of integral part in Eq. (4) by Eq. (5), the image intensity distribution can be expressed as:
exp(jkZ)
I(x, y) = I(Q) =
λ2Z2
∫∫
S
∫∫
S
J(P1,
P2)
×
ik
×
exp(—|(x 2Z
–
x2)2
–
(x
–
x1)2
+
(y
–
y2)2
–
– (y – y1)2|)dx1dx2dy1dy2.
(6)
For the expression convenience, the Fourier transform of plane intensity distribution is:
I~(u, v) =
exp(jkZ) λ2Z2 ∫∫S∫∫SJ(x1, x2; y1, y2)dx1dx2dy1dy2 ×
{ ik
× FT exp(2—Z |(x – x2)2 – (x – x1)2 +
{+ (y – y2)2 – (y – y1)2| .
(7)
Simplify the Fourier transform in the Eq. 7:
{ {FT
exp(—iπ [(x
λZ
–
x2)2
–
(x
–
]x1)2
=
{ { { {= exp
—iπ λZ
(x21
–
x22)
FT
exp(2πix
x2 – x1 λZ
=
{ {= λZexp
—iπ λZ
(x21
–
x22)
δ[x1 – (x2 – λZu)].
(8)
Take Eq. (8) into Eq. (7), integral with x1, y1, Eq. (9) can get:
I~(u, v) = [iπλZ(u2 + v2)] ×
{ {J(x2 – λZu, x2; y2 – λZv, y2) ×
× ∫∫ exp –i2π(ux2 + vy2) dx2dy2.
(9)
34 “Оптический журнал”, 80, 9, 2013
Similarly, convert the formula 2 to the frequency domain representation, and take it into the ∫J(x2 – λZu, x2; y2 – λZν, y2), and get:
J0(x2 – λZu, x2; y2 – λZν, y2) =
=
1 λ2D2
exp[
π λD
(λ2D2(u2
+
ν2)2λZ(x2u
+
y2v))]
× (10)
[ ]Z Z
× ∫∫I(O1)exp –i2π(x01—Du + y01 —D v) dx01dy01.
The S(u,ν) indicates the Fourier transform of light intensity angular distribution:
S(u,ν) = ∫∫I(O1)exp[–i2π(x0u + ]y0v) dx0dy0. (11)
Therefore, the integral in Eq. (11) can be
expressed
as
S(—Z u, D
Z —D v),
this
is
the
Fourier
transform of the effectively light intensity distribution, so Eq. (11) can be re-written as
J0(x2 – λZu, x2; y2 – λZν, y2) =
=
1 λ2D2
exp[
π λD
(λ2D2(u2
+
ν2)2λZ(x2u
+
y2v))]
× (12)
×
S(—Z u, D
Z —v). D
Take Eq. (12) and Eq. (3) into Eq. (9), the Eq. (13) can be got:
I~(u, v) = exp[iπλDM(u2 + v2)] ×
× ∫∫T(x, y)T*(x – λZu, y – λZv) ×
(13)
× exp{–2πiM(ux + vy}dxdyS(—Z u, —Z v). DD
In first part of Eq. (13), it is the expression of Fourier transform of image plane intensity on condition of an ideal point light sources, it has a relatively mature and accepted simplified expression as follows [12–14]:
[ ]I~point(u, v) = exp iπλDM(u2 + v2) ×
× ∫∫T(x, y)T*(x – λZu, y – λZv)exp{–2πiM(ux + vy} =
= δ(u, v) + 2sin[–πλZM(u2 + v2)](u, v) – – 2cos[–πλZM(u2 + v2)](u, v).
(14)
In this Eq. (14), M = Z/D is the magnification,
Ф(u, ν) is the Fourier transform of the object phase shift, H(u, ν) is the Fourier transform of the
object absorption, sin[–πλZM(u2 + v2)] is the phase
modulation function under the conditions of the
ideal coherent of point source. Combine Eq. (13)
and Eq. (14) together, the Fourier transform of
image intensity can be expressed as a simple form:
I~(u,
v)
=
S(—Z u, D
Z —v) D
I~point(u,
v).
(15)
The impact of the light source radius on the phase contrast imaging system, in the frequency domain, can be described as the Fourier transform of the light intensity angular distribution function multiply the image intensity Fourier transform of the ideal fully coherent conditions. Therefore, in order to study the phase modulation effect of the light source radius individually, substitute Eq. (14) into Eq. (15), the integral phase contrast modulation transfer function (IPC–MTF) can be defined as
MTFIPC
=
Z S(—u,
D
—Zv)sin[–πλZM(u2
D
+
v2)].
(16)
To calculate the MTFIPC, the light intensity distribution can be considered uniform for typical circular light source [15], and the light intensity distribution function can be expressed as Eq. (17), its Fourier transform is Eq. (18).
{r
Circle (—) =
1 r
≤
R0
,
R0 0
r > R0
(17)
Z Z
1
S(—u, D
D—v)
=
√ u2 + v2
J1(2πZR0)√ u2 + v2 / R).
(18)
In the Eq. (18), J1 first–order Bessel function, so the integral phase contrast modulation transfer function (IPC–MTF) described in Eq. (16), can be specifically written as a more specific shape:
1 MTFIPC = √ u2 + v2 J1(2πZR0)√ u2 + v2 / R) ×
(19)
× sin[–πλZM(u2 + v2)].
“Оптический журнал”, 80, 9, 2013
35
0 10 20 30 40 50 60 70 80 90 100 Fig. 2. Light source radius is 5 μm.
0 10 20 30 40 50 60 70 80 90 100 Fig. 3. Light source radius is 10 μm.
0 10 20 30 40 50 60 70 80 90 100 Fig. 4. Light source radius is 20 μm.
0 10 20 30 40 50 60 70 80 90 100 Fig. 5. Light source radius is 40 μm.
3. The simulation and experiment results
3.1 The impact of light source radius on the integral phase–contrast modulation
transfer function
According to the above theoretical model, set the parameters unchanged, just change the light source radius, the results are shown in Fig. 2–5. In these figures, the solid line indicates the integral phase-contrast transfer function curve, dotted line indicates the phase contrast transfer function under the conditions of ideal coherent light source, dashed line indicates the space modulation function curve of the light source size itself. Comparing these curves, we can find that the influence of light source size on the integral phase contrast transfer function is obvious. Therefore, the focus size is a critical system indicator for the microfocus X-ray phase contrast imaging system, smaller focus size can upgrade the overall system performance.
3.2 Choice of light source size
If the light source size is too small, the whole equipment cost will rise, and the luminous flux, as well as the entire tube power will be limited. Therefore, under the actual context of the specific experimental conditions, it is difficult to determine the appropriate focus sizes under the premise of the overall phasecontrast imaging performance. To this end, we set up an experiment using the detector resolution 50 lp/ mm, fix the object to detector distance, change the light source to object distance respectively at 0,2, 0,4, 0,6, 0,8, 1,0, 1,2 meters, the IPC-MTF changes with the light source radius are shown in Fig. 6. After that we fix light source to object distance, change the object to the detector respectively at 0.2,0.4,0.6,0.8,1.0,1.2 meters, the IPC-MTF changes with the light source radius are shown in Fig. 7.
3.3 The experiment results
The micro focus X-ray source was employed in this experiment according to the above theoretical
36 “Оптический журнал”, 80, 9, 2013
Fig. 6. Fix the object to detector distance.
model, the sample was an optical fiber with the radius of 200 μm, the images shown in the Fig.8 and 9 are obtained when micro focus spot radius was set 40 μm and 20 μm respectively. In our experiment, the tube potential was 30 kV, the tube current was 250 μA, and other parameters ware set at the optimization way.
In the Fig. 9, micro focus spot radius was set 20 μm , the boundary and overall contrast can be seen clearly, while in the Fig. 8, micro focus spot radius was changed to 40 μm, the boundary and overall contrast are much less distinct, which validates the prediction results of the theoretical formula and analysis in this paper.
Fig. 7. Fix the source to object distance. Fig. 8. The focus spot radius is 40 μm.
4. Conclusions
This paper considers the light source radius of actual micro focus X-ray phase contrast system, the impact of light source spatial coherence is analyzed based on free-space propagation of mutual intensity theory, then a new integral phase contrast modulation transfer function model is established. In the actual experimental system conditions, we propose the choice regulation of light source size, and give a quantitative basis and proposal.
On the basis of the research conclusion, we set the different experimental micro focus on the light source radius, the test results validate that the model and analysis proposed in this
Fig. 9. The focus spot radius is 20 μm.
paper are correct. In the actual system design and parameter optimization process, there are many other factors need to consider such as light intensity, sample size, current size, all of these should be discussed in the future.
*****
“Оптический журнал”, 80, 9, 2013
37
REFERENCES 1. Pogany A., Rev. sci. instrum, 68(1997) 2774. 2. Snigirev A. Rev. sci. instrum, 66(1995)5486. 3. Wilkins S.W. Nature, 384(1996)335. 4. Spanne P. Med. Biol, 44(1999)741. 5. Cloetens P. Phys J. D: Appl. Phys,32(1999)145. 6. Momose A. Opt. Express, 11(2003)2303. 7. Chapman D. Nature, 373(1995)595. 8. Montgomery D.S. Rev. sci. instrum, 75 (2004)3986. 9. Gureyev T.E., Pogany A., Paganin D.M. Optics Communications, 231(2004)53. 10. Shu-Ang Zhou, Anders Brahme. Physica Medica, 24(2008)129. 11. Chika Honda, Hiromu Ohara. European Journal of Radiology, 8(2008)69. 12. Zhi-Feng Huang, Ke-Jun Kang, Li Zhang. Phy. Rev. A 79(2009)13. 13. Fanbo Meng, Da Zhang a, Xizeng Wu. Optics Communications , 282(2009)3392. 14. Coan P., Gruener F., Glaser C., Schneider T. Physics Research A, 608(2009)44. 15. Olivo A., Rigon L., Vinnicombe S.J. Applied Radiation and Isotopes 69(2009)1033.
38 “Оптический журнал”, 80, 9, 2013
ВЫБОР РАДИУСА ИСТОЧНИКА В ФАЗОВОКОНТРАСТНОМ МЕТОДЕ ФОРМИРОВАНИЯ РЕНТГЕНОВСКИХ ИЗОБРАЖЕНИЙ
© 2013 г. Jie Wu
School of Medical Instrument and Food Engineering, University of Shanghai for Science and Technology, Shanghai, China
E-mail: jieusst@163.com
Based on the partially coherent optical theory, a new theoretical model is established about the X-ray light source radius of X-ray phase contrast imaging system. Through the integral phase contrast modulation transfer function, a comprehensive analysis about the light source radius is made. Then the light source radius selection methods are investigated. Finally, an actual imaging experiment is shown to confirm the choice method of light source radius in X-ray phase contrast imaging system.
Ключевые слова: X-ray phase contrast, light source radius, micro focus.
Поступила в редакцию 27.09.2012.
1. INTRODUCTION
From the 1990s, the X-ray phase contrast imaging technology has developed gradually, it relies on the X-ray phase shift degree, for those weak absorption material, the phase shift is often significantly greater than its absorption attenuation, even more than 1000 times higher [1, 2]. Therefore, the X-ray phase contrast imaging technology can effectively detect the internal structure of weak absorption material. This not only makes up for the weakness of traditional absorption imaging, but also extends the X-ray detection range to the weak absorption materials, and the imaging spatial resolution can reach the sub micron level [3, 4, 5].
At present, micro-focus X-ray phase contrast imaging is a research hot spot, because it has these characteristics, simple optical method, low cost, suitable for experiment and easy operation, etc. It records the Laplacian of edge details of the imaging objects, so it has broad application prospects in the clinical and laboratory research.
However, in the former published research literatures, the theoretical model basis can be divided into two categories, one is evolved directly from the hard X-ray synchrotron radiation imaging theory, the X-ray is assumed to be parallel light. Another category assumed microfocus point to be entirely ideal coherent light with ideal spherical wave, which are reported by
“Оптический журнал”, 80, 9, 2013
S. W. Wilkins, A. Pogany, A. Momos etc [4–6]. Lately, Chika Honda , A. Olivo, Xi-zeng Wu, and domestic Chen Min, Yu-hong, have introduced partial coherence theory to phase contrast imaging theoretical model analysis, but the light source radius of micro-focus has not included their theoretical model especially, and lacking of the concrete example data analysis in these literatures [7–9].
Therefore, in this paper, first of all, a new integral phase contrast modulation transfer function model is established considering of the light source radius of X-ray micro-focus , then the theoretical simulation and calculation are analyzed, after that, a micro-source selection principle and a parameter optimization method are proposed, finally, the actual imaging experiments verify the model and method.
2. Materials and methods
The micro-focus X-ray phase contrast imaging system diagram is shown in Fig. 1. X-ray is assumed to spread along the z direction, a experimental object is placed between the X-ray source and the image detector. Suppose that the light source is circular with a radius of R0 , the distance from the light source to the object is D, the distance from the object to image detector is Z, the light source coordinate system is x0o0y0 coordinate, the object
33
R1 ≈ Z +
(x – x1)2 + (y – y1)2 , 2Z
R2 ≈ Z +
(x – x2)2 + (y – y2)2 . 2Z
(5)
Fig. 1. Micro focus X-ray phase contrast imaging system diagram.
coordinate system is x1o1y1 coordinate, the image detector coordinate system is xoy coordinate. To simplify the theoretical model, assume that two unrelated points o1o2 emits the partially coherent X-ray, the thin object is weak absorption, the light path and other symbols are shown in Fig. 1.
The coherence of any two points in light field can be described as the mutual intensity, using Van Cittert-Zernike assumption, any two points on the light source is statistical independent [10, 11], the mutual intensity is:
J(O1, O2) = I(O1)δ(x01 – x02, y01 – y02). (1)
In the spread process from the source to the front surface of the object, according to the mutual intensity propagation theory, the mutual coherence function at the front surface of the object can be expressed as:
J0(P1,
P2)
=
1 — λ2
∫∫Ω I(O1)
exp ik(r1 r1r2
–
r2)
dS .
(2)
Assuming the object projection function with T, the mutual intensity after the object can be expressed as:
J(P1, P2) = T(P1)T*(P2)J0(P1, P2).
(3)
After passing through the object, X-ray continues to spread and overlap in image plane, similarly, according to the mutual intensity propagation theory, get the Eq. (4) :
1
I(Q)
=
— λ2
∫∫
S
∫∫
S
J(P1,
P2)
exp
ik(R1 R1R2
–
R2)
dS1dS2.
(4)
Under the paraxial approximation, using the binomial expansion approximation:
Substitute the denominator of integral part in Eq. (4) by Eq. (5), the image intensity distribution can be expressed as:
exp(jkZ)
I(x, y) = I(Q) =
λ2Z2
∫∫
S
∫∫
S
J(P1,
P2)
×
ik
×
exp(—|(x 2Z
–
x2)2
–
(x
–
x1)2
+
(y
–
y2)2
–
– (y – y1)2|)dx1dx2dy1dy2.
(6)
For the expression convenience, the Fourier transform of plane intensity distribution is:
I~(u, v) =
exp(jkZ) λ2Z2 ∫∫S∫∫SJ(x1, x2; y1, y2)dx1dx2dy1dy2 ×
{ ik
× FT exp(2—Z |(x – x2)2 – (x – x1)2 +
{+ (y – y2)2 – (y – y1)2| .
(7)
Simplify the Fourier transform in the Eq. 7:
{ {FT
exp(—iπ [(x
λZ
–
x2)2
–
(x
–
]x1)2
=
{ { { {= exp
—iπ λZ
(x21
–
x22)
FT
exp(2πix
x2 – x1 λZ
=
{ {= λZexp
—iπ λZ
(x21
–
x22)
δ[x1 – (x2 – λZu)].
(8)
Take Eq. (8) into Eq. (7), integral with x1, y1, Eq. (9) can get:
I~(u, v) = [iπλZ(u2 + v2)] ×
{ {J(x2 – λZu, x2; y2 – λZv, y2) ×
× ∫∫ exp –i2π(ux2 + vy2) dx2dy2.
(9)
34 “Оптический журнал”, 80, 9, 2013
Similarly, convert the formula 2 to the frequency domain representation, and take it into the ∫J(x2 – λZu, x2; y2 – λZν, y2), and get:
J0(x2 – λZu, x2; y2 – λZν, y2) =
=
1 λ2D2
exp[
π λD
(λ2D2(u2
+
ν2)2λZ(x2u
+
y2v))]
× (10)
[ ]Z Z
× ∫∫I(O1)exp –i2π(x01—Du + y01 —D v) dx01dy01.
The S(u,ν) indicates the Fourier transform of light intensity angular distribution:
S(u,ν) = ∫∫I(O1)exp[–i2π(x0u + ]y0v) dx0dy0. (11)
Therefore, the integral in Eq. (11) can be
expressed
as
S(—Z u, D
Z —D v),
this
is
the
Fourier
transform of the effectively light intensity distribution, so Eq. (11) can be re-written as
J0(x2 – λZu, x2; y2 – λZν, y2) =
=
1 λ2D2
exp[
π λD
(λ2D2(u2
+
ν2)2λZ(x2u
+
y2v))]
× (12)
×
S(—Z u, D
Z —v). D
Take Eq. (12) and Eq. (3) into Eq. (9), the Eq. (13) can be got:
I~(u, v) = exp[iπλDM(u2 + v2)] ×
× ∫∫T(x, y)T*(x – λZu, y – λZv) ×
(13)
× exp{–2πiM(ux + vy}dxdyS(—Z u, —Z v). DD
In first part of Eq. (13), it is the expression of Fourier transform of image plane intensity on condition of an ideal point light sources, it has a relatively mature and accepted simplified expression as follows [12–14]:
[ ]I~point(u, v) = exp iπλDM(u2 + v2) ×
× ∫∫T(x, y)T*(x – λZu, y – λZv)exp{–2πiM(ux + vy} =
= δ(u, v) + 2sin[–πλZM(u2 + v2)](u, v) – – 2cos[–πλZM(u2 + v2)](u, v).
(14)
In this Eq. (14), M = Z/D is the magnification,
Ф(u, ν) is the Fourier transform of the object phase shift, H(u, ν) is the Fourier transform of the
object absorption, sin[–πλZM(u2 + v2)] is the phase
modulation function under the conditions of the
ideal coherent of point source. Combine Eq. (13)
and Eq. (14) together, the Fourier transform of
image intensity can be expressed as a simple form:
I~(u,
v)
=
S(—Z u, D
Z —v) D
I~point(u,
v).
(15)
The impact of the light source radius on the phase contrast imaging system, in the frequency domain, can be described as the Fourier transform of the light intensity angular distribution function multiply the image intensity Fourier transform of the ideal fully coherent conditions. Therefore, in order to study the phase modulation effect of the light source radius individually, substitute Eq. (14) into Eq. (15), the integral phase contrast modulation transfer function (IPC–MTF) can be defined as
MTFIPC
=
Z S(—u,
D
—Zv)sin[–πλZM(u2
D
+
v2)].
(16)
To calculate the MTFIPC, the light intensity distribution can be considered uniform for typical circular light source [15], and the light intensity distribution function can be expressed as Eq. (17), its Fourier transform is Eq. (18).
{r
Circle (—) =
1 r
≤
R0
,
R0 0
r > R0
(17)
Z Z
1
S(—u, D
D—v)
=
√ u2 + v2
J1(2πZR0)√ u2 + v2 / R).
(18)
In the Eq. (18), J1 first–order Bessel function, so the integral phase contrast modulation transfer function (IPC–MTF) described in Eq. (16), can be specifically written as a more specific shape:
1 MTFIPC = √ u2 + v2 J1(2πZR0)√ u2 + v2 / R) ×
(19)
× sin[–πλZM(u2 + v2)].
“Оптический журнал”, 80, 9, 2013
35
0 10 20 30 40 50 60 70 80 90 100 Fig. 2. Light source radius is 5 μm.
0 10 20 30 40 50 60 70 80 90 100 Fig. 3. Light source radius is 10 μm.
0 10 20 30 40 50 60 70 80 90 100 Fig. 4. Light source radius is 20 μm.
0 10 20 30 40 50 60 70 80 90 100 Fig. 5. Light source radius is 40 μm.
3. The simulation and experiment results
3.1 The impact of light source radius on the integral phase–contrast modulation
transfer function
According to the above theoretical model, set the parameters unchanged, just change the light source radius, the results are shown in Fig. 2–5. In these figures, the solid line indicates the integral phase-contrast transfer function curve, dotted line indicates the phase contrast transfer function under the conditions of ideal coherent light source, dashed line indicates the space modulation function curve of the light source size itself. Comparing these curves, we can find that the influence of light source size on the integral phase contrast transfer function is obvious. Therefore, the focus size is a critical system indicator for the microfocus X-ray phase contrast imaging system, smaller focus size can upgrade the overall system performance.
3.2 Choice of light source size
If the light source size is too small, the whole equipment cost will rise, and the luminous flux, as well as the entire tube power will be limited. Therefore, under the actual context of the specific experimental conditions, it is difficult to determine the appropriate focus sizes under the premise of the overall phasecontrast imaging performance. To this end, we set up an experiment using the detector resolution 50 lp/ mm, fix the object to detector distance, change the light source to object distance respectively at 0,2, 0,4, 0,6, 0,8, 1,0, 1,2 meters, the IPC-MTF changes with the light source radius are shown in Fig. 6. After that we fix light source to object distance, change the object to the detector respectively at 0.2,0.4,0.6,0.8,1.0,1.2 meters, the IPC-MTF changes with the light source radius are shown in Fig. 7.
3.3 The experiment results
The micro focus X-ray source was employed in this experiment according to the above theoretical
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Fig. 6. Fix the object to detector distance.
model, the sample was an optical fiber with the radius of 200 μm, the images shown in the Fig.8 and 9 are obtained when micro focus spot radius was set 40 μm and 20 μm respectively. In our experiment, the tube potential was 30 kV, the tube current was 250 μA, and other parameters ware set at the optimization way.
In the Fig. 9, micro focus spot radius was set 20 μm , the boundary and overall contrast can be seen clearly, while in the Fig. 8, micro focus spot radius was changed to 40 μm, the boundary and overall contrast are much less distinct, which validates the prediction results of the theoretical formula and analysis in this paper.
Fig. 7. Fix the source to object distance. Fig. 8. The focus spot radius is 40 μm.
4. Conclusions
This paper considers the light source radius of actual micro focus X-ray phase contrast system, the impact of light source spatial coherence is analyzed based on free-space propagation of mutual intensity theory, then a new integral phase contrast modulation transfer function model is established. In the actual experimental system conditions, we propose the choice regulation of light source size, and give a quantitative basis and proposal.
On the basis of the research conclusion, we set the different experimental micro focus on the light source radius, the test results validate that the model and analysis proposed in this
Fig. 9. The focus spot radius is 20 μm.
paper are correct. In the actual system design and parameter optimization process, there are many other factors need to consider such as light intensity, sample size, current size, all of these should be discussed in the future.
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