Ke Li and Guang-Hong Chen - AMOS Online

40 Pages·2013·1.49 MB·English

by  Ke Li

Ke Li and Guang-Hong Chen
Brief introduction of x-ray differential

phase contrast (DPC) imaging
Intrinsic noise relationship between DPC

imaging and absorption imaging
Task-based model observer studies for

DPC imaging
Summary

2
G2 zgrating
T
Absorption Contrast
G1 grating
Differential Phase Contrast
TomosCyTn thesis
((xx,, yy))
Tube
G0 grating
A. Momose, et al, Optical Express, 11 (2303) (2003)
T. Weitkamp, et al, Opt. Exp. 12(16), pp. 6296–304, 2005.
F. Pfeiffer, et al, Nature Physics 2, pp. 258–261, Apr 2006.
Detector
3
x-ray shutter
active
grating area
phase-stepping stage
4
Zambelli et al.,” Med. Phys., 2010, Vol. 37, pp. 2473-2479
detector phase grating rotary stage
5
Zambelli et al.,” Med. Phys., 2010, Vol. 37, pp. 2473-2479
G – Absorption Grating

0
 15 µm opening
 37 µm pitch
 2 cm x 2 cm
 60 µm Au depth

G – Phase Grating (π differential shift for 50% of beam)

1
 4 µm opening
 8 µm pitch
 7 cm x 7 cm
 40 µm etch depth

G – Absorption Grating

2
 2.25 µm opening
 4.5 µm pitch
 7 cm x 7 cm size
 30 µm Au depth

All gratings were made by Joe Zambelli and Ke Li using the on-campus micro-
fabrication facility: Wisconsin Center for Microelectronics (WCAM) at UW-Madison.
6
Absorption
I
1
Phase
I
0
2 
       
I m,n;x  I m,n  I m,n cos x  m,n
 
g 0 1 g d
p
 
2
) Phase Step Modulation
s
t
in
u
800

.
b
r
a
( 750
la
n
g
iS 700

r
o
t
c
e 650
t
e 0 5 10 15 20 25 30
D
Grating Position (m)
7
 Absorption: Proj    x, ydl
A
l

Ramp filter

f
Convolution kernel:

0 f

2d 
 DPC: Proj    x, ydl
DPC
p  l
2

Hilbert filter

p sgn( f )
2
Convolution kernel:
2d 2i
0 f
8
 

log I
e k
Absorption
Log.
Projections
2
Raw NPS  NPS
dpc 2 ab
Detector
Counts I
k
Phase DPC
I
 1
Retrieval Projections
I
0
  I sin(2k / K) 
tan1  k 
  
I cos(2k / K)
 
k
G.-H. Chen et. al, Med. Phys. (2010)
9
Absorption
Log.
Projections
Without
grating

1 2
NPS   NPS
dpc  2 ab
Phase DPC
Retrieval Projections
With
grating

10