Tim
m W
eitkam
p,
Ana D
iaz,C
hristian D
avid
Labora
tory
for
Mic
ro-
and N
anote
chnolo
gy,
Paul S
cherr
er
Institu
t, V
illig
en, S
witzerland
Oliv
er
Bunk, A
mela
Gro
so,
Marc
oS
tam
panoni, F
ranz
Pfe
iffe
rS
wis
s L
ight S
ourc
e,P
aul S
cherr
er
Institu
t, V
illig
en, S
witzerland
Pete
rC
loete
ns,
Eric Z
iegle
rE
uro
pean S
ynchro
tron R
adia
tion
Facili
ty,
Gre
noble
, F
rance
Cohere
nce 2
005 W
ork
shop, P
orq
uero
lles, 15 J
une 2
005
X-r
ay p
hase im
agin
g w
ith g
rating inte
rfero
mete
rs
See c
opyright notice a
nd term
s o
f use o
n n
ext slid
e
Co
pyri
ght notice a
nd t
erm
s o
f use
The m
ate
rial in
this
file
is c
op
yrighte
d.
You m
ay
do
wn
load a
nd v
iew
the f
ile f
rom
its
we
b r
ep
ository
, but
ple
ase
•do n
ot
redis
trib
ute
this
file
or
an
y part
of
it o
r its c
onte
nts
in a
ny
form
,•
do n
ot
use a
ny o
f th
e c
onte
nts
of
this
file
in p
resenta
tions o
r public
atio
ns
without
pri
or
wri
tte
n c
onse
nt
of
the a
uth
ors
.
Thank y
ou.
Auth
ors
can b
e r
eached a
t th
e f
ollo
win
g a
ddre
sses:
Tim
mW
eitkam
p,
ES
RF
, 6 r
ue J
ule
s H
oro
witz,
38043 G
reno
ble
, F
rance
E-m
ail
tim
m.w
eitkam
p@
psi.ch,
we
itkam
p@
esrf
.fr
Christia
n D
avid
, P
aul S
cherr
er
Institu
t, 5
232 V
illig
en
PS
I, S
witzerla
nd
E-m
ail
christia
n.d
avid
@psi.ch
11 J
uly
20
05
Motivation
•H
ard
X r
ays
well
suite
dfo
rra
dio
gra
ph
ic im
agin
g(lon
g p
en
etr
ation
de
pth
, neglig
ible
refr
action
)
•G
enera
l se
tup u
ses a
bso
rpti
on
co
ntr
ast:
Are
a d
ete
cto
r behin
d s
am
ple
reco
rds inte
nsity v
ariations
cause
d b
y a
ttenuatio
n p
rofile
of th
e s
am
ple
•T
om
og
rap
hy:
takin
g 2
D r
ad
iogra
phs a
t diffe
rent
vie
win
g
ang
les y
ield
s 3
D d
istr
ibutio
n µ
(x,y
,z)
•B
ut fo
r lig
ht
mate
rials
(bio
log
ical tissue,
poly
mers
...)
, and
hig
h p
ho
ton
en
erg
ies,
ab
so
rpti
on
co
ntr
ast
is r
ela
tively
w
eak
•B
ett
er
image c
ontr
ast w
ould
resu
lt in
–S
ho
rter
exp
osu
re t
imes
(mate
rials
scie
nce a
pplic
ations)
–R
ed
uced
do
se d
ep
osit
ion
(bio
logy, m
edic
al im
agin
g)
Phase r
adio
gra
phy m
eth
ods
Cry
sta
l in
terf
ero
mete
rsB
onse
& H
art
19
65
Fre
e-s
pace p
ropagation
(“In
line p
hase c
ontr
ast”
)S
nig
irev
1995, W
ilkin
s 1
995, C
loete
ns
1996
Analy
zer-
cry
sta
l based
(“diffr
action-e
nhanced
imagin
g”,
DE
I)In
gal&
Belia
evska
ya
1995
D
�Lots
of diffe
rent
schem
es a
lre
ady
Why y
et ano
ther
meth
od?
•F
or
the c
om
bin
ation o
f...
–la
rge
fie
ld o
f vie
w(m
od
era
te r
eso
lutio
n),
–p
ossib
ility
of
use
with
an
X-r
ay t
ub
eso
urc
e,
•... th
e e
xis
ting m
eth
ods h
ave p
roble
ms:
–B
on
se
-Ha
rt:
cry
sta
l siz
e lim
its F
OV
–D
EI:
mo
no
ch
rom
aticity, co
llim
atio
n �
ne
ed
s S
R
–F
SP
: e
xce
llen
t fo
r h
igh
re
so
lutio
n,
bu
t a
t m
od
era
te r
eso
lutio
n,
larg
e d
ista
nce
s r
eq
uir
ed
•G
rating inte
rfero
mete
r:m
ay fill
this
dom
ain
d
beam
-split
ter
phase
gra
ting
inte
rfe
rence
patt
ern
s
•P
hase g
rating
as a
beam
split
ter
•W
avele
ngth�
1 �
, gra
ting p
eriod �
1 µ
m�
sm
all
diffr
action a
ng
les
�beam
s o
verl
ap
Ho
w c
an w
e d
ete
ct
the
local fr
inge p
ositio
n?
Gra
tin
g in
terf
ero
me
try
ca
mera
beam
-split
ter
phase
gra
ting
analy
zer
am
plit
ude
gra
ting
inte
rfe
rence
patt
ern
•A
bsorp
tio
n g
rating
with
sam
eperio
das f
ring
es
•A
cts
as t
ransm
issio
nm
ask
(not
as d
iffr
active
ele
ment!
)•
Tra
nsfo
rms
frin
ge
positio
ns
into
inte
nsity
sig
nal
�M
ay
use
dete
cto
rw
ith
pix
els
larg
er
than
frin
ge
wid
th
Gra
tin
g in
terf
ero
me
try
ca
mera
beam
-split
ter
phase
gra
ting
analy
zer
am
plit
ude
gra
ting
inte
rfe
rence
patt
ern
phase
obje
ct �
Diffe
rentia
lph
ase
contr
ast
imagin
gB
ut
how
to s
epara
te p
hase info
rmation f
rom
absorp
tion?
-O
bje
ct
in b
ea
m-
Dis
tort
sw
ave
front,
i.e
., d
eflects
beam
-F
ringes
loca
llydis
pla
ced
-D
iffe
rent
inte
nsity
on d
ete
cto
r-
Inte
nsity
corr
ela
ted
to f
irst
derivative
of
wa
vefr
ont
phase
Gra
tin
g in
terf
ero
me
try
(sam
ple
here
:poly
sty
ren
esp
here
sØ
100 a
nd 2
00
µm
)
Sam
ple
Beam
split
terA
naly
zer
scan
ned
Dete
cto
r
ES
RF
BM
5,
E=
12.4
keV
, p
1=
4 µ
m,
p2=
2.0
04 µ
m
Phase
-ste
ppin
gin
terf
ero
metr
yLin
ear
transvers
e s
can
of
one o
f th
e g
ratings:
�sig
nal oscill
ate
s
Phase
-ste
ppin
gin
terf
ero
metr
y
Phase
-ste
ppin
gin
terf
ero
metr
yC
onsid
er
indiv
idual
pix
els
:In
tensity
oscill
ate
s
Phase
-ste
ppin
gin
terf
ero
metr
y
�1�
2
a2
a1
aij
�P
rocessed
images:
�ij
Phase
-ste
ppin
gin
terf
ero
metr
y
�ij
Ph
ase g
rad
ien
tim
ag
e(p
erp
endic
ula
rto
gra
ting
lines)
---
all
absorp
tio
ncontr
ibutions
elim
inate
d
Can
be
inte
gra
ted
to y
ield
pro
jecte
dp
hase
shift
of
sam
ple
aij
�S
uited
for
tom
ogra
phic
reco
nstr
uction
�Q
uantita
tive:
(suited
for
tom
ogra
phic
reco
nstr
uction)
Mix
ture
of
absorp
tion
and in
line
phase
contr
ast
---
the
sam
eim
ag
e t
hat
wo
uld
be
ob
serv
ed
wit
ho
ut
the
inte
rfero
mete
rin
th
eb
eam
),
()
,(
2y
xdp
x
yx
ϕλ
=∂
Φ∂
Phase
-ste
ppin
g t
om
ogra
phy
Sam
ple
Beam
split
ter
Dete
cto
r
Fast axis
:phase s
teppin
gS
low
axis
:to
mo
rota
tion
Analy
zer
•T
wo s
can a
xes:
pro
jection a
ng
leand inte
rfero
mete
r phase
•N
um
ber
of pro
jection
angle
s:
100…
10
00
•N
um
ber
of phase-s
tepp
ing p
oin
tsper
angle
: 4 o
r m
ore
•R
esu
lts:
3D
dis
trib
utions �
(x,y
,z)
and µ
(x,y
,z)
ES
RF
ID
19, Jun
e 2
004
E=
12.4
keV
, p
1=
4 µ
m,
p2=
2 µ
m,
d=
23 m
m
Beam
split
ter
phase
gra
ting
(p=
4 µ
m)
and a
naly
zer
absorp
tion
gra
ting
(p=
2 µ
m)
4 µ
m4 µ
m4 µ
m
Phase g
rating
(Si)
Absorp
tion g
rating
(Au in S
i)
•S
ilicon w
et-
etc
hed
•D
epth
of str
uctu
res c
hosen s
o that
phase s
hift is
��
no z
ero
ord
er
•�
Effic
iency lim
it: 80 %
(fra
ction o
f usefu
l photo
ns)
•G
old
in g
aps o
f sili
con g
rating
•G
row
n e
lectr
ochem
ically
•P
eriod is h
alf that of S
igra
ting
•E
ffic
iency lim
it: 50 %
(fra
ction o
f tr
ansm
itte
d inte
nsity)
�P
oste
r P
9, A
. D
iaz e
t al.
1m
m0.5
mm
Tom
ogra
phy o
f a s
pid
er:
Isosurf
ace
renderi
ng o
f X
-ray r
efr
active in
de
x
1m
m0.5
mm
Tom
ogra
phy o
f a s
pid
er:
De
nsity-p
roje
ctio
n r
enderi
ng o
f X
-ray r
efr
active ind
ex
Non-i
nte
rfero
metr
icpro
jection
Non-i
nte
rfero
metr
icto
mogra
mIn
terf
ero
metr
icphase t
om
ogra
m
Inte
rfero
metr
icphase p
roje
ctio
n
0.5
mm
0.5
mm
0.5
mm
0.5
mm
Qua
ntita
tive p
hase r
econstr
uction I
Exa
mp
le:
ph
ase
pro
file
of
pa
rab
olic
re
fra
ctive
len
se
s
R
Bery
llium
refr
active lens,
R=
0.2
mm
�f=
61 m
at 14.4
keV
Be
ES
RF
BM
5,
9 J
une 2
005
Positio
n (
mm
)
Position (mm) Phase (�)P
hase (�
)
Colla
bora
tion w
ith J
. P
ato
mm
el, B
. Lengele
r(R
WT
H),
C. S
chro
er
(HA
SY
LA
B)
Qua
ntita
tive p
hase r
econstr
uction I
Qua
ntita
tive p
hase r
econstr
uction I
I:
pin
k-b
ea
m t
om
ogra
phy
Inte
rfero
metr
icphase t
om
ogra
mN
on-i
nte
rfero
metr
icto
mogra
m
Thre
efibers
•P
oly
am
ide Ø
225 µ
m•
Boro
n Ø
200 µ
m,
core
: W
Ø 1
0 µ
m•
PB
T Ø
190 µ
m
Sam
ple
:
SLS
Mate
rials
Scie
nce b
eam
line
July
200
4
E=
17.5
keV
,�
E=
1 k
eV
Poly
chro
matic
radia
tion
ca
mera
beam
-split
ter
phase
gra
ting
analy
zer
am
plit
ude
gra
ting
inte
rfe
rence
patt
ern
phase
obje
ct
� 1� 2
�Q
uasi-a
chro
matic
instr
um
ent
Lim
its o
f achro
maticity
•In
ter-
gra
ting d
ista
nce:
devia
tes fro
mT
alb
ot conditio
n,
•B
eam
split
ter:
phase s
hift
devia
tes fro
m �
,
•A
naly
zer:
changes
absorp
tion.
Effects
of energ
y c
hange (
aw
ay fro
m d
esig
n e
nerg
y)
on e
ffic
iency o
f a g
iven s
etu
p:
Measure
ment
(moiré f
ring
es)
Fit t
o t
heory
Desig
nenerg
y:
14.4
keV
(Gra
ting p
eri
od
s p
1=
4 µ
m, p
2=
2 m
, 3
rdT
alb
ot dis
tance d
3=
69
.7 m
m)
Data
taken a
t E
SR
F B
M5,
11 J
une 2
00
5
FW
HM
:
> 2
keV
Effic
iency v
s. energ
y
Bio
logic
al tissue s
am
ple
sin
aqu
eous e
nviron
ment
•C
on
ditio
ns s
imila
r to
na
tura
l e
nvir
on
me
nt,
i.e
., to
in-v
ivo
im
ag
ing
•C
on
tra
st
be
twe
en
tis
su
e a
nd
wa
ter
is v
ery
we
ak,
i.e
., a
re
al ch
alle
ng
e
•L
arg
e o
bje
ct,
mo
de
rate
re
so
lutio
n e
no
ug
h�
test ca
se
•O
ur
firs
t sa
mp
le:
the
he
art
of
a r
at, in
fo
rma
lin
Rat
heart
in f
orm
alin
-W
alls
of
vessels
cle
arl
y vis
ible
in t
he p
hase-c
ontr
ast
image
-…
but
not
in the a
bsorp
tion im
age
acquired w
ith t
he s
am
e d
ose
Absorp
tio
n im
age
3 m
m
Pix
el siz
e 1
4 µ
mIm
age s
titc
hed f
rom
5x4 d
ete
cto
r fr
am
es
SLS
beam
line
4S
, 29 J
an 2
00
5
Sam
ple
by T
. K
han,
Univ
. ho
spital Z
ürich
Rat
heart
in f
orm
alin
Phase-g
radie
nt
image
3 m
m
-W
alls
of
vessels
cle
arl
y vis
ible
in t
he p
hase-c
ontr
ast
image
-…
but
not
in the a
bsorp
tion im
age
acquired w
ith t
he s
am
e d
ose
-F
ield
of
vie
w h
ere
on
ly lim
ite
d b
ysynchro
tro
n b
eam
siz
e--
-not
by
the inte
rfero
mete
r
Pix
el siz
e 1
4 µ
mIm
age s
titc
hed f
rom
5x4 d
ete
cto
r fr
am
es
SLS
beam
line
4S
, 29 J
an 2
00
5
Sam
ple
by T
. K
han,
Univ
. ho
spital Z
ürich
X-r
ay tube?
•P
roble
m: cohere
nt flux
•H
ave to u
se m
icro
focus
sourc
eor
slit
a u
sual sourc
e d
ow
n
•N
o b
etter
solu
tion?
(i.e
., h
igher
flux)
–w
e d
on’t n
eed the h
igh
resolu
tion o
f a m
icro
focus
•M
aybe u
sin
g …
anoth
er
gra
ting?
Arr
ayed s
ourc
e
s
Ld
p0
p1
p2
Tra
de r
esolu
tion f
or
flu
x,
keep
ing c
ohere
nce
•F
ringe p
attern
s fro
m the d
iffe
rent virtu
al sourc
es s
uperim
pose
incohere
ntly, but constr
uctively
.•
Spatial re
solu
tion d
egra
des to (
s d
/ L
).•
But flux is incre
ased b
y a
facto
r of N
.
Nslit
s(v
irtu
al
sourc
es)
C. D
avid
, F
. P
feiffe
r, T
. W
eitkam
p,
pate
nt
pendin
g
X-r
ay t
ube r
esults
Sum
mary
•G
ratin
g in
terf
ero
me
ter
giv
es d
iffe
ren
tia
l p
ha
se
con
tra
st
(d�
/dx)
•P
ha
se
ste
pp
ing
se
pa
rate
s a
bso
rptio
n f
rom
ph
ase
, yie
ldin
g b
oth
p
ha
se
�a
nd
tra
nsm
issio
n s
ign
al
•P
ha
se
-ste
pp
ing
to
mo
gra
ph
yyie
lds r
efr
active
in
de
x �
(x,y
,z)
•R
esu
lts a
re q
ua
ntita
tive
•In
str
um
en
t is
la
rge
ly a
ch
rom
atic
•S
tab
le,
rob
ust,
alm
ost
no
alig
nm
en
t
•B
ett
er
co
ntr
ast
tha
n in
ab
so
rptio
n im
ag
ing
with
th
e s
am
e d
ose
•W
ith
an
arr
aye
d s
ou
rce
, e
ffic
ien
t u
se w
ith
X-r
ay t
ub
e
•C
an
be
sca
led
up
to h
igh
er
en
erg
ies a
nd
la
rge
r fie
lds o
f vie
w
�S
uita
ble
fo
r ra
dio
gra
ph
y a
nd
to
mo
gra
ph
y a
pp
lica
tio
ns w
ith
larg
e f
ield
s o
f vie
w,
mo
de
rate
re
so
lutio
nP
oste
rs:
•W
avefr
on
tsensin
g w
ith m
oiré inte
rfe
rom
etr
y(P
8,
Christian D
avid
et al.)
•F
abrication o
f g
ratings (
P9, A
na D
iaz e
t al.)
•C
ohere
nce c
hara
cte
rization (
P44, F
ranz P
feiffe
r et al.)
