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.)