infm shaping x-rays by diffractive coded...

$: INFM Shaping x-rays by diffractive coded nano-opticsstaff.chess.cornell.edu/~shen/workshop2003/presentations/...X-ray Coherence Berkeley, CA, 22-23 August 2003 TASC INFM Shaping x-rays$
X-ray Coherence Berkeley, CA, 22-23 August 2003

TASC

INFMShaping x-rays by diffractive

coded nano-optics

INFM - TASC

For correspondence: Enzo Di FabrizioTASC-INFM @ Elettra Synchrotron Light Source, Lilit Beam-lineS.S.14 Km 163.5, Area Science Park, 34012 Basovizza - Trieste (Italy)Tel: +39-040-375-8417 Fax: +39-040-3758400E-mail: [email protected]

Enzo Di Fabrizio 1, Dan Cojoc 1,3, Stefano Cabrini 1,2, Burkhard Kaulich 2, Thomas Wilheim 4, Jean Susini 5

1 TASC-INFM @ ELETTRA Synchrotron Light Source,Trieste, Italy2 ELETTRA – Sincrotrone Trieste, Italy3 ‘Politehnica’ Univ. of Bucharest, Romania 4 RheinAhrCampus, Remangen, Germany5 European Synchrotron Radiation Facility, Grenoble, France


TASC

INFM

Differential Interference Contrast (DIC) for XRM: purpose and main ingrediends

Fabrication of ZP Doublets

DIC measurements with ZPs Doublet

DOE for shaping X-ray

DOE for DIC measurements

DIC with variable phase shift

Outlook and future experiments

Outline


TASC

INFM

Purpose for microscopy techniquesusing phase information

Amplitude and phase contrast for a model protein C94H139N24O31

Absorption contrast:

Phase contrast:

~E -3

~E -1

Use of phase shifting, real partof refractive index

• orders of magnitude higher contrast

• tremendous reduction of dose appliedto object

• additional transmission information onlow side of absorption edges (XANES,XRF !)


TASC

INFMGeneral statements on DIC microscopy

Phase objects can be seen with great difficulty when in focus withordinary XRM (single ZP)

Phase objects retard or advance light that passes through them due to spatialvariation in their refractive index and/or thickness

Needs for DIC microscopyThe image of DIC microscopes is formed from the interference of two mutually

coherent waves with lateral displacements (shear) (of the order of the minimumsize of the imaged structure and are phase-shifted relative to each other.

Imaging characteristics. The intensity distribution in measured DIC images is given by a non

linear function of the spatial gradient of a specimen’s optical path length distribution along the direction of shear


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INFMDifferential Interference Contrast DIC

Visible light microscopy(Nomarsky set-up)

Shear of wave front division or distance of Airydisks in focal plane is smaller thanoptical resolution (“differential”)

DIC for X-ray microscopy with ZPs:

• Distance ∆f of both ZPs smaller than depth of focus• Displacement ∆s smaller than resolution δ

∆s < δ

∆f < D.O.F.


TASC

INFM Differential Interference Contrast DIC

incident

ZP1 ZP2

substrateplane wave

detector0.

0. O1

O2

monochromaticx-rays

zone plate doublet

sample

detector planesubstrate

ZP1 ZP2

laterally displaced images

condenser

Working principle

TXM set-up


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INFM

Coherence considerations

Interference contrastInterference contrast XX--ray imaging using two zone ray imaging using two zone platesplates

Used setup: ∆y = 14 µm, D = 44 µm ∆s ≈ 0.01 µm, lcoh ≈ 1.5 µm

f -f1 2 f2

f12

2

221

21

2

2)(

)(2 fyff

ffys

⋅

⋅−=

−⋅∆

≈∆

Temporal coherence

∆s < coherence length lcoh

( ) yfffy ⋅

−=∆

2

21

Spatial coherence

∆y < coherently illuminated field D


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INFM Coherence considerations

Spatial coherence (Van Cittert-Zernike) Temporal coherence

D: Diameter of coherently illuminatedplane

d: Source diameterL: Distance to observation plane

D = 0.61 = 1.22 Lλd/2

fλδ

Then:If the separation(∆x) of the two

superimposed images is below the resolution limit (δ ) the two images

will interfere without further restrictions to the spatial coherence

of the source or, DIC works independent, of the spatial

coherence of the illumination

∆x < δ = 1.22 drNZP shift

lcoh = > N = ∆smaxλ2

2 ∆λλ2

lcoh : coherence length∆smax: path length differenceN: Number of zones

λ∆λ

> N ≈ Neff=(r+∆x)2

λf

Then:No precautions to the source

spectrum or other than for imaging with a single ZP

ZPs have to be treated to bein the same plane ( within theirdepth of focus) (N>100)


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INFM ZP doublet for X-ray microscopy in DIC mode

First ZP doublet generated by E. Di Fabrizio and S. Cabrini

Technique: e-beam lithography and nanostructuring

Diameter: 75 µmOutermost zone width: 200 nmFocal length @ 4 keV: 50 mm

Efficiency: 10 %

Nominal displacement: 100 nm

Membrane

ZP1

ZP2


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INFM Alignment markers definition

Double face resist deposition

E-beam exposure

Developement

Electroplating and resist removal

On double face base platedSi3N4 membrane ( 1µm) Resist

Base plating

Si3N4 membrane

e-beam

To obtain self-aligned markers Self-aligned markers


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INFMDouble side ZP definition

Resist deposition

E-beam exposure

Electroplating and resist removal

“Front” side exposure aligned

to markers“Back” side exposure in controlled misalignment

“Back” side process“Front” side process

E-beam E-beam


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INFM

DIC objective (Back side view)-May 2000-

Zone plate Objective

Alignment markers

SiN membrane

ZP front side


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INFM

ηtot = tZP1ηZP2 + tZP2ηZP1 =9.6%

Xray lithographic image of the ZP doublet

Efficiency of each zp=14%( first order)

Efficiency of zero order =35%

5 µm

Resolution test~ 160 nm


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INFMDIC X-ray microscopy

with a full-field imaging microscope @ 4 keV

10 mµ

(a) (b)

(c) (d)

2 µm thick PMMA test structureswith a transmission of 98.8 % @ 4 keV

Absorption DICPixel

Inte

nsity

/ a.

u.

Contrast increase:x20 - x30

B. Kaulich, T. Wilhein, E. Di Fabrizio, S. Cabrini, F. Romanato, M. Altissimo, J. Susini (Nov 2000)


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INFMPMMA zone plate structure (250 nm)

2 micron thick:exposure time 10s

5 µm

Bright field X-DIC transmission


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INFMGeneral scheme of DOE shaping


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INFM DOE’s design

Numerical computation:

given a set of input data find the optimum output data which fit therequests

input data :•Source space: wavelength, size, geometry, intensity distribution

•Image space: intensity or/and phase or/and polarization field distribution

•DOE: size, resolution, material

output data:•DOE’s phase or/and amplitude function


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INFM

zo

Diffracting features

Propagation directionh

δD

Diffracted field in the plane z = zo

z

OK ! SW

DPW

Input fieldWavelength

Proportional phase delay

PDE profile

Outputplane

DOE’s phase function:

ΦDOE (x) = 2π (n-1) h(x) / λ

Diffractive optical element scheme

λ3d f


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INFMScalar versus Vectorial diffraction based models

Scalar based models•ray traycing, spherical wave propagation + superposition

•phase retrieval iterative algorithms (PRIA)

•global optimization methods: genetic algorithms, simulated annealing

Vectorial based models• Finite element method (FEM)

• Boundary element method (BEM)

• Method of moments (MOM)

• Finite-difference method (FDM)

• Finite-difference time-domain (FDTD)


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INFMSpherical wave approximation

Ns point sources

P1

PNs

P1

P2

Pg

PNg

DOE plane Image space

Source space

Array of Ng spots

xiyi

z


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INFM Comparison of the iterative algorithms

CEAAAAERA

SNR = - 10 log (MSE) MSE : Mean Square Error

[dB]

Intensity distribution

Phase DOE

CEA : Combined Error AlgorithmAAA : Adaptive Additive Algorithm

ERA: Error Reduction Algorithm


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INFM

a b c

Development of multi-spot X-ray DOE

Optical scheme and calculated layout

of 3 DOE’s that generate 2 and 4 spots

(a-b) on the same focal plane, and 2

spots along the same optical axis(c)

(d)Full beamshaping

The calculations are referred to a photon energy of 4 KeV and 5 cm focal length

a

b

c

monochromatic planewave illumination

OK !d


TASC

INFM Development of multi-spot X-ray DOE

DIC visible light micrographof 4-spot ZP

Calculated pattern of a 4 spot ZP

DOE size 0.1 x 0.1 mm2, pixel size: 100 nm, energy 4 keV designed and generated by the Lilit beamline group (2001)


TASC

INFMSEM pictures showing an overview of the DOE ( DOE area is 100x 100 µm2)

and details of the outermost area whose resolution is below 100 nm

Development of multi-spot X-Ray DOE


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INFM

Undulator

Double crystalmonochromator

2 spot DOEOSA

Rasterscanner

Off-axisphotodiode withaperture

(1,0)CS

Scanning X-ray microscope at ID21 beamline, ESRF

A S i p h o to d io d e w ith a 5 0 µ m ap e rtu re in fro n t w asp laced o n o n e f lan k o f an in te rfe ren ce frin g e in o rd e r tob e h ig h ly sen s itiv e to sh if ts o f th e frin g es re la ted too p tica l p a th d iffe ren ces in tro d u ced b y th e ra s te rscan n ed sp ec im en .


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INFM 2 spot DOE on SXTM at 4 KeV (February 2001)

2 µm thick PMMA test structureswith a transmission of 99 % @ 4 keV

Image taken with the scanningX-ray microscope at the ID21beamline, ESRF

Dwell time: 40ms / pxwith 200 x 200 px

Image contrast: 25% in DIC

1.10

1.05

1.00

0.95

0.90Inte

nsity

/ a.

u.

120100806040200Position / µm


TASC

INFMScanning transmission X-ray microscopy

in DIC mode using a 2-spot ZP

200 x 200 px40 ms/px dwell

2 µm thickgrating structuresin PMMA

4 keV

Brightfield (BF) DIC1.15

1.10

1.05

1.00

0.95

0.90

0.85

Inte

nsity

/ a.

u.

50403020100Position / µm

1.15

1.10

1.05

1.00

0.95

0.90

Inte

nsity

/a.u

.

806040200Position / µm

2 µm

Contrast:

BF: 1 %DIC: 25 %


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INFM

Air Pollution SiO2 fiber Filter(Trieste)2 spot DIC&XRF measurements (July 2002)

Absorption contrast Diff. Interf. contrast

7.2 KeV X-ray 4 KeV X-ray

Cr XRF map Fe XRF mapCa XRF map K XRF map


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INFM Optical setup of DIC full field microscope


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INFM PMMA test structures (June 2001)test structures(a=squares, b=toroids) 1 µm thick with a transmission of 99.99 % @ 4

keV

Objective lens : ZP

2 confocalspots DOE

4 confocalspots DOE

2 coaxial spots DOE

10 µm

10 µm

a

b


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INFM Yeast cells: imaging in TXM at 4 keVby using diffractive optics

5 µm


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INFMComplete X-ray- beam shaping

Optical setup of DIC full field microscope

a


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INFMComplete X-ray- beam shaping (June 2001)

b

b - SEM image of the fabricated OK! DOE c - The intermediate image formed by the DOE at the focal plane located at 50 mm is magnified 150 times on a CCD detector by a ZP that acts as an objective lens

5 µm

10 µm

c


TASC

INFM DIC Image formation with coherent illumination

Transmission function of the phase object

Ideal PSF from ray-tracing (geometrical optics)

=Shear in x direction

=constant phase bias

C. Preza et. al. J. Opt. Soc. Soc. Am. A/Vol. 16, No. 9. 1999


TASC

INFM Field Intensity in the DIC image

If the shear very small (differential) comapared to the size of the detailsof the specimen (or the resolution of the ZP) ==> the phase difference can be written as a phase gradient:

With DOE is possible to control the contrast through the bias ∆Θ


TASC

INFM Bias retardation in DIC

pixelspixels

Intensity(a.u.)

Phase(radians)

∆+

∂∂

∆= θφxyxxayxi ),(sin),( 2

(a) The phase function of a one dimensional object described in 250 pixels; (b) Intensity distributions obtained with the same shear ∆x= 2 but different bias values:

∆θ = 0 - first line, ∆θ = π/4 - second line, and ∆θ = 3π/4 - third line; the signals are offset by 2 a.u. for a clear representation


TASC

INFM To calculate the phase function ΦPDE, we assume that the lightsource which illuminates the PDE and the intensity distributionproduced by the PDE can be described by point sources generatingspherical waves

ΦPDE= {arg[Wout] - arg[Win]}2π

Ns point sources

array of Ng spots

P1

PNs

P1

P2

Pg

PNg

PDE (Phase Diffractive Element)

WinWout

Win(out)= ∑s(g) as(g) exp[j(krs(g)+φ s(g))]/ rs(g)

Spherical wave propagation approach


TASC

INFM

DOEs producing the same beam shearing (1 mm) but different bias: a) no bias, b) bias = π at 1 m from the DOE (DOE size= 2 cm, described in 480 pixels)


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INFMThe intensity distribution obtained in the focal plane(∆x=1 mm λ=532 nm DOE made by Hamamatsu SLM)


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INFM

Phase distributions obtained in the focal plane of the DOE. For the 3D graphics(a,b) the phase is represented in radians on the z axis, the distances represented on x and y axes being expressed in microns. The phase distributions along the lines indicated in a) and b) are represented in the second line c) and d) clearly showingthe presence of the π bias

a) b)

c) d)

X

y

x

y


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INFMThe interference patterns obtained after the focal plane of the DOEs implemented on the phase SLM Hamamatsu; the left pattern corresponding to the DOE without bias is shifted with half of a fringe with respect to the right pattern which corresponds to the DOE with bias π


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INFM Complete set of objectives and condenser lens fabricatedBy e-beam lithography

2 spots at 6.5 KeV 50 nm res.

2 spots at 2.5 KeV 50 nm res.

Top hat condenser at 4 KeV 150 and 200 nm res.

Work in progress


TASC

INFM ∆Θ=0 ∆Θ=π/2

∆Θ= π ∆Θ= 2π/3

DOE for Bias control


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INFMc

10 µm

Further DOE already fabricated to be tested

• Top Hat for TXM microscope (to replace the conderser lens)

•New annular distribution forDIC microscopy

•Sub micron Intensity patternfor maskless lithography andCVD induced by X-rays


TASC

INFM50 nm smaller pixel size with 30 nm details

30 nm

50 nm


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INFM Outlook and future investigations

Two different DIC techniques using ZP doublet and X-Ray DOE

Spatial resolution according to the design

Technique has no limitation in spectral range as far as ZPs can be applied

Full beam shaping achieved at X-ray wavelength

Future investigations:

Extension of experiments to soft and harder X-rays

Resolution limit toward state-of-art- fabrication technique

Theoretical investigations and simulations (transfer function)

Combination with spectro-microscopy for biological samples


TASC

INFM Acknowledgements

L. Vaccari, M. Altissimo, L. Businaro, P. Candeloro

TASC-INFM at ELETTRA, LILIT, Italy

O. Dhez, B. Fayard, U. Neuhaeusler, M. Salome, R. Baker

ESRF, ID21, Grenoble, France

F. Polack, D. Joyeux,

Lure Universite Paris-Sud & IOTA, Orsay, France

F. Perennes, A. Barinov, M. Kiskinova

Sincrotrone Trieste SCpA – ELETTRA, Italy

infm shaping x-rays by diffractive coded...

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