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2. Focusing

Date post: 18-Jan-2016
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2. Focusing. Microscopy Object placed close to secondary source: => strong magnification The smaller the focus, the sharper the image!. Spectroscopy, tomography large depth of field scanning beam over sample (diffraction, SAXS, XAS, fluorescence…). Small focus requires - PowerPoint PPT Presentation
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1 2. Focusing Microscopy Object placed close to secondary source: => strong magnification The smaller the focus, the sharper the image! Spectroscopy, tomography large depth of field scanning beam over sample (diffraction, SAXS, XAS,
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Page 1: 2. Focusing

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2. Focusing

MicroscopyObject placed close tosecondary source:=> strong magnification

The smaller the focus,the sharper the image!

Spectroscopy, tomography large depth of field scanning beam over sample (diffraction, SAXS, XAS, fluorescence…)

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Small focus requires

1. small source

2. long distance L1 source-lens

3. small focal length and large effective aperture of lens

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-1.0 -0.5 0.0 0.5 1.00

200000

400000

600000

0.55 mm

39 CRLs no CRLs

Inte

nsity

Vertical position

15 m

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.00

20000

40000

60000

80000

100000

1.57 mm

39 CRLs no CRLs

Inte

nsity

Horizontall position

239 m

a. FOCUSING with

rotationally parabolic Be lenses ( R = 1500µm)

Image of the ID18 source at ESRF 14.4125eV 39 Be lenses R = 1500µm

f = 11.718m geometric aperture: 2.5mm

(A. Chumakov ESRF)

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Intensity profile in the horizontal: ID18

well fitted by a Gaussian with 239 µm FWHM

(very low background in the wings)

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b. Focusing with Be lens at energies as low as 2keV

ID12 at ESRF (A. Rogalev)

gain in intensity on sample at 2 keV:

factor 500 compared to situation without lens!

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c. Prefocusing with linear lenses Be, Al and Ni

R = 200 to 1000µm, length 2.5 mm

* collecting more intensity

* for making spot on sample more circular (on storage rings)

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SEM image of linear Be lens (R=500µm)

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Focusing with 2 independent linear lenses in cross-geometry

• Ratio of horizontal to vertical source size in storage rings: 20 and more =>elongated spot on sample

• Generation of more circular spot size by astigmatic imaging of source via 2 independent linear lenses in cross geometry

• Example: experiment at DIAMOND Light Source by A. Snigirev et al with 1D Be from RXOPTICS

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B16

Si-111

12 keVHR X-ray CCD

4 m

44 m from source

1D Be Vert 1D Be Hor

1.4 m

7.5 m

7.5

m

Astigmatic focusing with 2 crossed, linear Be lenses

Vertical Horizontal Crossed N=17 R=300µm N=17 R=200µm gain: 1200 L2 ~ 4m N=15 R=300µm L2 ~ 1.4m

Page 10: 2. Focusing

Vertical focusing:Be CRLN = 17, R = 300 mL2 = ~ 4 m

Horizontal focusing:Be CRLN = 17 R = 200 mN = 15 R = 300 mL2 = ~ 1.4 m

Gain = 1200

Porous Si; 2.5 m pitchIn front of horizontal CRL

Astigmatic-Cross focusing with 2 linear Be CRLs

1D and 2D Fourier transform

Profile: vertical horizontal 7.5 µm FWHM 7.5 µm FWHM

Astigmatic focusing with 2 crossed, linear Be lenses

I & A Snigirev, I. Dolbnya, K. SawhneyCollaboration with Optics Group at DIAMOND

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3. Coherent flux

* diffraction of individual large molecules, nanoparticles

* speckle spectroscopy

Illuminated area on sample must be smaller than the lateral coherence area at the sample position. Then all monochromatic photons are undistinguishable, i.e. they are in the same mode!

* coherent photon flux is a property of the brillance B of the source and of the degree of monochromaticity

2cF B

* the coherent flux can at best be conserved, it cannot be increased by a focusing optic.

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Example: ID13 at ESRF

Be lens: R = 50µm, N = 162, f = 205.9mm, Deff = 295µm, dtr = 42nm

L1 = 100m, L2 = 206.3mm

geometric image of source 2

1

LS S

L

FWHM S (µm)

S‘ geom (nm)

S‘ incl diffr (nm)

horizontal 120 248 251

vertical 20 41 59

diffraction limited in the vertical !

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Example: low-betha undulator at ESRF

1. Be lenses, 17 keV, N = 162, f = 205.9mm, dtr = 42nm

L1 = 100 m, L2 = 0.2063 m

2.

Source size FWHM

Geometric image FWHM

horizontal 120µm 248 nm

vertical 20µm 41nm

Image is diffraction limited in the vertical: => coherent illumination in the vertical

Not so in the horizontal!

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3. remedy for horizontal direction

* insert a linear lens (prefocussing lens) which focuses only in the horizontal

* the secondary source S‘ must have a lateral coherence length at the postion of lens 2 which is equal to the effective aperture of lens2.

S S‘

Prefocusing lens Lens 2

50m 50m

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Prefocusing lens

Be linear: R = 500µm, N = 55, f = 3.854m, Deff = 1048µm

Image S‘ at b1 = 4.168m behind horizontal lens

lateral (horizontal) coherence length at position of lens 2: 295µm

this is equal to Deff of lens 2: only the coherent flux passes through lens 2, the rest is peeled off.

gain in flux (compared to no prefocusing): about factor 10.

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Coherent Imaging (Ptychography)

(see talk by F. Seiboth, C. Schroer)

* illuminate sample coherently in a small spot by means of Be-lenses

* Scan this microfocus over sample with overlaping neighboring scans

* take a diffraction image on each position

* overlap of images allows for reconstruction of the object when each spot is illuminated coherently

Our Be lenses preserve coherence well enough to give a resolution which is 10 times better than the spot size!

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MANY THANKS

To

my former students,

Anatoly and Irina Snigirev from ESRF

Christian Schroer and collaborators from TU Dresden

for many years of efficient and pleasant collaboration


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