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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
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