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…)
1
Small focus requires
1. small source
2. long distance L1 source-lens
3. small focal length and large effective aperture of lens
2
a. FOCUSING with
rotationally parabolic
Be lenses
( R = 1500µm)
Image of the ID18
source at ESRF
Intensity
600000
39 CRLs
no CRLs
400000
15 m
200000
14.4125eV
39 Be lenses
R = 1500µm
0.55 mm
0
-1.0
-0.5
0.0
0.5
Vertical position
100000
39 CRLs
no CRLs
80000
(A. Chumakov ESRF)
60000
Intensity
f = 11.718m
geometric aperture:
2.5mm
1.0
239 m
40000
20000
1.57 mm
0
-2.0
-1.5
-1.0
-0.5
0.0
0.5
Horizontall position
1.0
1.5
2.0
3
Intensity profile in the horizontal: ID18
well fitted by a Gaussian with 239 µm FWHM
(very low background in the wings)
4
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!
5
c. Prefocusing with linear lenses
R = 200 to 1000µm,
Be, Al and Ni
length 2.5 mm
* collecting more intensity
* for making spot on sample more circular (on storage rings)
6
SEM image of linear Be lens (R=500µm)
7
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
8
Astigmatic focusing with 2 crossed, linear Be lenses
HR X-ray
CCD
12 keV
Si-111
1D Be Vert
1D Be Hor
B16
4m
1.4 m
44 m from
source
7.5 m
7.5 m
Vertical
N=17 R=300µm
L2 ~ 4m
Horizontal
N=17 R=200µm
N=15 R=300µm
L2 ~ 1.4m
Crossed
gain: 1200
9
Astigmatic-Cross focusing with 2 linear Be CRLs
Astigmatic focusing with 2 crossed, linear Be lenses
I & A Snigirev, I. Dolbnya, K. Sawhney
Collaboration with Optics Group at DIAMOND
Profile:
7.5 µm
Vertical focusing:
Be CRL
N = 17, R = 300 m
L2 = ~ 4 m
Intensity, arb. un.
FWHM
Horizontal focusing:
Be CRL
N = 17
R = 200 m
N = 15
R = 300 m
L2 = ~ 1.4 m 30000
25000
Gain = 1200
1D and 2D Fourier transform
15000
10000
20000
15000
10000
5000
5000
0
0
0
Porous
7.5 µm FWHM
horizontal focusing
vertical focusing
25000
20000
horizontal
Intensity, arb. un.
30000
vertical
Si;
2.5 m pitch
Distance, microns
In front of horizontal CRL
10
20
30
40
10
20
30
Distance, microns
40
50
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


* the coherent flux can at best be conserved, it cannot be
increased by a focusing optic.
Fc  B 2
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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
S  S
L2
L1
S‘ geom
(nm)
S‘ incl diffr
(nm)
FWHM
S
(µm)
horizontal
120
248
251
vertical
20
41
59
diffraction limited in the vertical !
12
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.
horizontal
Source size
FWHM
120µm
vertical
20µm
Geometric image
FWHM
248 nm
41nm
Image is diffraction limited in the vertical:
=> coherent illumination in the vertical
Not so in the horizontal!
13
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
50m
Lens 2
50m
14
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.
15
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!
16
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
17