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# -*- coding: utf-8 -*-
r"""
.. _SoftiMAX:
SoftiMAX at MAX IV
------------------
The images below are produced by scripts in
``\examples\withRaycing\14_SoftiMAX``.
The beamline will have two branches:
- STXM (Scanning Transmission X-ray Microscopy) and
- CXI (Coherent X-ray Imaging),
see the scheme provided by K. Thånell.
.. imagezoom:: _images/softiMAX_layout.*
STXM branch
~~~~~~~~~~~
.. rubric:: Rays vs. hybrid
The propagation through the first optical elements – from undulator to front
end (FE) slit, to M1, to M2 and to plane grating (PG) – is done with rays:
+------------+------------+------------+------------+
| FE | M1 | M2 | PG |
+============+============+============+============+
| |st_rFE| | |st_rM1| | |st_rM2| | |st_rPG| |
+------------+------------+------------+------------+
.. |st_rFE| imagezoom:: _images/stxm-2D-1-rays-0emit-0enSpread-monoE-00-FE.*
.. |st_rM1| imagezoom:: _images/stxm-2D-1-rays-0emit-0enSpread-monoE-01-M1local.*
.. |st_rM2| imagezoom:: _images/stxm-2D-1-rays-0emit-0enSpread-monoE-02-M2local.*
.. |st_rPG| imagezoom:: _images/stxm-2D-1-rays-0emit-0enSpread-monoE-02a-PGlocal.*
:loc: upper-right-corner
Starting from PG – to M3, to exit slit, to Fresnel zone plate (FZP) and to
variously positioned sample screen – the propagation is done by rays or waves,
as compared below. Despite the M3 footprint looks not perfect (not black at
periphery), the field at normal surfaces (exit slit, FZP (not shown) and sample
screen) is of perfect quality. At the best focus, rays and waves result in a
similar image. Notice a micron-sized depth of focus.
+-----------+---------------------+---------------------+
| | rays | wave |
+===========+=====================+=====================+
| M3 | |st_rM3| | |st_hM3| |
+-----------+---------------------+---------------------+
| exit slit | |st_rES| | |st_hES| |
+-----------+---------------------+---------------------+
| sample | |st_rS| | |st_hS| |
+-----------+---------------------+---------------------+
.. |st_rM3| imagezoom:: _images/stxm-2D-1-rays-0emit-0enSpread-monoE-03-M3local.*
.. |st_hM3| imagezoom:: _images/stxm-2D-2-hybr-0emit-0enSpread-monoE-03-M3local.*
:loc: upper-right-corner
.. |st_rES| imagezoom:: _images/stxm-2D-1-rays-0emit-0enSpread-monoE-04-ExitSlit.*
.. |st_hES| imagezoom:: _images/stxm-2D-2-hybr-0emit-0enSpread-monoE-04-ExitSlit.*
:loc: upper-right-corner
.. |st_rS| animation:: _images/stxm-2D-1-rays-0emit-0enSpread-monoE-06i-ExpFocus-Is
.. |st_hS| imagezoom:: _images/stxm-2D-2-hybr-0emit-0enSpread-monoE-06i-ExpFocus-Is
:loc: upper-right-corner
.. rubric:: Influence of emittance
Non-zero emittance radiation is treated in xrt by incoherent addition of single
electron intensities. The single electron (filament) fields are considered as
fully coherent and are resulted from filament trajectories (one per repeat)
that attain positional and angular shifts within the given emittance
distribution. The following images are calculated for the exit slit and the
focus screen for zero and non-zero emittance
(for MAX IV 3 GeV ring: ε\ :sub:`x`\ =263 pm·rad,
β\ :sub:`x`\ =9 m, ε\ :sub:`z`\ =8 pm·rad, β\ :sub:`z`\ =2 m). At the real
emittance, the horizontal focal size increases by ~75%. A finite energy band,
as determined by vertical size of the exit slit, results in somewhat bigger
broadening due to a chromatic dependence of the focal length.
+-----------+---------------------+---------------------+---------------------+
| | 0 emittance | real emittance | |refeb| |
+===========+=====================+=====================+=====================+
| exit slit | |st_hESb| | |st_hES2| | |st_hES3| |
+-----------+---------------------+---------------------+---------------------+
| sample | |st_hSb| | |st_hS2| | |st_hS3| |
+-----------+---------------------+---------------------+---------------------+
.. |refeb| replace:: real emittance, finite energy band
.. |st_hESb| imagezoom:: _images/stxm-2D-2-hybr-0emit-0enSpread-monoE-04-ExitSlit.*
.. |st_hES2| imagezoom:: _images/stxm-2D-2-hybr-non0e-0enSpread-monoE-04-ExitSlit.*
.. |st_hS2| animation:: _images/stxm-2D-2-hybr-non0e-0enSpread-monoE-06i-ExpFocus-Is
.. |st_hES3| imagezoom:: _images/stxm-2D-2-hybr-non0e-0enSpread-wideE-04-ExitSlit.*
:loc: upper-right-corner
.. |st_hSb| imagezoom:: _images/stxm-2D-2-hybr-0emit-0enSpread-monoE-06i-ExpFocus-Is
.. |st_hS3| animation:: _images/stxm-2D-2-hybr-non0e-0enSpread-wideE-06i-ExpFocus-Is
:loc: upper-right-corner
.. rubric:: Correction of emittance effects
The increased focal size can be amended by closing the exit slit. With flux
loss of about 2/3, the focal size is almost restored.
+-----------+--------------------+--------------------+
| | 80 µm exit slit | 20 µm exit slit |
+===========+====================+====================+
| exit slit | |st_hES2b| | |st_hES4| |
+-----------+--------------------+--------------------+
| sample | |st_hS2b| | |st_hS4| |
+-----------+--------------------+--------------------+
.. |st_hES2b| imagezoom:: _images/stxm-2D-2-hybr-non0e-0enSpread-monoE-04-ExitSlit.*
.. |st_hES4| imagezoom:: _images/stxm-2D-2-hybr-non0e-0enSpread-monoE-025H-04-ExitSlit.*
:loc: upper-right-corner
.. |st_hS2b| animation:: _images/stxm-2D-2-hybr-non0e-0enSpread-monoE-06i-ExpFocus-Is
.. |st_hS4| animation:: _images/stxm-2D-2-hybr-non0e-0enSpread-monoE-025H-06i-ExpFocus-Is
:loc: upper-right-corner
.. rubric:: Coherence signatures
The beam improvement can also be viewed via the coherence properties by the
four available methods (see :ref:`coh_signs`). As the horizontal exit slit
becomes smaller, one can observe the increase of the coherent fraction ζ and
the increase of the primary (coherent) mode weight. The width of degree of
coherence (DoC) relative to the width of the intensity distribution determines
the coherent beam fraction. Both widths vary with varying screen position
around the focal point such that their ratio is not invariant, so that the
coherent fraction also varies, which is counter-intuitive. An important
advantage of the eigen-mode or PCA methods is a simple definition of the
coherent fraction as the eigenvalue of the zeroth mode (component); this
eigenvalue appears to be invariant around the focal point, see below. Note that
the methods 2 and 3 give equal results. The method 4 that gives the degree of
transverse coherence (DoTC) is also invariant around the focal point, see DoTC
values on the pictures of Principal Components.
+-----------+--------------------------+--------------------------+
| | 80 µm exit slit | 20 µm exit slit |
+===========+==========================+==========================+
| method 1 | |st_hS80m1| | |st_hS20m1| |
+-----------+--------------------------+--------------------------+
| method 2 | |st_hS80m3| | |st_hS20m3| |
+-----------+--------------------------+--------------------------+
| method 3, | |st_hS80m4| | |st_hS20m4| |
| method 4b | | |
+-----------+--------------------------+--------------------------+
.. |st_hS80m1| animation:: _images/stxm-IDOC-2D-2-hybr-non0e-0enSpread-monoE
.. |st_hS20m1| animation:: _images/stxm-IDOC-2D-2-hybr-non0e-0enSpread-monoE-025H
:loc: upper-right-corner
.. |st_hS80m3| animation:: _images/stxm-Modes-2D-2-hybr-non0e-0enSpread-monoE
.. |st_hS20m3| animation:: _images/stxm-Modes-2D-2-hybr-non0e-0enSpread-monoE-025H
:loc: upper-right-corner
.. |st_hS80m4| animation:: _images/stxm-PCA-2D-2-hybr-non0e-0enSpread-monoE
.. |st_hS20m4| animation:: _images/stxm-PCA-2D-2-hybr-non0e-0enSpread-monoE-025H
:loc: upper-right-corner
CXI branch
~~~~~~~~~~
.. rubric:: 2D vs 1D
Although the sample screen images are of good quality (the dark field is almost
black), the mirror footprints may be noisy and not well convergent in the
periphery. Compare the M3 footprint with that in the previous section (STXM
branch) where the difference is in the mirror area and thus in the sample
density. The used 10\ :sup:`6` wave samples (i.e. 10\ :sup:`12` possible paths)
are not enough for the slightly enlarged area in the present example. The
propagation is therefore performed in separated horizontal and vertical
directions, which dramatically improves the quality of the footprints.
Disadvantages of the cuts are losses in visual representation and incorrect
evaluation of the flux.
+------+----------------------+-----------------------+-----------------------+
| | 2D | 1D horizontal cut | 1D vertical cut |
+======+======================+=======================+=======================+
| |M3| | |cxiM32D| | |cxiM31Dh| | |cxiM31Dv| |
+------+----------------------+-----------------------+-----------------------+
| |SS| | |cxiS2D| | |cxiS1Dh| | |cxiS1Dv| |
+------+----------------------+-----------------------+-----------------------+
.. |M3| replace:: M3 footprint
.. |SS| replace:: sample screen
.. |cxiM32D| imagezoom:: _images/cxi_2D-2-hybr-0emit-0enSpread-monoE-03-M3local.*
.. |cxiM31Dh| imagezoom:: _images/cxi_1D-2-hybr-1e6hor-0emit-0enSpread-monoE-03-M3local.*
.. |cxiM31Dv| imagezoom:: _images/cxi_1D-2-hybr-1e6ver-0emit-0enSpread-monoE-03-M3local.*
:loc: upper-right-corner
.. |cxiS2D| animation:: _images/cxi_S2D
.. |cxiS1Dh| animation:: _images/cxi_S1Dh
.. |cxiS1Dv| animation:: _images/cxi_S1Dv
:loc: upper-right-corner
.. _wavefronts:
.. rubric:: Flat screen vs normal-to-k screen (wave front)
The following images demonstrate the correctness of the directional
Kirchhoff-like integral (see :ref:`seq_prop`). Five diffraction integrals are
calculated on flat screens around the focus position: for two polarizations and
for three directional components. The latter ones define the wave fronts at
every flat screen position; these wave fronts are further used as new curved
screens. The calculated diffraction fields on these curved screens have narrow
phase distributions, as shown by the color histograms, which is indeed expected
for a wave front by its definition. In contrast, the *flat* screens at the same
positions have rapid phase variation over several Fresnel zones.
.. note::
In the process of wave propagation, wave fronts -- surfaces of
constant phase -- are not used in any way. We therefore call it “wave
propagation”, not “wave *front* propagation” as frequently called by
others. The wave fronts in this example were calculated to solely
demonstrate the correctness of the local propagation directions after
having calculated the diffracted field.
+------------------------------+------------------------------+
| flat screen | curved screen (wave front) |
+==============================+==============================+
| |cxiFlat| | |cxiFront| |
+------------------------------+------------------------------+
.. |cxiFlat| animation:: _images/cxi-S1DhFlat
.. |cxiFront| animation:: _images/cxi-S1DhFront
:loc: upper-right-corner
The curvature of the calculated wave fronts varies across the focus position.
The wave fronts become more flat as one approaches the focus, see the figure
below. This is in contrast to *ray* propagation, where the angular ray
distribution is invariant at any position between two optical elements.
.. imagezoom:: _images/cxi_waveFronts.*
.. rubric:: Rays, waves and hybrid
The following images are horizontal cuts at the footprints and sample screens
calculated by
- rays,
- rays + waves hybrid (rays up to PG and wave from PG) and
- purely by waves.
+-----------------+-------------------+-------------------+-------------------+
| | rays | hybrid | waves |
+=================+===================+===================+===================+
| front end slit | |cxi-hFE| | same as rays | |cxi-wFE| |
+-----------------+-------------------+-------------------+-------------------+
| footprint on M1 | |cxi-hM1| | same as rays | |cxi-wM1| |
+-----------------+-------------------+-------------------+-------------------+
| footprint on M2 | |cxi-hM2| | same as rays | |cxi-wM2| |
+-----------------+-------------------+-------------------+-------------------+
| footprint on PG | |cxi-hPG| | same as rays | |cxi-wPG| |
+-----------------+-------------------+-------------------+-------------------+
| footprint on M3 | |cxi-rM3| | |cxi-hM3| | |cxi-wM3| |
+-----------------+-------------------+-------------------+-------------------+
| exit slit | |cxi-rES| | |cxi-hES| | |cxi-wES| |
+-----------------+-------------------+-------------------+-------------------+
| footprint on M4 | |cxi-rM4| | |cxi-hM4| | |cxi-wM4| |
+-----------------+-------------------+-------------------+-------------------+
| footprint on M5 | |cxi-rM5| | |cxi-hM5| | |cxi-wM5| |
+-----------------+-------------------+-------------------+-------------------+
| sample screen | |cxi-rS| | |cxi-hS| | |cxi-wS| |
+-----------------+-------------------+-------------------+-------------------+
.. |cxi-hFE| imagezoom:: _images/cxi_1D-1-rays-hor-0emit-0enSpread-monoE-00-FE.*
.. |cxi-wFE| imagezoom:: _images/cxi_1D-3-wave-hor-0emit-0enSpread-monoE-00-FE.*
:loc: upper-right-corner
.. |cxi-hM1| imagezoom:: _images/cxi_1D-1-rays-hor-0emit-0enSpread-monoE-01-M1local.*
.. |cxi-wM1| imagezoom:: _images/cxi_1D-3-wave-hor-0emit-0enSpread-monoE-01-M1local.*
:loc: upper-right-corner
.. |cxi-hM2| imagezoom:: _images/cxi_1D-1-rays-hor-0emit-0enSpread-monoE-02-M2local.*
.. |cxi-wM2| imagezoom:: _images/cxi_1D-3-wave-hor-0emit-0enSpread-monoE-02-M2local.*
:loc: upper-right-corner
.. |cxi-hPG| imagezoom:: _images/cxi_1D-1-rays-hor-0emit-0enSpread-monoE-02-PGlocal.*
.. |cxi-wPG| imagezoom:: _images/cxi_1D-3-wave-hor-0emit-0enSpread-monoE-02-PGlocal.*
:loc: upper-right-corner
.. |cxi-rM3| imagezoom:: _images/cxi_1D-1-rays-hor-0emit-0enSpread-monoE-03-M3local.*
.. |cxi-hM3| imagezoom:: _images/cxi_1D-2-hybr-hor-0emit-0enSpread-monoE-03-M3local.*
.. |cxi-wM3| imagezoom:: _images/cxi_1D-3-wave-hor-0emit-0enSpread-monoE-03-M3local.*
:loc: upper-right-corner
.. |cxi-rES| imagezoom:: _images/cxi_1D-1-rays-hor-0emit-0enSpread-monoE-04-ExitSlit.*
.. |cxi-hES| imagezoom:: _images/cxi_1D-2-hybr-hor-0emit-0enSpread-monoE-04-ExitSlit.*
.. |cxi-wES| imagezoom:: _images/cxi_1D-3-wave-hor-0emit-0enSpread-monoE-04-ExitSlit.*
:loc: upper-right-corner
.. |cxi-rM4| imagezoom:: _images/cxi_1D-1-rays-hor-0emit-0enSpread-monoE-05-M4local.*
.. |cxi-hM4| imagezoom:: _images/cxi_1D-2-hybr-hor-0emit-0enSpread-monoE-05-M4local.*
.. |cxi-wM4| imagezoom:: _images/cxi_1D-3-wave-hor-0emit-0enSpread-monoE-05-M4local.*
:loc: upper-right-corner
.. |cxi-rM5| imagezoom:: _images/cxi_1D-1-rays-hor-0emit-0enSpread-monoE-06-M5local.*
.. |cxi-hM5| imagezoom:: _images/cxi_1D-2-hybr-hor-0emit-0enSpread-monoE-06-M5local.*
.. |cxi-wM5| imagezoom:: _images/cxi_1D-3-wave-hor-0emit-0enSpread-monoE-06-M5local.*
:loc: upper-right-corner
.. |cxi-rS| animation:: _images/cxi-rS
.. |cxi-hS| animation:: _images/cxi-hS
.. |cxi-wS| animation:: _images/cxi-wS
:loc: upper-right-corner
.. rubric:: Coherence signatures
This section demonstrates the methods 1 and 3 from :ref:`coh_signs`. Notice
again the difficulty in determining the width of DoC owing to its complex shape
(at real emittance) or the restricted field of view (the 0 emittance case). In
contrast, the eigen mode analysis yields an almost invariant well defined
coherent fraction.
+-----------+--------------------------+--------------------------+
| | 0 emittance | real emittance |
+===========+==========================+==========================+
| method 1 | |cxi-coh1-0emit| | |cxi-coh1-non0e| |
+-----------+--------------------------+--------------------------+
| method 3 | |cxi-coh3-0emit| | |cxi-coh3-non0e| |
+-----------+--------------------------+--------------------------+
.. |cxi-coh1-0emit| animation:: _images/cxi-coh1-0emit
.. |cxi-coh1-non0e| animation:: _images/cxi-coh1-non0e
.. |cxi-coh3-0emit| animation:: _images/cxi-coh3-0emit
.. |cxi-coh3-non0e| animation:: _images/cxi-coh3-non0e
:loc: upper-right-corner
"""
pass
|
