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irp
Fresnel
Commits
8dc38167
Commit
8dc38167
authored
Feb 10, 2021
by
Leon Merten Lohse
Browse files
split up fdsolver and propagation. introduce wavelength as parameter
parent
b4693942
Changes
7
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examples/Test2d.ipynb
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8dc38167
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examples/Test3d.ipynb
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examples/TestCS.ipynb
View file @
8dc38167
%% Cell type:code id: tags:
```
python
import
sys
import
numpy
as
np
import
xraylib
as
xrl
import
matplotlib.pyplot
as
plt
import
fresnel.
solver
as
solver
import
fresnel.
propagate
as
propagate
```
%% Cell type:code id: tags:
```
python
%
matplotlib
inline
```
%% Cell type:code id: tags:
```
python
energy
=
12.
# keV
# geometry
wavelength
=
1.2398
/
(
energy
*
1e3
)
*
1e-3
# mm
nx
=
1024
ny
=
512
nz
=
1000
ztot
=
0.4
# mm
wg_radius
=
25e-6
xtot
=
10
*
wg_radius
# mm
# units
dx
=
xtot
/
nx
/
wavelength
dz
=
ztot
/
nz
/
wavelength
print
(
f
"dx:
{
dx
}
, dz:
{
dz
}
wavelengths"
)
```
%%%% Output: stream
dx: 2.36303234392644, dz: 3871.592192289079 wavelengths
%% Cell type:code id: tags:
```
python
density_Ge
=
xrl
.
ElementDensity
(
xrl
.
SymbolToAtomicNumber
(
'Ge'
))
density_Polyimide
=
1.42
density_Si
=
xrl
.
ElementDensity
(
xrl
.
SymbolToAtomicNumber
(
'Si'
))
n_Ge
=
xrl
.
Refractive_Index
(
'Ge'
,
energy
,
density_Ge
)
n_Si
=
xrl
.
Refractive_Index
(
'Si'
,
energy
,
density_Si
)
n_PI
=
xrl
.
Refractive_Index
(
'Kapton Polyimide Film'
,
energy
,
density_Polyimide
)
xx
=
np
.
linspace
(
-
xtot
/
2
,
xtot
/
2
,
nx
)
core
=
(
np
.
abs
(
xx
)
<
wg_radius
)
cladding
=
~
core
refractive_index
=
n_Ge
*
cladding
+
1
*
core
```
%% Cell type:code id: tags:
```
python
boundary
=
(
0
,
0
,)
u0
=
np
.
exp
(
-
xx
**
2
/
(
2
*
(
2
*
wg_radius
)
**
2
)).
astype
(
np
.
complex128
)
```
%% Cell type:code id: tags:
```
python
propagator
=
solver
.
PropagatorCS
(
refractive_index
,
u0
,
dz
,
dx
)
propagator
=
propagate
.
FD
PropagatorCS
(
refractive_index
,
u0
,
dz
,
dx
)
```
%% Cell type:code id: tags:
```
python
field
=
np
.
zeros
((
nz
,
nx
),
dtype
=
np
.
complex128
)
field
[
0
,...]
=
u0
for
iz
in
range
(
1
,
nz
):
boundary
=
(
0
,
0
)
field
[
iz
,
...]
=
propagator
.
step
(
refractive_index
,
boundary
)
```
%% Cell type:code id: tags:
```
python
result
=
field
.
transpose
()
fig
,
ax
=
plt
.
subplots
()
im
=
ax
.
imshow
(
np
.
abs
(
result
[:,:])
**
2
,
aspect
=
'auto'
,
clim
=
(
0
,
3
),
cmap
=
'jet'
,
extent
=
[
0
,
ztot
,
-
xtot
/
2
*
1e6
,
xtot
/
2
*
1e6
])
ax
.
set_ylim
(
-
2e6
*
wg_radius
,
2e6
*
wg_radius
)
fig
.
colorbar
(
im
)
ax
.
set_xlabel
(
r
'$z$ (mm)'
)
ax
.
set_ylabel
(
r
'$x$ (nm)'
)
```
%%%% Output: execute_result
Text(0, 0.5, '$x$ (nm)')
%%%% Output: display_data
%% Cell type:code id: tags:
```
python
```
...
...
fresnel/
solver
.py
→
fresnel/
finite_differences
.py
View file @
8dc38167
...
...
@@ -2,8 +2,6 @@ import numpy as np
from
.
import
_solver
_k
=
2
*
np
.
pi
# all lengths are in units of the wavelength
_compute_potential
=
lambda
n
:
_k
**
2
*
(
1
-
n
*
n
)
class
Solver2d
():
"""
...
...
@@ -186,63 +184,4 @@ class Solver3d():
u_T
=
_solver
.
step2d_A0Fs
(
self
.
rz
,
self
.
rxx
,
self
.
ryy
,
fp
.
T
,
self
.
f
.
T
,
up
.
T
,
u
.
T
)
self
.
u
=
u_T
.
T
return
self
.
u
class
Propagator2d
(
Solver2d
):
def
__init__
(
self
,
n0
,
u0
,
dz
,
dx
):
Az
=
2j
*
_k
Axx
=
1
F0
=
_compute_potential
(
n0
)
super
().
__init__
(
Az
,
Axx
,
F0
,
u0
,
dz
,
dx
)
def
step
(
self
,
n
,
boundary
):
F
=
_compute_potential
(
n
)
return
super
().
step
(
F
,
boundary
)
class
PropagatorCS
(
Solver2dfull
):
def
__init__
(
self
,
n0
,
u0
,
dz
,
dx
):
nx
=
u0
.
shape
[
-
1
]
self
.
_x
=
np
.
linspace
(
-
nx
*
dx
/
2
,
nx
*
dx
/
2
,
nx
)
Az
=
2j
*
_k
*
self
.
_x
Axx
=
self
.
_x
Ax
=
1
F0
=
_compute_potential
(
n0
)
super
().
__init__
(
Az
,
Axx
,
Ax
,
F0
,
u0
,
dz
,
dx
)
def
step
(
self
,
n
,
boundary
):
F
=
_compute_potential
(
n
)
*
self
.
_x
return
super
().
step
(
F
,
boundary
)
class
Propagator3d
(
Solver3d
):
def
__init__
(
self
,
n0
,
u0
,
dz
,
dy
,
dx
):
Az
=
2j
*
_k
Axx
=
1
Ayy
=
1
F0
=
_compute_potential
(
n0
)
super
().
__init__
(
Az
,
Axx
,
Ayy
,
F0
,
u0
,
dz
,
dy
,
dx
)
def
step
(
self
,
n
,
boundary
):
F
=
_compute_potential
(
n
)
return
super
().
step
(
F
,
boundary
)
return
self
.
u
\ No newline at end of file
fresnel/misc.py
0 → 100644
View file @
8dc38167
import
numpy
as
np
from
pyfftw.interfaces.numpy_fft
import
fftfreq
,
ifftshift
,
fftshift
def
fftfreqn
(
N
,
d
=
1.0
):
ndim
=
len
(
N
)
d
*=
np
.
ones
(
ndim
)
# index trick: n'th line is a list of ones with a -1 on n'th position
shapes
=
np
.
ones
((
ndim
,
ndim
),
dtype
=
'int'
)
-
2
*
np
.
eye
(
ndim
,
dtype
=
'int'
)
xi
=
[
np
.
reshape
(
2
*
np
.
pi
*
fftfreq
(
N
[
dim
],
d
[
dim
]),
tuple
(
shapes
[
dim
,
:]))
for
dim
in
range
(
ndim
)]
return
xi
def
crop
(
a
,
crop_width
):
slices
=
[
slice
(
w
[
0
],
-
w
[
1
]
if
w
[
1
]
>
0
else
None
)
for
w
in
crop_width
]
return
a
[
tuple
(
slices
)]
fresnel/propagat
ion
.py
→
fresnel/propagat
e
.py
View file @
8dc38167
from
pyfftw.interfaces.numpy_fft
import
fftn
,
fftfreq
,
ifftn
,
ifftshift
,
fftshift
from
pyfftw.interfaces.numpy_fft
import
fft
,
fftn
,
fftfreq
,
ifftn
,
ifftshift
,
fftshift
import
numpy
as
np
from
.
import
finite_differences
as
fd
from
.misc
import
fftfreqn
,
crop
_k
=
2
*
np
.
pi
# all lengths are in units of the wavelength
_compute_potential
=
lambda
n
:
_k
**
2
*
(
1
-
n
*
n
)
_lambda0
=
1.
# all lengths are in units of the wavelength
_k0
=
2
*
np
.
pi
/
_lambda0
_compute_potential
=
lambda
n_
,
k_
=
_k0
:
k_
*
k_
*
(
1
-
n_
*
n_
)
def
fftfreqn
(
N
):
ndim
=
len
(
N
)
# index trick: n'th line is a list of ones with a -1 on n'th position
shapes
=
np
.
ones
((
ndim
,
ndim
),
dtype
=
'int'
)
-
2
*
np
.
eye
(
ndim
,
dtype
=
'int'
)
def
fresnelKernel
(
shape
,
fresnelNumbers
,
method
=
'TF'
):
xi
=
[
np
.
reshape
(
2
*
np
.
pi
*
fftfreq
(
N
[
dim
]),
tuple
(
shapes
[
dim
,
:]))
for
dim
in
range
(
ndim
)]
return
xi
def
crop
(
a
,
crop_width
):
slices
=
[
slice
(
w
[
0
],
-
w
[
1
]
if
w
[
1
]
>
0
else
None
)
for
w
in
crop_width
]
return
a
[
tuple
(
slices
)]
def
fresnelKernel
(
N
,
fresnelNumbers
):
ndim
=
len
(
N
)
ndim
=
len
(
shape
)
if
np
.
isscalar
(
fresnelNumbers
):
fresnelNumbers
=
fresnelNumbers
*
np
.
ones
(
ndim
)
kernel
=
np
.
ones
(
N
,
dtype
=
np
.
complex128
)
xi
=
fftfreqn
(
N
)
kernel
=
np
.
ones
(
shape
,
dtype
=
np
.
complex128
)
if
method
is
'TF'
:
# transfer function (TF) method
xi
=
fftfreqn
(
shape
,
1
)
for
dim
in
range
(
ndim
):
kernel
*=
np
.
exp
((
-
1j
/
(
2
*
_k0
*
fresnelNumbers
[
dim
]))
*
xi
[
dim
]
**
2
)
for
dim
in
range
(
ndim
):
kernel
*=
np
.
exp
((
-
1j
/
(
2
*
_k
*
fresnelNumbers
[
dim
]))
*
xi
[
dim
]
**
2
)
return
kernel
return
kernel
if
method
is
'IR'
:
# impulse response (IR) method
# phase factor
kernel
*=
np
.
prod
(
np
.
sqrt
(
abs
(
fresnelNumbers
)))
*
np
.
exp
((
-
1j
*
np
.
pi
/
4
)
*
np
.
sign
(
fresnelNumbers
))
# TODO: use dedicated function for this to avoid loss of precision
x
=
fftfreqn
(
shape
,
1
/
shape
)
for
dim
in
range
(
ndim
):
kernel
*=
fft
(
np
.
exp
(
1j
*
np
.
pi
*
fresnelNumbers
[
dim
]
*
x
[
dim
]
**
2
))
return
kernel
raise
ValueError
(
f
'Invalid method "
{
method
}
". Must be "TF" or "IR".'
)
class
FresnelPropagator2d
():
class
FresnelPropagator
():
"""
Multi-Slice approximation
Paganin, Coherent X-Ray Optics, p101
"""
dtype
=
np
.
complex128
def
__init__
(
self
,
u0
,
d
,
wl
=
1.
,
method
=
'TF'
):
ndim
=
len
(
d
)
# TODO: check input
# assert u0 is array
# assert d is tuple
# assert wl is scalar numeric
# assert ndim == u0.ndim + 1
def
__init__
(
self
,
u0
,
dz
,
dx
):
self
.
_dz
=
d
[
0
]
self
.
_dperp
=
np
.
array
(
d
[
1
:])
self
.
_ones
=
np
.
ones
(
u0
.
shape
,
dtype
=
self
.
dtype
)
self
.
_k
=
_k0
/
wl
self
.
_nx
=
u0
.
shape
[
-
1
]
self
.
_ones
=
np
.
ones
((
self
.
_nx
,),
dtype
=
self
.
dtype
)
self
.
_dz
=
dz
fresnelNumber
=
dx
**
2
/
dz
# in units of wavelength
self
.
_fourierKernel
=
fresnelKernel
(
self
.
_ones
.
shape
,
fresnelNumber
)
fresnelNumbers
=
self
.
_dperp
**
2
/
(
self
.
_dz
*
wl
)
self
.
_fourierKernel
=
fresnelKernel
(
self
.
_ones
.
shape
,
fresnelNumbers
,
method
)
self
.
u
=
ifftshift
(
u0
)
def
step
(
self
,
n
):
F
=
_compute_potential
(
ifftshift
(
n
))
*
self
.
_ones
nshift
=
ifftshift
(
n
)
self
.
_realKernel
=
np
.
exp
(
-
1j
/
(
2
*
_k
)
*
self
.
_dz
*
F
)
F
=
_compute_potential
(
nshift
,
self
.
_k
)
*
self
.
_ones
self
.
_realKernel
=
np
.
exp
(
-
1j
/
(
2
*
self
.
_k
)
*
self
.
_dz
*
F
)
up
=
self
.
u
self
.
u
=
ifftn
(
self
.
_fourierKernel
*
fftn
(
self
.
_realKernel
*
up
))
...
...
@@ -69,38 +88,71 @@ class FresnelPropagator2d():
return
fftshift
(
self
.
u
)
class
FresnelPropagator3d
():
"""
Multi-Slice approximation
Paganin, Coherent X-Ray Optics, p101
"""
dtype
=
np
.
complex128
class
FDPropagator2d
(
fd
.
Solver2d
):
def
__init__
(
self
,
u0
,
dz
,
d
y
,
dx
):
def
__init__
(
self
,
n0
,
u0
,
dz
,
d
x
,
wl
=
1.
):
self
.
_nx
=
u0
.
shape
[
-
1
]
self
.
_nx
=
u0
.
shape
[
-
2
]
self
.
_ones
=
np
.
ones
((
self
.
_ny
,
self
.
_nx
,),
dtype
=
self
.
dtype
)
self
.
_k
=
_k0
/
wl
self
.
_dz
=
dz
fresnelNumber
=
dx
**
2
/
dz
# in units of wavelength
self
.
_fourierKernel
=
fresnelKernel
(
self
.
_ones
.
shape
,
fresnelNumber
)
self
.
u
=
ifftshift
(
u0
)
Az
=
2j
*
self
.
_k
Axx
=
1
F0
=
_compute_potential
(
n0
,
self
.
_k
)
super
().
__init__
(
Az
,
Axx
,
F0
,
u0
,
dz
,
dx
)
def
step
(
self
,
n
,
boundary
):
F
=
_compute_potential
(
n
,
self
.
_k
)
return
super
().
step
(
F
,
boundary
)
class
FDPropagatorCS
(
fd
.
Solver2dfull
):
def
__init__
(
self
,
n0
,
u0
,
dz
,
dx
,
wl
=
1.
):
nx
=
u0
.
shape
[
-
1
]
self
.
_x
=
np
.
linspace
(
-
nx
*
dx
/
2
,
nx
*
dx
/
2
,
nx
)
def
step
(
self
,
n
):
F
=
_compute_potential
(
ifftshift
(
n
))
*
self
.
_ones
self
.
_realKernel
=
np
.
exp
(
-
1j
/
(
2
*
_k
)
*
self
.
_dz
*
F
)
up
=
self
.
u
self
.
u
=
ifftn
(
self
.
_fourierKernel
*
fftn
(
self
.
_realKernel
*
up
))
self
.
_k
=
_k0
/
wl
Az
=
2j
*
self
.
_k
*
self
.
_x
Axx
=
self
.
_x
Ax
=
1
F0
=
_compute_potential
(
n0
,
self
.
_k
)
*
self
.
_x
super
().
__init__
(
Az
,
Axx
,
Ax
,
F0
,
u0
,
dz
,
dx
)
def
step
(
self
,
n
,
boundary
):
F
=
_compute_potential
(
n
,
self
.
_k
)
*
self
.
_x
return
super
().
step
(
F
,
boundary
)
class
FDPropagator3d
(
fd
.
Solver3d
):
def
__init__
(
self
,
n0
,
u0
,
dz
,
dy
,
dx
,
wl
=
1.
):
self
.
_k
=
_k0
/
wl
Az
=
2j
*
self
.
_k
Axx
=
1
Ayy
=
1
F0
=
_compute_potential
(
n0
,
self
.
_k
)
super
().
__init__
(
Az
,
Axx
,
Ayy
,
F0
,
u0
,
dz
,
dy
,
dx
)
return
fftshift
(
self
.
u
)
def
step
(
self
,
n
,
boundary
):
F
=
_compute_potential
(
n
,
self
.
_k
)
return
super
().
step
(
F
,
boundary
)
def
fresnelPropagate
(
im
,
fresnelNumbers
,
sizePad
=
None
,
sizeOut
=
None
,
padMode
=
'edge'
):
...
...
source/finite_difference.h
View file @
8dc38167
...
...
@@ -2,7 +2,7 @@
#include <complex>
#include <Eigen/Dense>
#include <iostream>
//
#include <iostream>
namespace
algebra
{
...
...
@@ -174,7 +174,7 @@ namespace finite_differences{
size_t
nx
=
u
.
rows
()
-
2
;
size_t
ny
=
u
.
cols
()
-
2
;
std
::
cout
<<
"nx "
<<
u
.
cols
()
<<
", ny "
<<
u
.
rows
()
<<
std
::
endl
;
//
std::cout << "nx " << u.cols() << ", ny " << u.rows() << std::endl;
// first halfstep
// x at i + 1/2
...
...
@@ -264,7 +264,7 @@ namespace finite_differences{
size_t
nx
=
u
.
rows
()
-
2
;
size_t
ny
=
u
.
cols
()
-
2
;
std
::
cout
<<
"nx "
<<
u
.
cols
()
<<
", ny "
<<
u
.
rows
()
<<
std
::
endl
;
//
std::cout << "nx " << u.cols() << ", ny " << u.rows() << std::endl;
// first halfstep
// x at i + 1/2
...
...
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