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LAM-GRD-public
maoppy
Commits
e0fbfa4d
Commit
e0fbfa4d
authored
3 years ago
by
rfetick
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normalize gradient r0 up to infinity
parent
41b99d2c
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!2
Add derivatives computation
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maoppy/example/psfao_derivative.py
+95
-0
95 additions, 0 deletions
maoppy/example/psfao_derivative.py
maoppy/psfmodel.py
+16
-10
16 additions, 10 deletions
maoppy/psfmodel.py
with
111 additions
and
10 deletions
maoppy/example/psfao_derivative.py
0 → 100644
+
95
−
0
View file @
e0fbfa4d
# -*- coding: utf-8 -*-
"""
Created on Tue Jun 1 10:20:53 2021
Show the analytical and numerical derivatives for Psfao
@author: rfetick
"""
import
matplotlib.pyplot
as
plt
import
numpy
as
np
import
copy
from
maoppy.psfmodel
import
Psfao
from
maoppy.instrument
import
muse_nfm
Npix
=
64
# pixel size of PSF
wvl
=
600
*
1e-9
# wavelength [m]
#%% Initialize PSF model
samp
=
muse_nfm
.
samp
(
wvl
)
# sampling (2.0 for Shannon-Nyquist)
Pmodel
=
Psfao
((
Npix
,
Npix
),
system
=
muse_nfm
,
samp
=
samp
)
#%% Choose parameters
r0
=
0.15
# Fried parameter [m]
bck
=
1e-5
# Phase PSD background [rad² m²]
amp
=
5.0
# Phase PSD Moffat amplitude [rad²]
alpha
=
1
# Phase PSD Moffat alpha [1/m]
ratio
=
1.2
theta
=
np
.
pi
/
4
beta
=
1.6
# Phase PSD Moffat beta power law
param
=
[
r0
,
bck
,
amp
,
alpha
,
ratio
,
theta
,
beta
]
#%% Compute PSD derivative
psd
,
_
,
g
,
_
=
Pmodel
.
psd
(
param
,
grad
=
True
)
gnum
=
0
*
g
eps
=
1e-5
for
i
in
range
(
len
(
param
)):
dp
=
copy
.
copy
(
param
)
dp
[
i
]
+=
eps
psd2
,
_
=
Pmodel
.
psd
(
dp
)
gnum
[
i
,...]
=
(
psd2
-
psd
)
/
eps
#%% Plot results
names
=
[
'
r0
'
,
'
bck
'
,
'
amp
'
,
'
alpha
'
,
'
ratio
'
,
'
theta
'
,
'
beta
'
]
plt
.
figure
(
1
)
plt
.
clf
()
for
i
in
range
(
len
(
param
)):
plt
.
subplot
(
2
,
len
(
param
),
i
+
1
)
plt
.
pcolormesh
(
g
[
i
,...])
plt
.
axis
(
'
image
'
)
plt
.
axis
(
'
off
'
)
plt
.
title
(
names
[
i
])
plt
.
colorbar
(
orientation
=
'
horizontal
'
)
plt
.
subplot
(
2
,
len
(
param
),
i
+
1
+
len
(
param
))
plt
.
pcolormesh
(
gnum
[
i
,...])
plt
.
axis
(
'
image
'
)
plt
.
axis
(
'
off
'
)
#plt.title(names[i])
plt
.
colorbar
(
orientation
=
'
horizontal
'
)
#%% Compute PSF derivative
psf
,
g
=
Pmodel
(
param
,
grad
=
True
)
gnum
=
0
*
g
eps
=
1e-5
for
i
in
range
(
len
(
param
)):
dp
=
copy
.
copy
(
param
)
dp
[
i
]
+=
eps
psf2
=
Pmodel
(
dp
)
gnum
[
i
,...]
=
(
psf2
-
psf
)
/
eps
#%% Plot results
names
=
[
'
r0
'
,
'
bck
'
,
'
amp
'
,
'
alpha
'
,
'
ratio
'
,
'
theta
'
,
'
beta
'
]
plt
.
figure
(
2
)
plt
.
clf
()
for
i
in
range
(
len
(
param
)):
plt
.
subplot
(
2
,
len
(
param
),
i
+
1
)
plt
.
pcolormesh
(
g
[
i
,...])
plt
.
axis
(
'
image
'
)
plt
.
axis
(
'
off
'
)
plt
.
title
(
names
[
i
])
plt
.
colorbar
(
orientation
=
'
horizontal
'
)
plt
.
subplot
(
2
,
len
(
param
),
i
+
1
+
len
(
param
))
plt
.
pcolormesh
(
gnum
[
i
,...])
plt
.
axis
(
'
image
'
)
plt
.
axis
(
'
off
'
)
#plt.title(names[i])
plt
.
colorbar
(
orientation
=
'
horizontal
'
)
\ No newline at end of file
This diff is collapsed.
Click to expand it.
maoppy/psfmodel.py
+
16
−
10
View file @
e0fbfa4d
...
...
@@ -514,7 +514,7 @@ class ParametricPSFfromPSD(ParametricPSF):
def
_otfTurbulent
(
self
,
x0
,
grad
=
False
):
L
=
self
.
system
.
D
*
self
.
_samp_over
if
grad
:
PSD
,
integral
,
g
=
self
.
psd
(
x0
,
grad
=
True
)
PSD
,
integral
,
g
,
integral_g
=
self
.
psd
(
x0
,
grad
=
True
)
else
:
PSD
,
integral
=
self
.
psd
(
x0
,
grad
=
False
)
...
...
@@ -527,8 +527,8 @@ class ParametricPSFfromPSD(ParametricPSF):
g2
=
_np
.
zeros
(
g
.
shape
,
dtype
=
complex
)
# I cannot override 'g' here due to float to complex type
for
i
in
range
(
len
(
x0
)):
Bg
=
_fft
.
fft2
(
_fft
.
fftshift
(
g
[
i
,...]))
/
L
**
2
#
BUG: grad is normalized on the FoV, that is different of the otf!
Bphi
=
_fft
.
fftshift
(
_np
.
real
(
Bg
[
0
,
0
]
-
Bg
))
# normalized
on the numerical FoV
#
Bphi = _fft.fftshift(_np.real(Bg[0, 0] - Bg)) # normalized on the numerical FoV
Bphi
=
_fft
.
fftshift
(
_np
.
real
(
integral_g
[
i
]
-
Bg
))
# normalized
up to infinity
g2
[
i
,...]
=
-
Bphi
*
otf
return
otf
,
g2
return
otf
...
...
@@ -577,7 +577,7 @@ class ParametricPSFfromPSD(ParametricPSF):
if
grad
:
g2
=
_np
.
zeros
((
len
(
x0
),
psf
.
shape
[
0
]
//
k
,
psf
.
shape
[
1
]
//
k
))
for
i
in
range
(
len
(
x0
)):
g2
[
i
,...]
=
_binning
(
g
[
i
,...],
k
)
g2
[
i
,...]
=
_binning
(
g
[
i
,...]
.
astype
(
float
)
,
k
)
return
_binning
(
psf
,
k
),
g2
return
_binning
(
psf
,
k
)
# undersample PSF if needed (if it was oversampled for computations)
...
...
@@ -646,14 +646,17 @@ class Turbulent(ParametricPSFfromPSD):
integral_out
=
0.0229
*
6
*
_np
.
pi
/
5
*
(
r0
*
fmax
)
**
(
-
5.
/
3.
)
# analytical sum (outside the array's tangent circle)
integral
=
integral_in
+
integral_out
# TODO: I can also compute the integral gradient
if
grad
:
g
=
_np
.
zeros
((
len
(
x0
),)
+
F2
.
shape
)
g
[
0
,...]
=
PSD
*
(
-
5.
/
3
)
/
r0
g
[
1
,...]
=
PSD
*
(
-
11.
/
6
)
/
((
1.
/
Lext
**
2.
)
+
F2
)
*
(
-
2
/
Lext
**
3
)
# compute integral gradient
integral_g
=
[
0
,
0
]
for
i
in
range
(
2
):
integral_g
[
i
]
=
_np
.
sum
(
g
[
i
,...]
*
(
F2
<
(
fmax
**
2
)))
*
self
.
_pix2freq
**
2
# numerical sum (in the array's tangent circle)
integral_g
[
0
]
+=
integral_out
*
(
-
5.
/
3
)
/
r0
if
grad
:
return
PSD
,
integral
,
g
if
grad
:
return
PSD
,
integral
,
g
,
integral_g
return
PSD
,
integral
#%% PSFAO MODEL
...
...
@@ -765,9 +768,12 @@ class Psfao(ParametricPSFfromPSD):
# Remove central freq from all derivative
g
[:,
nx0
,
ny0
]
=
0
#TODO: I can also compute the integral gradient towards the parameters!
if
grad
:
return
PSD
,
integral
,
g
# Compute integral gradient
integral_g
=
_np
.
zeros
(
len
(
x0
))
for
i
in
range
(
len
(
x0
)):
integral_g
[
i
]
=
_np
.
sum
(
g
[
i
,...]
*
(
F2
<
(
fmax
**
2
)))
*
self
.
_pix2freq
**
2
# numerical sum
integral_g
[
0
]
+=
integral_out
*
(
-
5.
/
3
)
/
r0
if
grad
:
return
PSD
,
integral
,
g
,
integral_g
return
PSD
,
integral
def
tofits
(
self
,
param
,
filename
,
*
args
,
keys
=
None
,
overwrite
=
False
,
**
kwargs
):
...
...
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