def test_sample_Gaussian():
"""
Test SampleImage 'Gaussian'.
"""
# SampleImage options, recon tolerance
param = [(dict(), 4e-4), (dict(n=501), 5e-4), (dict(n=501,
sigma=50), 3e-9)]
# test transform using Daun with cubic splines (the most accurate)
for kwargs, tol in param:
test = SampleImage(name='Gaussian', **kwargs)
recon = Transform(test.abel,
method='daun',
symmetry_axis=(0, 1),
transform_options={
'degree': 3,
'verbose': False
}).transform
assert_allclose(recon,
test.func,
atol=tol,
err_msg='-> abel, {}'.format(kwargs))
# test even size
n = 10
r_max = 4.5 # (n - 1) / 2
sigma = 2
x = np.arange(n) - r_max
ref = np.exp(-(x**2 + x[:, None]**2) / sigma**2)
test = SampleImage(n=n, name='Gaussian', sigma=sigma)
assert test.r_max == r_max
assert_allclose(test.r, x)
assert_allclose(test.func, ref)
assert_allclose(test.abel, np.sqrt(np.pi) * sigma * ref)
def test_sample_Ominus():
"""
Test SampleImage 'Ominus'.
"""
# SampleImage options, recon tolerance
param = [(dict(), 0.2), (dict(n=501), 0.073), (dict(sigma=3), 0.056),
(dict(n=501, sigma=3), 0.14), (dict(temperature=100), 0.2)]
# test transform using Daun with cubic splines (the most accurate)
for kwargs, tol in param:
test = SampleImage(name='Ominus', **kwargs)
recon = Transform(test.abel,
method='daun',
symmetry_axis=(0, 1),
transform_options={
'degree': 3,
'verbose': False
}).transform
assert_allclose(recon,
test.func,
atol=tol,
err_msg='-> abel, {}'.format(kwargs))
# test transform tol
test = SampleImage(name='Ominus')
abel = test.abel.copy() # default, ≲5e-3
abel4 = test.transform(1e-4)
abel5 = test.transform(1e-5)
ampl = np.max(abel5)
assert_allclose(abel, abel5, atol=3e-3 * ampl)
assert_allclose(abel4, abel5, atol=0.3e-4 * ampl)
def test_sample_Dribinski():
"""
Test SampleImage 'Dribinski'.
"""
# test deprecated attribute
test = SampleImage(name='dribinski') # (test lower-case)
with catch_warnings():
simplefilter('ignore', category=DeprecationWarning)
assert_equal(test.image, test.func)
# .abel is difficult to test reliably due to the huge dynamic range
# test scaling
n = 501
test1 = SampleImage(n=n, name='Dribinski', sigma=2)
test2 = SampleImage(n=n // 2 + 1, name='Dribinski', sigma=1) # halved
assert test2.r_max == test1.r_max / 2
assert_allclose(test2.func, test1.func[::2, ::2])
assert_allclose(test2.abel, test1.abel[::2, ::2] / 2, atol=2e-6)
def plot(method, strength=None):
# test distribution
source = SampleImage(n=2 * rmax - 1).image / scale
Isrc, _ = Ibeta(source)
Inorm = (Isrc**2).sum()
# simulated projection fith Poissonian noise
proj, _ = rbasex_transform(source, direction='forward')
proj[proj < 0] = 0
proj = np.random.RandomState(0).poisson(proj) # (reproducible, see NEP 19)
# reconstructed image and intensity
if strength is None:
reg = method
else:
reg = (method, strength)
im, distr = rbasex_transform(proj, reg=reg)
I, _ = distr.Ibeta()
# plot...
fig = plt.figure(figsize=(7, 3.5), frameon=False)
# image
plt.subplot(121)
fig = plt.imshow(rescaleI(im), vmin=-vlim, vmax=vlim, cmap='bwr')
plt.axis('off')
plt.text(0, 2 * rmax, method, va='top')
# intensity
ax = plt.subplot2grid((3, 2), (0, 1), rowspan=2)
ax.plot(Isrc, c='r', lw=1)
ax.plot(I, c='k', lw=1)
ax.set_xlim((0, rmax))
ax.set_ylim(Ilim)
# error
plt.subplot(326)
plt.axhline(c='r', lw=1)
plt.plot(I - Isrc, c='b', lw=1)
plt.xlim((0, rmax))
plt.ylim(dIlim)
# finish
plt.subplots_adjust(left=0,
right=0.97,
wspace=0.1,
bottom=0.08,
top=0.98,
hspace=0.5)
def test_sample_Gerber():
"""
Test SampleImage 'Gerber'.
"""
# test transform with forward Daun with cubic splines (the most accurate)
test = SampleImage(n=513, name='Gerber') # original resolution, rmax = 256
proj = Transform(test.func,
method='daun',
direction='forward',
symmetry_axis=(0, 1),
transform_options={
'degree': 3,
'verbose': False
}).transform
assert_allclose(proj, test.abel, atol=6e-3 * np.max(proj))
# test sigma-independence of total intensity
test1 = SampleImage(name='Gerber', sigma=1)
test2 = SampleImage(name='Gerber', sigma=2)
assert_allclose(test1.abel.sum(), test2.abel.sum(), rtol=1e-3)
def test_sample_O2():
"""
Test SampleImage 'O2'.
"""
# test transform with forward Daun with cubic splines (the most accurate)
test = SampleImage(n=1001, name='O2') # ~high resolution
proj = Transform(test.func,
method='daun',
direction='forward',
symmetry_axis=(0, 1),
transform_options={
'degree': 3,
'verbose': False
}).transform
assert_allclose(proj, test.abel, atol=9e-4 * np.max(proj))
def test_radial_integration():
"""
Basic test of radial integration.
"""
# test image (not projected)
IM = SampleImage(name='dribinski').func
Beta, Amplitude, Rmidpt, _, _ = \
vmi.radial_integration(IM, radial_ranges=([(65, 75), (80, 90), (95, 105)]))
assert_equal(Rmidpt, [70, 85, 100], err_msg='Rmidpt')
assert_allclose([b[0] for b in Beta], [0, 1.58, -0.85], atol=0.01,
err_msg='Beta')
assert_allclose([a[0] for a in Amplitude], [880, 600, 560], rtol=0.01,
err_msg='Amplitude')
def test_toPES():
"""
Basic test of toPES conversion.
"""
# test image (not projected)
IM = SampleImage(name='Ominus').func
eBE, PES = vmi.toPES(*vmi.angular_integration_3D(IM),
energy_cal_factor=1.2e-5,
photon_energy=1.0e7/808.6, Vrep=-100,
zoom=IM.shape[-1]/2048)
assert_allclose(eBE[PES.argmax()], 11780, rtol=0.001,
err_msg='-> eBE @ max PES')
assert_allclose(PES.max(), 16620, rtol=0.001,
err_msg='-> max PES')
from __future__ import division, print_function
import numpy as np
import matplotlib.pyplot as plt
from abel.tools.analytical import SampleImage
from abel.tools.vmi import Ibeta
from abel.rbasex import rbasex_transform
# test distribution
rmax = 200
scale = 10000
source = SampleImage(n=2 * rmax - 1).image / scale
Isrc, _ = Ibeta(source)
Inorm = (Isrc**2).sum()
# simulated projection fith Poissonian noise
proj, _ = rbasex_transform(source, direction='forward')
proj[proj < 0] = 0
proj = np.random.RandomState(0).poisson(proj) # (reproducible, see NEP 19)
# calculate relative RMS error for given regularization parameters
def rmse(method, strengths=None):
if strengths is None:
_, distr = rbasex_transform(proj, reg=method, out=None)
I, _ = distr.Ibeta()
return ((I - Isrc)**2).sum() / Inorm
err = np.empty_like(strengths, dtype=float)
for n, strength in enumerate(strengths):
# but with its artifacts masked, showing good agreement with the actual # distributions. # Third, the rBasex method is used to transform the initial damaged image with # the experimental artifacts masked, yielding a correct and cleaner # reconstructed image and correct reconstructed distributions. R = 150 # image radius N = 2 * R + 1 # full image width and height block_r = 20 # beam-block disk radius block_w = 5 # beam-block holder width vlim = 3.6 # intensity limits for images ylim = (-1.3, 2.7) # limits for plots # create source distribution and its profiles for reference source = SampleImage(N).func / 100 r_src, P0_src, P2_src = rharmonics(source) # simulate experimental image: # projection im, _ = rbasex_transform(source, direction='forward') # Poissonian noise im[im < 0] = 0 im = np.random.RandomState(0).poisson(im) # image coordinates im_x = np.arange(float(N)) - R im_y = R - np.arange(float(N))[:, None] im_r = np.sqrt(im_x**2 + im_y**2) # simulate beam-block shadow im = im / (1 + np.exp(-(im_r - block_r))) im[:R] *= 1 / (1 + np.exp(-(np.abs(im_x) - block_w)))
# but with its artifacts masked, showing good agreement with the actual # distributions. # Third, the rBasex method is used to transform the initial damaged image with # the experimental artifacts masked, yielding a correct and cleaner # reconstructed image and correct reconstructed distributions. R = 150 # image radius N = 2 * R + 1 # full image width and height block_r = 20 # beam-block disk radius block_w = 5 # beam-block holder width vlim = 3.6 # intensity limits for images ylim = (-1.3, 2.7) # limits for plots # create source distribution and its profiles for reference source = SampleImage(N).image / 100 r_src, P0_src, P2_src = rharmonics(source) # simulate experimental image: # projection im, _ = rbasex_transform(source, direction='forward') # Poissonian noise im[im < 0] = 0 im = np.random.RandomState(0).poisson(im) # image coordinates im_x = np.arange(float(N)) - R im_y = R - np.arange(float(N))[:, None] im_r = np.sqrt(im_x**2 + im_y**2) # simulate beam-block shadow im = im / (1 + np.exp(-(im_r - block_r))) im[:R] *= 1 / (1 + np.exp(-(np.abs(im_x) - block_w)))
from __future__ import division, print_function
import numpy as np
import matplotlib.pyplot as plt
from abel.tools.analytical import SampleImage
from abel.tools.vmi import Ibeta
from abel.rbasex import rbasex_transform
# test distribution
rmax = 200
scale = 10000
source = SampleImage(n=2 * rmax - 1).func / scale
Isrc, _ = Ibeta(source)
Inorm = (Isrc**2).sum()
# simulated projection fith Poissonian noise
proj, _ = rbasex_transform(source, direction='forward')
proj[proj < 0] = 0
proj = np.random.RandomState(0).poisson(proj) # (reproducible, see NEP 19)
# calculate relative RMS error for given regularization parameters
def rmse(method, strengths=None):
if strengths is None:
_, distr = rbasex_transform(proj, reg=method, out=None)
I, _ = distr.Ibeta()
return ((I - Isrc)**2).sum() / Inorm
err = np.empty_like(strengths, dtype=float)
for n, strength in enumerate(strengths):