def test_angle_offset():
"""
Tests if things are still correct when there is a 2PI offset in the angles.
"""
sino, angles = create_test_sino_2d()
parameters = get_test_parameter_set(2)
# reference
r1 = []
for p in parameters:
f1 = odtbrain.backpropagate_2d(sino, angles, weight_angles=False, **p)
r1.append(f1)
# with offset
angles[::2] += 2*np.pi*np.arange(angles[::2].shape[0])
r2 = []
for p in parameters:
f2 = odtbrain.backpropagate_2d(sino, angles, weight_angles=False, **p)
r2.append(f2)
# with offset and weights
r3 = []
for p in parameters:
f3 = odtbrain.backpropagate_2d(sino, angles, weight_angles=True, **p)
r3.append(f3)
assert np.allclose(np.array(r1).flatten().view(float),
np.array(r2).flatten().view(float))
assert np.allclose(np.array(r2).flatten().view(float),
np.array(r3).flatten().view(float))
def test_bpp_2d():
sino, angles = create_test_sino_2d(N=10)
p = get_test_parameter_set(1)[0]
# complex
jmc = mp.Value("i", 0)
jmm = mp.Value("i", 0)
odtbrain.backpropagate_2d(sino,
angles,
padval=0,
count=jmc,
max_count=jmm,
**p)
assert jmc.value == jmm.value
assert jmc.value != 0
def test_2d_backprop_full():
myframe = sys._getframe()
sino, angles = create_test_sino_2d(ampl_range=(0.9, 1.1))
parameters = get_test_parameter_set(2)
r = list()
for p in parameters:
f = odtbrain.backpropagate_2d(sino, angles, **p)
r.append(cutout(f))
if WRITE_RES:
write_results(myframe, r)
assert np.allclose(np.array(r).flatten().view(float), get_results(myframe))
def test_2d_backprop_real():
"""
Check if the real reconstruction matches the real part
of the complex reconstruction.
"""
sino, angles = create_test_sino_2d()
parameters = get_test_parameter_set(2)
# complex
r = list()
for p in parameters:
f = odtbrain.backpropagate_2d(sino, angles, padval=0, **p)
r.append(f)
# real
r2 = list()
for p in parameters:
f = odtbrain.backpropagate_2d(sino,
angles,
padval=0,
onlyreal=True,
**p)
r2.append(f)
assert np.allclose(np.array(r).real, np.array(r2))
def test_angle_swap():
"""
Test if everything still works, when angles are swapped.
"""
sino, angles = create_test_sino_2d()
# remove elements so that we can see that weighting works
angles = angles[:-2]
sino = sino[:-2, :]
parameters = get_test_parameter_set(2)
# reference
r1 = []
for p in parameters:
f1 = odtbrain.backpropagate_2d(sino, angles, weight_angles=True, **p)
r1.append(f1)
# change order of angles
order = np.argsort(angles % .5)
angles = angles[order]
sino = sino[order, :]
r2 = []
for p in parameters:
f2 = odtbrain.backpropagate_2d(sino, angles, weight_angles=True, **p)
r2.append(f2)
assert np.allclose(np.array(r1).flatten().view(float),
np.array(r2).flatten().view(float))
lD = cfg["lD"] # measurement distance in wavelengths
lC = cfg["lC"] # displacement from center of image
size = cfg["size"]
res = cfg["res"] # px/wavelengths
A = cfg["A"] # number of projections
#phantom = np.loadtxt(arc.open("mie_phantom.txt"))
x = np.arange(size)-size/2.0
X,Y = np.meshgrid(x,x)
rad_px = radius*res
phantom = np.array(((Y-lC*res)**2+X**2)<rad_px**2, dtype=np.float)*(ncyl-nmed)+nmed
# Born
u_sinB = (sino/u0*u0_single-u0_single) #fake born
fB = odt.backpropagate_2d(u_sinB, angles, res, nmed, lD*res)
nB = odt.odt_to_ri(fB, res, nmed)
# Rytov
u_sinR = odt.sinogram_as_rytov(sino/u0)
fR = odt.backpropagate_2d(u_sinR, angles, res, nmed, lD*res)
nR = odt.odt_to_ri(fR, res, nmed)
# Rytov 50
u_sinR50 = odt.sinogram_as_rytov((sino/u0)[::5,:])
fR50 = odt.backpropagate_2d(u_sinR50, angles[::5], res, nmed, lD*res)
nR50 = odt.odt_to_ri(fR50, res, nmed)
# Plot sinogram phase and amplitude
ph = unwrap.unwrap(np.angle(sino/u0))
## Setup background
t_RealBack = float('-1.60175172169E-02')
t_ImagBack = float('-1.85142597885E-02')
t_ComplexBack = t_RealBack + 1j*t_ImagBack
# t_SinoBack = np.tile(t_ComplexBack, t_SudutProj*t_SensorInterp).reshape(t_SudutProj, t_SensorInterp)
t_SinoBack = np.tile(t_ComplexBack, t_SudutInterp*t_SensorInterp).reshape(t_SudutInterp, t_SensorInterp)
# print(t_SinoBack)
## Prep for Reconstruksi Citra
t_Theta = np.linspace(0., 360., t_SudutInterp, endpoint=False)
## Do Fasa background corrected
t_SinoCorrected = t_SinoSudutInterp/t_SinoBack
## Do backpropagate 2D
u_sinR = odt.sinogram_as_rytov(t_SinoCorrected)
angles = np.linspace(0, 2*np.pi, t_SudutInterp, endpoint=False)
res = 9.0
nmed = 2.4
lD = 1.0
fR = odt.backpropagate_2d(u_sinR, angles, res, nmed, lD * res)
nR = odt.odt_to_ri(fR, res, nmed)
## plot data
fig, (ax1) = plt.subplots(1, 1)
ax1.imshow(ndimage.median_filter(nR.real*-1, size=7))
ax1.set_xlabel('pixel')
ax1.set_ylabel('pixel')
plt.show()
X, Y = np.meshgrid(x, x)
rad_px = radius * res
phantom = np.array(((Y - lC * res)**2 + X**2) < rad_px**2,
dtype=np.float) * (ncyl - nmed) + nmed
u_sinR = odt.sinogram_as_rytov(sino / u0)
# Rytov 200 projections
# remove 50 projections from total of 250 projections
remove200 = np.argsort(angles % .0002)[:50]
angles200 = np.delete(angles, remove200, axis=0)
u_sinR200 = np.delete(u_sinR, remove200, axis=0)
ph200 = unwrap.unwrap(np.angle(sino / u0))
ph200[remove200] = 0
fR200 = odt.backpropagate_2d(u_sinR200, angles200, res, nmed, lD * res)
nR200 = odt.odt_to_ri(fR200, res, nmed)
fR200nw = odt.backpropagate_2d(u_sinR200,
angles200,
res,
nmed,
lD * res,
weight_angles=False)
nR200nw = odt.odt_to_ri(fR200nw, res, nmed)
# Rytov 50 projections
remove50 = np.argsort(angles % .0002)[:200]
angles50 = np.delete(angles, remove50, axis=0)
u_sinR50 = np.delete(u_sinR, remove50, axis=0)
ph50 = unwrap.unwrap(np.angle(sino / u0))
ph50[remove50] = 0
lD = cfg["lD"] # measurement distance in wavelengths
lC = cfg["lC"] # displacement from center of image
size = cfg["size"]
res = cfg["res"] # px/wavelengths
A = cfg["A"] # number of projections
x = np.arange(size) - size / 2
X, Y = np.meshgrid(x, x)
rad_px = radius * res
phantom = np.array(((Y - lC * res)**2 + X**2) < rad_px**2,
dtype=np.float) * (ncyl - nmed) + nmed
# Born
u_sinB = (sino / u0 * u0_single - u0_single) # fake born
fB = odt.backpropagate_2d(u_sinB, angles, res, nmed, lD * res)
nB = odt.odt_to_ri(fB, res, nmed)
# Rytov
u_sinR = odt.sinogram_as_rytov(sino / u0)
fR = odt.backpropagate_2d(u_sinR, angles, res, nmed, lD * res)
nR = odt.odt_to_ri(fR, res, nmed)
# Rytov 50
u_sinR50 = odt.sinogram_as_rytov((sino / u0)[::5, :])
fR50 = odt.backpropagate_2d(u_sinR50, angles[::5], res, nmed, lD * res)
nR50 = odt.odt_to_ri(fR50, res, nmed)
# Plot sinogram phase and amplitude
ph = odt.sinogram_as_radon(sino / u0)
x = np.arange(size) - size / 2.0
X, Y = np.meshgrid(x, x)
rad_px = radius * res
phantom = np.array(((Y - lC * res)**2 + X**2) < rad_px**2,
dtype=np.float) * (ncyl - nmed) + nmed
u_sinR = odt.sinogram_as_rytov(sino / u0)
# Rytov 100 projections evenly distributed
removeeven = np.argsort(angles % .002)[:150]
angleseven = np.delete(angles, removeeven, axis=0)
u_sinReven = np.delete(u_sinR, removeeven, axis=0)
pheven = odt.sinogram_as_radon(sino / u0)
pheven[removeeven] = 0
fReven = odt.backpropagate_2d(u_sinReven, angleseven, res, nmed, lD * res)
nReven = odt.odt_to_ri(fReven, res, nmed)
fRevennw = odt.backpropagate_2d(u_sinReven,
angleseven,
res,
nmed,
lD * res,
weight_angles=False)
nRevennw = odt.odt_to_ri(fRevennw, res, nmed)
# Rytov 100 projections more than 180
removemiss = 249 - \
np.concatenate((np.arange(100), 100 + np.arange(150)[::3]))
anglesmiss = np.delete(angles, removemiss, axis=0)
u_sinRmiss = np.delete(u_sinR, removemiss, axis=0)
phmiss = odt.sinogram_as_radon(sino / u0)
x = np.arange(size)-size/2.0
X,Y = np.meshgrid(x,x)
rad_px = radius*res
phantom = np.array(((Y-lC*res)**2+X**2)<rad_px**2, dtype=np.float)*(ncyl-nmed)+nmed
u_sinR = odt.sinogram_as_rytov(sino/u0)
# Rytov 200 projections
# remove 50 projections from total of 250 projections
remove200 = np.argsort(angles % .002)[:50]
angles200 = np.delete(angles, remove200, axis=0)
u_sinR200 = np.delete(u_sinR, remove200, axis=0)
ph200 = unwrap.unwrap(np.angle(sino/u0))
ph200[remove200] = 0
fR200 = odt.backpropagate_2d(u_sinR200, angles200, res, nmed, lD*res)
nR200 = odt.odt_to_ri(fR200, res, nmed)
fR200nw = odt.backpropagate_2d(u_sinR200, angles200, res, nmed, lD*res, weight_angles=False)
nR200nw = odt.odt_to_ri(fR200nw, res, nmed)
# Rytov 50 projections
remove50 = np.argsort(angles % .002)[:200]
angles50 = np.delete(angles, remove50, axis=0)
u_sinR50 = np.delete(u_sinR, remove50, axis=0)
ph50 = unwrap.unwrap(np.angle(sino/u0))
ph50[remove50] = 0
fR50 = odt.backpropagate_2d(u_sinR50, angles50, res, nmed, lD*res)
nR50 = odt.odt_to_ri(fR50, res, nmed)
fR50nw = odt.backpropagate_2d(u_sinR50, angles50, res, nmed, lD*res, weight_angles=False)
def backpropagate_sinogram(
sinogram,
angles,
approx,
res,
nm,
ld=0,
):
"""Backpropagate a 2D or 3D sinogram
Parameters
----------
sinogram: complex ndarray
The scattered field data
angles: 1d ndarray
The angles at which the sinogram data were recorded
approx: str
Approximation to use, one of ["radon", "born", "rytov"]
res: float
Size of vacuum wavelength in pixels
nm: float
Refractive index of surrounding medium
ld: float
Reconstruction distance. Values !=0 only make sense for the
Born approximation (which itself is not very usable).
See the ODTbrain documentation for more information.
Returns
-------
ri: ndarray
The 2D or 3D reconstructed refractive index
"""
sshape = len(sinogram.shape)
assert sshape in [2, 3], "sinogram must have dimension 2 or 3"
uSin = sinogram
assert approx in ["radon", "born", "rytov"]
if approx == "rytov":
uSin = odt.sinogram_as_rytov(uSin)
elif approx == "radon":
uSin = odt.sinogram_as_radon(uSin)
if approx in ["born", "rytov"]:
# Perform reconstruction with ODT
if sshape == 2:
f = odt.backpropagate_2d(uSin,
angles=angles,
res=res,
nm=nm,
lD=ld)
else:
f = odt.backpropagate_3d(uSin,
angles=angles,
res=res,
nm=nm,
lD=ld)
ri = odt.odt_to_ri(f, res, nm)
else:
# Perform reconstruction with OPT
# works in 2d and 3d
f = rt.backproject(uSin, angles=angles)
ri = odt.opt_to_ri(f, res, nm)
return ri
print("Example: Backpropagation from 2d FDTD simulations")
print("Refractive index of medium:", cfg["nm"])
print("Measurement position from object center:", cfg["lD"])
print("Wavelength sampling:", cfg["res"])
print("Performing backpropagation.")
## Apply the Rytov approximation
sinoRytov = odt.sinogram_as_rytov(sino)
## perform backpropagation to obtain object function f
f = odt.backpropagate_2d( uSin=sinoRytov,
angles=angles,
res=cfg["res"],
nm=cfg["nm"],
lD=cfg["lD"]*cfg["res"]
)
## compute refractive index n from object function
n = odt.odt_to_ri(f, res=cfg["res"], nm=cfg["nm"])
## compare phantom and reconstruction in plot
fig, axes = plt.subplots(1, 3, figsize=(12,4), dpi=300)
axes[0].set_title("FDTD phantom")
axes[0].imshow(phantom, vmin=phantom.min(), vmax=phantom.max())
sino_phase = np.unwrap(np.angle(sino), axis=1)
axes[0].set_xlabel("x")
f_phantom="fdtd_phantom.txt",
)
print("Example: Backpropagation from 2D FDTD simulations")
print("Refractive index of medium:", cfg["nm"])
print("Measurement position from object center:", cfg["lD"])
print("Wavelength sampling:", cfg["res"])
print("Performing backpropagation.")
# Apply the Rytov approximation
sino_rytov = odt.sinogram_as_rytov(sino)
# perform backpropagation to obtain object function f
f = odt.backpropagate_2d(uSin=sino_rytov,
angles=angles,
res=cfg["res"],
nm=cfg["nm"],
lD=cfg["lD"] * cfg["res"])
# compute refractive index n from object function
n = odt.odt_to_ri(f, res=cfg["res"], nm=cfg["nm"])
# compare phantom and reconstruction in plot
fig, axes = plt.subplots(1, 3, figsize=(8, 2.8))
axes[0].set_title("FDTD phantom")
axes[0].imshow(phantom, vmin=phantom.min(), vmax=phantom.max())
sino_phase = np.unwrap(np.angle(sino), axis=1)
axes[1].set_title("phase sinogram")
axes[1].imshow(sino_phase,
#phantom = np.loadtxt(arc.open("mie_phantom.txt"))
x = np.arange(size)-size/2.0
X,Y = np.meshgrid(x,x)
rad_px = radius*res
phantom = np.array(((Y-lC*res)**2+X**2)<rad_px**2, dtype=np.float)*(ncyl-nmed)+nmed
u_sinR = odt.sinogram_as_rytov(sino/u0)
# Rytov 100 projections evenly distributed
removeeven = np.argsort(angles % .002)[:150]
angleseven = np.delete(angles, removeeven, axis=0)
u_sinReven = np.delete(u_sinR, removeeven, axis=0)
pheven = unwrap.unwrap(np.angle(sino/u0))
pheven[removeeven] = 0
fReven = odt.backpropagate_2d(u_sinReven, angleseven, res, nmed, lD*res)
nReven = odt.odt_to_ri(fReven, res, nmed)
fRevennw = odt.backpropagate_2d(u_sinReven, angleseven, res, nmed, lD*res, weight_angles=False)
nRevennw = odt.odt_to_ri(fRevennw, res, nmed)
# Rytov 100 projections more than 180
removemiss = 249 - np.concatenate((np.arange(100), 100+np.arange(150)[::3]))
anglesmiss = np.delete(angles, removemiss, axis=0)
u_sinRmiss = np.delete(u_sinR, removemiss, axis=0)
phmiss = unwrap.unwrap(np.angle(sino/u0))
phmiss[removemiss] = 0
fRmiss = odt.backpropagate_2d(u_sinRmiss, anglesmiss, res, nmed, lD*res)
nRmiss = odt.odt_to_ri(fRmiss, res, nmed)
fRmissnw = odt.backpropagate_2d(u_sinRmiss, anglesmiss, res, nmed, lD*res, weight_angles=False)
