def f_Refl_Thick_Film_and_Substrate_fit(Data):
strain = Data[0]
DW = Data[1]
dat = Data[2]
wl = dat[0]
t = dat[1]
N = dat[2]
phi = dat[3]
t_l = dat[4]
thB_S = dat[6]
G = dat[7]
F0 = dat[8]
FH = dat[9]
FmH = dat[10]
b_Sub = dat[11]
thB_Sub = dat[12]
G_Sub = dat[13]
F0_Sub = dat[14]
FH_Sub = dat[15]
FmH_Sub = dat[16]
t_film = dat[17]
dw_film = dat[18]
th = dat[19]
delta_t = t_film - t
thB = thB_S - strain * tan(thB_S) # angle de Bragg dans chaque lamelle
temp1 = -b_Sub*(th-thB_Sub)*sin(2*thB_Sub) - (0.5*G_Sub*F0_Sub[0]*(1-b_Sub))
temp2 = (abs(b_Sub)**0.5) * G_Sub * (FH_Sub[0]*FmH_Sub[0])**0.5
eta = temp1/temp2
res = (eta - signe(eta.real)*((eta*eta - 1)**0.5))
g0 = sin(thB[0] - phi) # gamma 0
gH = -sin(thB[0] + phi) # gamma H
b = g0 / gH
T = pi * G * ((FH[0]*FmH[0])**0.5) * delta_t * dw_film / (wl * (abs(g0*gH)**0.5))
eta = (-b*(th-thB[0])*sin(2*thB_S) - 0.5*G*F0[0]*(1-b)) / ((abs(b)**0.5) * G * dw_film * (FH[0]*FmH[0])**0.5)
S1 = (res - eta + (eta*eta-1)**0.5)*exp(-1j*T*(eta*eta-1)**0.5)
S2 = (res - eta - (eta*eta-1)**0.5)*exp(1j*T*(eta*eta-1)**0.5)
res = (eta + ((eta*eta-1)**0.5) * ((S1+S2)/(S1-S2)))
n = 1
while (n <= N):
g0 = sin(thB[n] - phi) # gamma 0
gH = -sin(thB[n] + phi) # gamma H
b = g0 / gH
T = pi * G * ((FH[n]*FmH[n])**0.5) * t_l * DW[n] * dw_film / (wl * (abs(g0*gH)**0.5))
eta = (-b*(th-thB[n])*sin(2*thB_S) - 0.5*G*F0[n]*(1-b)) / ((abs(b)**0.5) * G * DW[n] * dw_film * (FH[n]*FmH[n])**0.5 )
S1 = (res - eta + (eta*eta-1)**0.5)*exp(-1j*T*(eta*eta-1)**0.5)
S2 = (res - eta - (eta*eta-1)**0.5)*exp(1j*T*(eta*eta-1)**0.5)
res = (eta + ((eta*eta-1)**0.5) * ((S1+S2)/(S1-S2)))
n += 1
return res
def f_Refl_Substrate_fit(Data):
a = P4Rm()
G = a.ParamDict['G']
thB_S = a.ParamDict['thB_S']
resol = a.ParamDict['resol']
b_S = a.ParamDict['b_S']
FH = a.ParamDict['FH']
FmH = a.ParamDict['FmH']
F0 = a.ParamDict['F0']
th = a.ParamDict['th']
eta = (-b_S*(th-thB_S)*sin(2*thB_S) - 0.5*G*F0[0]*(1-b_S)) / ((abs(b_S)**0.5) * G * (FH[0]*FmH[0])**0.5)
res = (eta - signe(eta.real)*((eta*eta - 1)**0.5)) * (FH[0] / FmH[0])**0.5
return convolve(abs(res)**2, resol, mode='same')
def f_Refl_Default():
a = P4Rm()
wl = a.AllDataDict['wavelength']
t = a.AllDataDict['damaged_depth']
N = a.AllDataDict['number_slices']
G = a.ParamDict['G']
thB_S = a.ParamDict['thB_S']
resol = a.ParamDict['resol']
b_S = a.ParamDict['b_S']
phi = a.ConstDict['phi']
t_l = a.ParamDict['t_l']
z = a.ParamDict['z']
FH = a.ParamDict['FH']
FmH = a.ParamDict['FmH']
F0 = a.ParamDict['F0']
sp = a.ParamDict['sp']
dwp = a.ParamDict['dwp']
th = a.ParamDict['th']
spline_DW = a.splinenumber[1]
spline_strain = a.splinenumber[0]
param = a.ParamDict['par']
strain = f_strain(z, param[:len(sp):], t, spline_strain)
DW = f_DW(z, param[len(sp):len(sp) + len(dwp):], t, spline_DW)
thB = thB_S - strain * tan(thB_S) # angle de Bragg dans chaque lamelle
eta = ((-b_S * (th - thB_S) * sin(2 * thB_S) - 0.5 * G * F0[0] *
(1 - b_S)) / ((abs(b_S)**0.5) * G * (FH[0] * FmH[0])**0.5))
res = (eta - signe(eta.real) * ((eta * eta - 1)**0.5))
n = 1
while (n <= N):
g0 = sin(thB[n] - phi) # gamma 0
gH = -sin(thB[n] + phi) # gamma H
b = g0 / gH
T = (pi * G * ((FH[n] * FmH[n])**0.5) * t_l * DW[n] /
(wl * (abs(g0 * gH)**0.5)))
eta = ((-b * (th - thB[n]) * sin(2 * thB_S) - 0.5 * G * F0[n] *
(1 - b)) / ((abs(b)**0.5) * G * DW[n] * (FH[n] * FmH[n])**0.5))
S1 = (res - eta + sqrt(eta * eta - 1)) * exp(
-1j * T * sqrt(eta * eta - 1))
S2 = (res - eta - sqrt(eta * eta - 1)) * exp(
1j * T * sqrt(eta * eta - 1))
res = (eta + ((eta * eta - 1)**0.5) * ((S1 + S2) / (S1 - S2)))
n += 1
return convolve(abs(res)**2, resol, mode='same')
def f_Refl_Substrate_fit(Data):
a = P4Rm()
G = a.ParamDict['G']
thB_S = a.ParamDict['thB_S']
resol = a.ParamDict['resol']
b_S = a.ParamDict['b_S']
FH = a.ParamDict['FH']
FmH = a.ParamDict['FmH']
F0 = a.ParamDict['F0']
th = a.ParamDict['th']
eta = (-b_S * (th - thB_S) * sin(2 * thB_S) - 0.5 * G * F0[0] *
(1 - b_S)) / ((abs(b_S)**0.5) * G * (FH[0] * FmH[0])**0.5)
res = (eta - signe(eta.real) *
((eta * eta - 1)**0.5)) * (FH[0] / FmH[0])**0.5
return convolve(abs(res)**2, resol, mode='same')
def f_Refl_Default():
a = P4Rm()
wl = a.AllDataDict['wavelength']
t = a.AllDataDict['damaged_depth']
N = a.AllDataDict['number_slices']
G = a.ParamDict['G']
thB_S = a.ParamDict['thB_S']
resol = a.ParamDict['resol']
b_S = a.ParamDict['b_S']
phi = a.ConstDict['phi']
t_l = a.ParamDict['t_l']
z = a.ParamDict['z']
FH = a.ParamDict['FH']
FmH = a.ParamDict['FmH']
F0 = a.ParamDict['F0']
sp = a.ParamDict['sp']
dwp = a.ParamDict['dwp']
th = a.ParamDict['th']
spline_DW = a.splinenumber[1]
spline_strain = a.splinenumber[0]
param = a.ParamDict['par']
strain = f_strain(z, param[:len(sp):], t, spline_strain)
DW = f_DW(z, param[len(sp):len(sp)+len(dwp):], t, spline_DW)
thB = thB_S - strain * tan(thB_S) # angle de Bragg dans chaque lamelle
eta = ((-b_S*(th-thB_S)*sin(2*thB_S) - 0.5*G*F0[0]*(1-b_S)) /
((abs(b_S)**0.5) * G * (FH[0]*FmH[0])**0.5))
res = (eta - signe(eta.real)*((eta*eta - 1)**0.5))
n = 1
while (n <= N):
g0 = sin(thB[n] - phi) # gamma 0
gH = -sin(thB[n] + phi) # gamma H
b = g0 / gH
T = (pi * G * ((FH[n] * FmH[n])**0.5) * t_l * DW[n] /
(wl * (abs(g0 * gH)**0.5)))
eta = ((-b*(th-thB[n])*sin(2*thB_S) - 0.5*G*F0[n]*(1-b)) /
((abs(b)**0.5) * G * DW[n] * (FH[n]*FmH[n])**0.5))
S1 = (res - eta + sqrt(eta*eta-1))*exp(-1j*T*sqrt(eta*eta-1))
S2 = (res - eta - sqrt(eta*eta-1))*exp(1j*T*sqrt(eta*eta-1))
res = (eta + ((eta*eta-1)**0.5) * ((S1+S2)/(S1-S2)))
n += 1
return convolve(abs(res)**2, resol, mode='same')
def f_Refl_Default_fit(Data):
strain = Data[0]
DW = Data[1]
dat = Data[2]
wl = dat[0]
N = dat[2]
phi = dat[3]
t_l = dat[4]
b_S = dat[5]
thB_S = dat[6]
G = dat[7]
F0 = dat[8]
FH = dat[9]
FmH = dat[10]
th = dat[19]
thB = thB_S - strain * tan(thB_S) # angle de Bragg dans chaque lamelle
eta = ((-b_S * (th - thB_S) * sin(2 * thB_S) - 0.5 * G * F0[0] *
(1 - b_S)) / ((abs(b_S)**0.5) * G * (FH[0] * FmH[0])**0.5))
res = (eta - signe(eta.real) * ((eta * eta - 1)**0.5))
n = 1
while (n <= N):
g0 = sin(thB[n] - phi) # gamma 0
gH = -sin(thB[n] + phi) # gamma H
b = g0 / gH
T = (pi * G * ((FH[n] * FmH[n])**0.5) * t_l * DW[n] /
(wl * (abs(g0 * gH)**0.5)))
eta = ((-b * (th - thB[n]) * sin(2 * thB_S) - 0.5 * G * F0[n] *
(1 - b)) / ((abs(b)**0.5) * G * DW[n] * (FH[n] * FmH[n])**0.5))
S1 = (res - eta + sqrt(eta * eta - 1)) * exp(
-1j * T * sqrt(eta * eta - 1))
S2 = (res - eta - sqrt(eta * eta - 1)) * exp(
1j * T * sqrt(eta * eta - 1))
res = (eta + ((eta * eta - 1)**0.5) * ((S1 + S2) / (S1 - S2)))
n += 1
return res
def f_Refl_Default_fit(Data):
strain = Data[0]
DW = Data[1]
dat = Data[2]
wl = dat[0]
N = dat[2]
phi = dat[3]
t_l = dat[4]
b_S = dat[5]
thB_S = dat[6]
G = dat[7]
F0 = dat[8]
FH = dat[9]
FmH = dat[10]
th = dat[19]
thB = thB_S - strain * tan(thB_S) # angle de Bragg dans chaque lamelle
eta = ((-b_S*(th-thB_S)*sin(2*thB_S) - 0.5*G*F0[0]*(1-b_S)) /
((abs(b_S)**0.5) * G * (FH[0]*FmH[0])**0.5))
res = (eta - signe(eta.real)*((eta*eta - 1)**0.5))
n = 1
while (n <= N):
g0 = sin(thB[n] - phi) # gamma 0
gH = -sin(thB[n] + phi) # gamma H
b = g0 / gH
T = (pi * G * ((FH[n] * FmH[n])**0.5) * t_l * DW[n] /
(wl * (abs(g0 * gH)**0.5)))
eta = ((-b*(th-thB[n])*sin(2*thB_S) - 0.5*G*F0[n]*(1-b)) /
((abs(b)**0.5) * G * DW[n] * (FH[n]*FmH[n])**0.5))
S1 = (res - eta + sqrt(eta*eta-1))*exp(-1j*T*sqrt(eta*eta-1))
S2 = (res - eta - sqrt(eta*eta-1))*exp(1j*T*sqrt(eta*eta-1))
res = (eta + ((eta*eta-1)**0.5) * ((S1+S2)/(S1-S2)))
n += 1
return res
def f_Refl_Thick_Film_and_Substrate():
a = P4Rm()
wl = a.AllDataDict['wavelength']
t = a.AllDataDict['damaged_depth']
N = a.AllDataDict['number_slices']
t_film = a.AllDataDict['film_thick']
dw_film = a.AllDataDict['dw_thick']
G = a.ParamDict['G']
thB_S = a.ParamDict['thB_S']
resol = a.ParamDict['resol']
phi = a.ConstDict['phi']
t_l = a.ParamDict['t_l']
z = a.ParamDict['z']
FH = a.ParamDict['FH']
FmH = a.ParamDict['FmH']
F0 = a.ParamDict['F0']
sp = a.ParamDict['sp']
dwp = a.ParamDict['dwp']
th = a.ParamDict['th']
spline_DW = a.splinenumber[1]
spline_strain = a.splinenumber[0]
param = a.ParamDict['par']
b_Sub = a.ParamDict['b_S_s']
thB_Sub = a.ParamDict['thB_S_s']
G_Sub = a.ParamDict['G_s']
F0_Sub = a.ParamDict['F0_s']
FH_Sub = a.ParamDict['FH_s']
FmH_Sub = a.ParamDict['FmH_s']
delta_t = t_film - t
strain = f_strain(z, param[:len(sp):], t, spline_strain)
DW = f_DW(z, param[len(sp):len(sp)+len(dwp):], t, spline_DW)
thB = thB_S - strain * tan(thB_S) # angle de Bragg dans chaque lamelle
temp1 = -b_Sub*(th-thB_Sub)*sin(2*thB_Sub) - (0.5*G_Sub*F0_Sub[0]*(1-b_Sub))
temp2 = (abs(b_Sub)**0.5) * G_Sub * (FH_Sub[0]*FmH_Sub[0])**0.5
eta = temp1/temp2
res = (eta - signe(eta.real)*((eta*eta - 1)**0.5))
g0 = sin(thB[0] - phi) # gamma 0
gH = -sin(thB[0] + phi) # gamma H
b = g0 / gH
T = pi * G * ((FH[0]*FmH[0])**0.5) * delta_t * dw_film / (wl * (abs(g0*gH)**0.5))
eta = (-b*(th-thB[0])*sin(2*thB_S) - 0.5*G*F0[0]*(1-b)) / ((abs(b)**0.5) * G * dw_film * (FH[0]*FmH[0])**0.5)
S1 = (res - eta + (eta*eta-1)**0.5)*exp(-1j*T*(eta*eta-1)**0.5)
S2 = (res - eta - (eta*eta-1)**0.5)*exp(1j*T*(eta*eta-1)**0.5)
res = (eta + ((eta*eta-1)**0.5) * ((S1+S2)/(S1-S2)))
n = 1
while (n <= N):
g0 = sin(thB[n] - phi) # gamma 0
gH = -sin(thB[n] + phi) # gamma H
b = g0 / gH
T = pi * G * ((FH[n]*FmH[n])**0.5) * t_l * DW[n] * dw_film / (wl * (abs(g0*gH)**0.5))
eta = (-b*(th-thB[n])*sin(2*thB_S) - 0.5*G*F0[n]*(1-b)) / ((abs(b)**0.5) * G * DW[n] * dw_film * (FH[n]*FmH[n])**0.5)
S1 = (res - eta + (eta*eta-1)**0.5)*exp(-1j*T*(eta*eta-1)**0.5)
S2 = (res - eta - (eta*eta-1)**0.5)*exp(1j*T*(eta*eta-1)**0.5)
res = (eta + ((eta*eta-1)**0.5) * ((S1+S2)/(S1-S2)))
n += 1
return convolve(abs(res)**2, resol, mode='same')
def f_Refl_Thick_Film_and_Substrate():
a = P4Rm()
wl = a.AllDataDict['wavelength']
t = a.AllDataDict['damaged_depth']
N = a.AllDataDict['number_slices']
t_film = a.AllDataDict['film_thick']
dw_film = a.AllDataDict['dw_thick']
G = a.ParamDict['G']
thB_S = a.ParamDict['thB_S']
resol = a.ParamDict['resol']
phi = a.ConstDict['phi']
t_l = a.ParamDict['t_l']
z = a.ParamDict['z']
FH = a.ParamDict['FH']
FmH = a.ParamDict['FmH']
F0 = a.ParamDict['F0']
sp = a.ParamDict['sp']
dwp = a.ParamDict['dwp']
th = a.ParamDict['th']
spline_DW = a.splinenumber[1]
spline_strain = a.splinenumber[0]
param = a.ParamDict['par']
b_Sub = a.ParamDict['b_S_s']
thB_Sub = a.ParamDict['thB_S_s']
G_Sub = a.ParamDict['G_s']
F0_Sub = a.ParamDict['F0_s']
FH_Sub = a.ParamDict['FH_s']
FmH_Sub = a.ParamDict['FmH_s']
delta_t = t_film - t
strain = f_strain(z, param[:len(sp):], t, spline_strain)
DW = f_DW(z, param[len(sp):len(sp) + len(dwp):], t, spline_DW)
thB = thB_S - strain * tan(thB_S) # angle de Bragg dans chaque lamelle
temp1 = -b_Sub * (th - thB_Sub) * sin(2 * thB_Sub) - (0.5 * G_Sub *
F0_Sub[0] *
(1 - b_Sub))
temp2 = (abs(b_Sub)**0.5) * G_Sub * (FH_Sub[0] * FmH_Sub[0])**0.5
eta = temp1 / temp2
res = (eta - signe(eta.real) * ((eta * eta - 1)**0.5))
g0 = sin(thB[0] - phi) # gamma 0
gH = -sin(thB[0] + phi) # gamma H
b = g0 / gH
T = pi * G * (
(FH[0] * FmH[0])**0.5) * delta_t * dw_film / (wl * (abs(g0 * gH)**0.5))
eta = (-b * (th - thB[0]) * sin(2 * thB_S) - 0.5 * G * F0[0] *
(1 - b)) / ((abs(b)**0.5) * G * dw_film * (FH[0] * FmH[0])**0.5)
S1 = (res - eta + (eta * eta - 1)**0.5) * exp(-1j * T *
(eta * eta - 1)**0.5)
S2 = (res - eta - (eta * eta - 1)**0.5) * exp(1j * T *
(eta * eta - 1)**0.5)
res = (eta + ((eta * eta - 1)**0.5) * ((S1 + S2) / (S1 - S2)))
n = 1
while (n <= N):
g0 = sin(thB[n] - phi) # gamma 0
gH = -sin(thB[n] + phi) # gamma H
b = g0 / gH
T = pi * G * ((FH[n] * FmH[n])**
0.5) * t_l * DW[n] * dw_film / (wl * (abs(g0 * gH)**0.5))
eta = (-b * (th - thB[n]) * sin(2 * thB_S) - 0.5 * G * F0[n] *
(1 - b)) / ((abs(b)**0.5) * G * DW[n] * dw_film *
(FH[n] * FmH[n])**0.5)
S1 = (res - eta + (eta * eta - 1)**0.5) * exp(-1j * T *
(eta * eta - 1)**0.5)
S2 = (res - eta - (eta * eta - 1)**0.5) * exp(1j * T *
(eta * eta - 1)**0.5)
res = (eta + ((eta * eta - 1)**0.5) * ((S1 + S2) / (S1 - S2)))
n += 1
return convolve(abs(res)**2, resol, mode='same')
def f_Refl_Thick_Film_and_Substrate_fit(Data):
strain = Data[0]
DW = Data[1]
dat = Data[2]
wl = dat[0]
t = dat[1]
N = dat[2]
phi = dat[3]
t_l = dat[4]
thB_S = dat[6]
G = dat[7]
F0 = dat[8]
FH = dat[9]
FmH = dat[10]
b_Sub = dat[11]
thB_Sub = dat[12]
G_Sub = dat[13]
F0_Sub = dat[14]
FH_Sub = dat[15]
FmH_Sub = dat[16]
t_film = dat[17]
dw_film = dat[18]
th = dat[19]
delta_t = t_film - t
thB = thB_S - strain * tan(thB_S) # angle de Bragg dans chaque lamelle
temp1 = -b_Sub * (th - thB_Sub) * sin(2 * thB_Sub) - (0.5 * G_Sub *
F0_Sub[0] *
(1 - b_Sub))
temp2 = (abs(b_Sub)**0.5) * G_Sub * (FH_Sub[0] * FmH_Sub[0])**0.5
eta = temp1 / temp2
res = (eta - signe(eta.real) * ((eta * eta - 1)**0.5))
g0 = sin(thB[0] - phi) # gamma 0
gH = -sin(thB[0] + phi) # gamma H
b = g0 / gH
T = pi * G * (
(FH[0] * FmH[0])**0.5) * delta_t * dw_film / (wl * (abs(g0 * gH)**0.5))
eta = (-b * (th - thB[0]) * sin(2 * thB_S) - 0.5 * G * F0[0] *
(1 - b)) / ((abs(b)**0.5) * G * dw_film * (FH[0] * FmH[0])**0.5)
S1 = (res - eta + (eta * eta - 1)**0.5) * exp(-1j * T *
(eta * eta - 1)**0.5)
S2 = (res - eta - (eta * eta - 1)**0.5) * exp(1j * T *
(eta * eta - 1)**0.5)
res = (eta + ((eta * eta - 1)**0.5) * ((S1 + S2) / (S1 - S2)))
n = 1
while (n <= N):
g0 = sin(thB[n] - phi) # gamma 0
gH = -sin(thB[n] + phi) # gamma H
b = g0 / gH
T = pi * G * ((FH[n] * FmH[n])**
0.5) * t_l * DW[n] * dw_film / (wl * (abs(g0 * gH)**0.5))
eta = (-b * (th - thB[n]) * sin(2 * thB_S) - 0.5 * G * F0[n] *
(1 - b)) / ((abs(b)**0.5) * G * DW[n] * dw_film *
(FH[n] * FmH[n])**0.5)
S1 = (res - eta + (eta * eta - 1)**0.5) * exp(-1j * T *
(eta * eta - 1)**0.5)
S2 = (res - eta - (eta * eta - 1)**0.5) * exp(1j * T *
(eta * eta - 1)**0.5)
res = (eta + ((eta * eta - 1)**0.5) * ((S1 + S2) / (S1 - S2)))
n += 1
return res
