def correl_swsw(self, angle, nz1, nz2, h1, h2, method='quad'):
"""Correlation coeficients between two spherical waves."""
alpha = angle * 4.85*1.e-6
R = self.pupil_diameter / 2.
R1 = (h1-self.h_profile) / h1 * R
R2 = (h2-self.h_profile) / h2 * R
zeta = alpha * self.h_profile / R1
w = R2 / R1
Lam = 2. * np.pi * R1 / self.large_scale
n1, m1 = zernike.noll2zern(nz1)
n2, m2 = zernike.noll2zern(nz2)
k1, k2 = _kvalues(n1, n2, m1, m2, nz1, nz2)
results = np.zeros(len(self.h_profile))
for idx in np.arange(len(self.h_profile)):
if method == 'quad':
result_quad = quad(_chassat_integral, 0, np.inf, args=(zeta[idx], Lam[idx], w[idx], k1, k2, n1, n2, m1, m2))
results[idx] = result_quad[0] * self.cn2[idx] * R1[idx]**(5./3.)
elif method == 'romberg':
result_quad = romberg(_modified_chassat, 1.e-26,np.pi/2., args=(zeta[idx], Lam[idx], w[idx], k1, k2, n1, n2, m1, m2), vec_func = False)
results[idx] = result_quad * self.cn2[idx] * R1[idx]**(5./3.)
if len(results) < 2:
final_integral = results / (self.cn2 * R1**(5./3.))
else:
final_integral = trapz(results, x=self.h_profile) / trapz(self.cn2 * R1**(5./3.), x=self.h_profile)
final_integral = 3.895 * (-1.)**((n1+n2-m1-m2)/2.) * np.sqrt((n1+1.)*(n2+1.)) * self.dr0**(5./3.) * final_integral
return final_integral
def compmask(nz1, nz2):
first = 2
masku = np.zeros((nz1,nz2))
for i in range(nz1):
for j in range(i, nz2):
masku[i,j] = (zernike.noll2zern(i+first)[1] % 2) == (zernike.noll2zern(j+first)[1] % 2)
return masku.astype(int)
def correl_swsw(angle,
nz1,
nz2,
h1,
h2,
pupil_diameter,
cn2,
h_profile,
large_scale,
method='quad'):
"""Correlation coeficients between two spherical waves."""
alpha = angle * 4.85 * 1.e-6
R = pupil_diameter / 2.
R1 = (h1 - h_profile) / h1 * R
R2 = (h2 - h_profile) / h2 * R
zeta = alpha * h_profile / R1
w = R2 / R1
Lam = 2. * np.pi * R1 / large_scale
n1, m1 = zernike.noll2zern(nz1)
n2, m2 = zernike.noll2zern(nz2)
k1, k2 = _kvalues(n1, n2, m1, m2, nz1, nz2)
results = np.zeros(len(h_profile))
for idx in np.arange(len(h_profile)):
if method == 'quad':
result_quad = quad(_chassat_integral,
0,
np.inf,
args=(zeta[idx], Lam[idx], w[idx], k1, k2, n1,
n2, m1, m2))
results[idx] = result_quad[0] * cn2[idx] * R1[idx]**(5. / 3.)
elif method == 'romberg':
result_quad = romberg(_modified_chassat,
1.e-26,
np.pi / 2.,
args=(zeta[idx], Lam[idx], w[idx], k1, k2,
n1, n2, m1, m2),
vec_func=False)
results[idx] = result_quad * cn2[idx] * R1[idx]**(5. / 3.)
if len(results) < 2:
final_integral = results / (cn2 * R1**(5. / 3.))
else:
final_integral = trapz(results, x=h_profile) / trapz(
cn2 * R1**(5. / 3.), x=h_profile)
final_integral = 3.895 * (-1.)**((n1 + n2 - m1 - m2) / 2.) * np.sqrt(
(n1 + 1.) * (n2 + 1.)) * final_integral
return final_integral
def Dfitting(self, lambdaim, fc_constant=0.37):
"""Fitting error structure function."""
rho, phi, mask = polar2(self.pixdiam, length=2*self.pixdiam, center=[self.pixdiam,self.pixdiam])
radial, azi = zernike.noll2zern(self.nz1)
tot_correletion_aiaj = np.zeros((2*self.pixdiam,2*self.pixdiam))
r0 = 1. / self.dr0
Fc = fc_constant * (radial + 1.)
for i in range(2*self.pixdiam):
for j in range(2*self.pixdiam):
lower_bound = 2. * np.pi * Fc * rho[i,j]
result_quad = quad(lambda x: x**(-8./3.)*(1.-jv(0,x)), lower_bound, 150.)
tot_correletion_aiaj[i,j] = result_quad[0] * (rho[i,j]/r0)**(5./3.)
return 0.023 * 2.**(11./3.) * np.pi**(8./3.) * tot_correletion_aiaj
def correl_osos_general(angle,
diam,
hsource1,
hsource2,
cn2,
profil_h,
dr0=1.,
num_zern1=2,
num_zern2=2,
gd_echelle=1.,
borne_min=1.e-6,
borne_max=1000.,
npas=1000):
num_poly1 = num_zern1
num_poly2 = num_zern2
L0 = gd_echelle
rayon = diam / 2.
Rayon_spherique1 = (hsource1 - profil_h) / hsource1 * rayon
Rayon_spherique2 = (hsource2 - profil_h) / hsource2 * rayon
nangle = len(angle)
nint = npas
radial1, asimut1 = zernike.noll2zern(num_poly1)
radial2, asimut2 = zernike.noll2zern(num_poly2)
if radial1 == 1:
borne_max = 100
else:
borne_max = 500
if borne_max > 1000:
borne_max = 1000.
if asimut1 == 0:
if asimut2 == 0: S1 = 1
if asimut2 != 0 and (num_poly2 % 2) == 0:
S1 = (-1.)**(asimut2) * np.sqrt(2.)
if asimut2 != 0 and (num_poly2 % 2) != 0: S1 = 0
if asimut1 != 0 and (num_poly1 % 2) == 0:
if asimut2 == 0: S1 = np.sqrt(2.)
if asimut2 != 0 and (num_poly2 % 2) == 0: S1 = (-1.)**(asimut2)
if asimut2 != 0 and (num_poly2 % 2) != 0: S1 = 0
if asimut1 != 0 and (num_poly1 % 2) != 0:
if asimut2 == 0: S1 = 0
if asimut2 != 0 and (num_poly2 % 2) == 0: S1 = 0
if asimut2 != 0 and (num_poly2 % 2) != 0: S1 = (-1.)**(asimut2 + 1)
if asimut1 == 0: S2 = 0.
if asimut1 != 0 and (num_poly1 % 2) == 0:
if asimut2 == 0: S2 = 0.
if asimut2 != 0 and (num_poly2 % 2) == 0:
if (asimut2 + asimut1) % 2 == 0:
S2 = 1
else:
if (asimut1 - asimut2) < 0:
S2 = -1
else:
S2 = 1
if asimut2 != 0 and (num_poly2 % 2) != 0: S2 = 0
if asimut1 != 0 and (num_poly1 % 2) != 0:
if asimut2 == 0: S2 = 0.
if asimut2 != 0 and (num_poly2 % 2) == 0: S2 = 0.
if asimut2 != 0 and (num_poly2 % 2) != 0:
if (asimut2 + asimut1) % 2 == 0:
S2 = 1.
else:
if (asimut1 - asimut2) < 0:
S2 = -1.
else:
S2 = 1.
alpha = 0.
correl_final = np.zeros(nangle)
bmin = borne_min
bmax = bmin * 100.
n_profil_h = len(profil_h)
for iii in range(0, nangle):
correl = 0.
alpha = angle[iii]
alpha = alpha * 4.85 * 1.e-6
for num in range(0, n_profil_h):
borne_max1 = borne_max
correl1 = 0.
test = 0
bmin = borne_min
bmax = bmin * 100.
hi = profil_h[num]
Rayon_s = Rayon_spherique1[num]
RatioR = Rayon_spherique2[num] / Rayon_spherique1[num]
if radial1 == 1:
test = 1
if hi * alpha / Rayon_s >= 10.:
borne_max1 = 100
if hi * alpha / Rayon_s >= 50.:
borne_max1 = 100
if hi * alpha / Rayon_s >= 100.:
borne_max1 = 50
if hi * alpha / Rayon_s >= 500.:
borne_max1 = 20
if hi * alpha / Rayon_s >= 1000.:
borne_max1 = 10
if hi * alpha / Rayon_s >= 5000.:
borne_max1 = 5
if hi * alpha / Rayon_s >= 20000.:
borne_max1 = 1
if hi * alpha / Rayon_s >= 100000.:
borne_max1 = 0.1
if hi * alpha / Rayon_s >= 500000.:
test = 0
else:
if radial1 == 2 and hi * alpha / Rayon_s <= 10.:
test = 1
if radial1 == 3 and hi * alpha / Rayon_s <= 10.:
test = 1
borne_max = 300
if radial1 == 4 and hi * alpha / Rayon_s <= 5.:
test = 1
borne_max = 200
if radial1 == 5 and hi * alpha / Rayon_s <= 5.:
test = 1
borne_max = 200
if radial1 == 6 and hi * alpha / Rayon_s <= 2.:
test = 1
borne_max = 100
if radial1 == 7 and hi * alpha / Rayon_s <= 2.:
test = 1
borne_max = 100.
if radial1 == 8 and hi * alpha / Rayon_s <= 2.:
test = 1
borne_max = 100.
if radial1 == 9 and hi * alpha / Rayon_s <= 2.:
test = 1
borne_max = 50.
if radial1 > 9 and hi * alpha / Rayon_s <= 2.:
test = 1
borne_max = 50.
if test == 1:
if alpha <= 1.e-5 and (asimut1 + asimut2) > 1.e-4 and np.abs(
asimut1 - asimut2) > 1.e-4:
correl1 = 0.
else:
while True:
correl1 = correl1 + calc_1_couche_s_num(
alpha, hi, Rayon_s, RatioR, radial1, radial2,
asimut1, asimut2, S1, S2, L0, nint, bmin, bmax)
bmin = bmax
bmax = bmax * 100.
if borne_max1 / bmax < 100.: break
correl1 = correl1 + calc_1_couche_s_num(
alpha, hi, Rayon_s, RatioR, radial1, radial2, asimut1,
asimut2, S1, S2, L0, nint, bmin, borne_max1)
correl1 = correl1 * cn2[num] * Rayon_s**(5. / 3.)
correl = correl + correl1
correl = 3.895 * (-1.)**(
(radial1 + radial2 - asimut1 - asimut2) / 2) * np.sqrt(
(radial1 + 1.) *
(radial2 + 1.)) * (dr0)**(5. / 3.) * correl / np.sum(
cn2 * Rayon_spherique1**(5. / 3.))
correl_final[iii] = correl
return correl_final