def calc_offspec_BA(self, show_plot=True, add_specular=True):
overlap = self.calc_overlap_BA()
offspec = sum(sum(overlap * array(self.dFTs)[:,:,:,newaxis], axis=0), axis=1) # first over layers, then Qy
if add_specular == True:
specular = ones((self.qx.shape[0], self.qy.shape[1], self.qz.shape[2]), dtype=complex128)
specular *= complex128(2)*pi/self.Lx * normgauss(self.qx, FWHM_to_sigma(2.0*pi/self.Lx), x0=0.0)
specular *= complex128(2)*pi/self.Ly * normgauss(self.qy, FWHM_to_sigma(2.0*pi/self.Ly), x0=0.0)
specular *= 2.0*1j*self.kz_in*self.wf_in.r*self.Lx*self.Ly
specular = sum(specular, axis=1)/self.qy.shape[1] # sum over Qy, taking average
self.specular = specular
offspec += specular
self.offspec_BA = offspec
if show_plot == True:
self.plot_offspec_BA()
def calc_gisans(self, alpha_in=None, show_plot=True, add_specular=False):
if alpha_in is not None:
self.update_Qs(alpha_in)
overlap = self.calc_overlap()
gisans = sum(sum(overlap * array(self.dFTs)[:,:,:,newaxis], axis=0), axis=0) # first over layers, then Qx
# now if you want to add specular back in...
if add_specular == True:
specular = ones((self.qx.shape[0], self.qy.shape[1], self.qz.shape[2]), dtype=complex128)
specular *= complex128(2)*pi/self.Lx * normgauss(self.qx, FWHM_to_sigma(2.0*pi/self.Lx), x0=0.0)
specular *= complex128(2)*pi/self.Ly * normgauss(self.qy, FWHM_to_sigma(2.0*pi/self.Ly), x0=0.0)
specular *= 2.0*1j*self.kz_in*self.wf_in.r*self.Lx*self.Ly
specular = sum(specular, axis=0)/self.qx.shape[0] # sum over Qx, taking average
self.specular = specular
gisans += specular
self.gisans = gisans
if show_plot == True:
self.plot_gisans()
def calc_offspec_BA(self, show_plot=True, add_specular=True):
overlap = self.calc_overlap_BA()
offspec = sum(sum(overlap * array(self.dFTs)[:, :, :, newaxis],
axis=0),
axis=1) # first over layers, then Qy
if add_specular == True:
specular = ones(
(self.qx.shape[0], self.qy.shape[1], self.qz.shape[2]),
dtype=complex128)
specular *= complex128(2) * pi / self.Lx * normgauss(
self.qx, FWHM_to_sigma(2.0 * pi / self.Lx), x0=0.0)
specular *= complex128(2) * pi / self.Ly * normgauss(
self.qy, FWHM_to_sigma(2.0 * pi / self.Ly), x0=0.0)
specular *= 2.0 * 1j * self.kz_in * self.wf_in.r * self.Lx * self.Ly
specular = sum(
specular,
axis=1) / self.qy.shape[1] # sum over Qy, taking average
self.specular = specular
offspec += specular
self.offspec_BA = offspec
if show_plot == True:
self.plot_offspec_BA()
def calc_gisans(self, alpha_in=None, show_plot=True, add_specular=False):
if alpha_in is not None:
self.update_Qs(alpha_in)
overlap = self.calc_overlap()
gisans = sum(sum(overlap * array(self.dFTs)[:, :, :, newaxis], axis=0),
axis=0) # first over layers, then Qx
# now if you want to add specular back in...
if add_specular == True:
specular = ones(
(self.qx.shape[0], self.qy.shape[1], self.qz.shape[2]),
dtype=complex128)
specular *= complex128(2) * pi / self.Lx * normgauss(
self.qx, FWHM_to_sigma(2.0 * pi / self.Lx), x0=0.0)
specular *= complex128(2) * pi / self.Ly * normgauss(
self.qy, FWHM_to_sigma(2.0 * pi / self.Ly), x0=0.0)
specular *= 2.0 * 1j * self.kz_in * self.wf_in.r * self.Lx * self.Ly
specular = sum(
specular,
axis=0) / self.qx.shape[0] # sum over Qx, taking average
self.specular = specular
gisans += specular
self.gisans = gisans
if show_plot == True:
self.plot_gisans()
def calc_gisans(self, alpha_in, show_plot=True, add_specular=False):
k0 = 2 * pi / self.wavelength
kz_in_0 = array([k0 * sin(alpha_in * pi / 180.0)], dtype=complex128)
kx_in_0 = array([k0 * cos(alpha_in * pi / 180.0)], dtype=complex128)
kz_out_0 = kz_in_0 - self.qz
self.kz_out_0 = kz_out_0
ky_out_0 = -self.qy
kx_out_0 = sqrt(k0**2 - kz_out_0[newaxis, newaxis, :]**2 -
ky_out_0[newaxis, :, newaxis]**2)
qx = kx_in_0 - kx_out_0
self.qx_derived = qx
kz_out_neg = kz_out_0 < 0
kz_in_neg = kz_in_0 < 0
wf_in = dwbaWavefunction((kz_in_0), self.SLDArray)
wf_out = dwbaWavefunction(
(-kz_out_0),
self.SLDArray) # solve 1d equation for time-reversed state
self.wf_in = wf_in
self.wf_out = wf_out
kz_in_l = wf_in.kz_l # inside the layers
#kz_in_l[:, kz_in_neg] *= -1.0
kz_in_p_l = -kz_in_l # prime
kz_out_l = -wf_out.kz_l # inside the layers
#kz_out_l[:, kz_out_neg] *= -1.0
kz_out_p_l = -kz_out_l # kz_f_prime in the Sinha paper notation
dz = self.SLDArray[1:-1, 1][:, newaxis]
zs = cumsum(self.SLDArray[1:-1, 1]) - self.SLDArray[
1, 1] # start at zero with first layer
z_array = array(zs)[:, newaxis]
thickness = sum(self.SLDArray[1:-1, 1])
qrt_inside = -kz_in_l[1:-1] - kz_out_l[1:-1]
qtt_inside = -kz_in_l[1:-1] + kz_out_l[1:-1]
qtr_inside = +kz_in_l[1:-1] + kz_out_l[1:-1]
qrr_inside = +kz_in_l[1:-1] - kz_out_l[1:-1]
# the overlap is the forward-moving amplitude c in psi_in multiplied by
# the forward-moving amplitude in the time-reversed psi_out, which
# ends up being the backward-moving amplitude d in the non-time-reversed psi_out
# (which is calculated by the wavefunction calculator)
# ... and vice-verso for d and c in psi_in and psi_out
overlap = wf_out.c[1:-1] * wf_in.c[1:-1] / (1j * qtt_inside) * (
exp(1j * qtt_inside * dz) - 1.0) * exp(1j * qtt_inside * z_array)
overlap += wf_out.d[1:-1] * wf_in.d[1:-1] / (1j * qrr_inside) * (
exp(1j * qrr_inside * dz) - 1.0) * exp(1j * qrr_inside * z_array)
overlap += wf_out.c[1:-1] * wf_in.d[1:-1] / (1j * qtr_inside) * (
exp(1j * qtr_inside * dz) - 1.0) * exp(1j * qtr_inside * z_array)
overlap += wf_out.d[1:-1] * wf_in.c[1:-1] / (1j * qrt_inside) * (
exp(1j * qrt_inside * dz) - 1.0) * exp(1j * qrt_inside * z_array)
self.overlap = overlap
overlap_BA = 1.0 / (1j * self.qz) * (exp(1j * self.qz * dz) -
1.0) * exp(1j * self.qz * z_array)
self.overlap_BA = overlap_BA
gisans = sum(sum(overlap * array(self.dFTs)[:, :, :, newaxis], axis=0),
axis=0) # first over layers, then Qx
# now if you want to add specular back in...
if add_specular == True:
specular = complex128(2) * pi / self.Lx * normgauss(
qx, FWHM_to_sigma(2.0 * pi / self.Lx), x0=0.0)
specular *= complex128(2) * pi / self.Ly * normgauss(
self.qy[newaxis, :, newaxis],
FWHM_to_sigma(2.0 * pi / self.Ly),
x0=0.0)
specular *= 2.0 * 1j * kz_in_0 * wf_in.r[
newaxis, newaxis, :] * self.Lx * self.Ly
specular = sum(
specular,
axis=0) / self.qx.shape[0] # sum over Qx, taking average
self.specular = specular
gisans += specular
gisans_BA = sum(sum(overlap_BA * array(self.FTs)[:, :, :, newaxis],
axis=0),
axis=0)
extent = [self.qy.min(), self.qy.max(), self.qz.min(), self.qz.max()]
self.alpha_in = alpha_in
self.gisans = gisans
self.gisans_BA = gisans_BA
if show_plot == True:
from pylab import imshow, figure, colorbar
zmax = max(
log10(abs(gisans)**2).max(),
log10(abs(gisans_BA)**2).max())
zmin = min(
log10(abs(gisans)**2).min(),
log10(abs(gisans_BA)**2).min())
figure()
imshow(log10(abs(gisans)**2).T,
origin='lower',
extent=extent,
aspect='auto',
vmax=zmax,
vmin=zmin)
colorbar()
figure()
imshow(log10(abs(gisans_BA)**2).T,
origin='lower',
extent=extent,
aspect='auto',
vmax=zmax,
vmin=zmin)
colorbar()
def calc_gisans(self, alpha_in, show_plot=True, add_specular=False):
k0 = 2*pi/self.wavelength
kz_in_0 = array([k0 * sin(alpha_in * pi/180.0)], dtype=complex128)
kx_in_0 = array([k0 * cos(alpha_in * pi/180.0)], dtype=complex128)
kz_out_0 = kz_in_0 - self.qz
self.kz_out_0 = kz_out_0
ky_out_0 = -self.qy
kx_out_0 = sqrt(k0**2 - kz_out_0[newaxis,newaxis,:]**2 - ky_out_0[newaxis,:,newaxis]**2)
qx = kx_in_0 - kx_out_0
self.qx_derived = qx
kz_out_neg = kz_out_0 < 0
kz_in_neg = kz_in_0 < 0
wf_in = dwbaWavefunction((kz_in_0), self.SLDArray)
wf_out = dwbaWavefunction((-kz_out_0), self.SLDArray) # solve 1d equation for time-reversed state
self.wf_in = wf_in
self.wf_out = wf_out
kz_in_l = wf_in.kz_l # inside the layers
#kz_in_l[:, kz_in_neg] *= -1.0
kz_in_p_l = -kz_in_l # prime
kz_out_l = -wf_out.kz_l # inside the layers
#kz_out_l[:, kz_out_neg] *= -1.0
kz_out_p_l = -kz_out_l # kz_f_prime in the Sinha paper notation
dz = self.SLDArray[1:-1,1][:,newaxis]
zs = cumsum(self.SLDArray[1:-1,1]) - self.SLDArray[1,1] # start at zero with first layer
z_array = array(zs)[:,newaxis]
thickness = sum(self.SLDArray[1:-1,1])
qrt_inside = -kz_in_l[1:-1] - kz_out_l[1:-1]
qtt_inside = -kz_in_l[1:-1] + kz_out_l[1:-1]
qtr_inside = +kz_in_l[1:-1] + kz_out_l[1:-1]
qrr_inside = +kz_in_l[1:-1] - kz_out_l[1:-1]
# the overlap is the forward-moving amplitude c in psi_in multiplied by
# the forward-moving amplitude in the time-reversed psi_out, which
# ends up being the backward-moving amplitude d in the non-time-reversed psi_out
# (which is calculated by the wavefunction calculator)
# ... and vice-verso for d and c in psi_in and psi_out
overlap = wf_out.c[1:-1] * wf_in.c[1:-1] / (1j * qtt_inside) * (exp(1j * qtt_inside * dz) - 1.0)*exp(1j*qtt_inside*z_array)
overlap += wf_out.d[1:-1] * wf_in.d[1:-1] / (1j * qrr_inside) * (exp(1j * qrr_inside * dz) - 1.0)*exp(1j*qrr_inside*z_array)
overlap += wf_out.c[1:-1] * wf_in.d[1:-1] / (1j * qtr_inside) * (exp(1j * qtr_inside * dz) - 1.0)*exp(1j*qtr_inside*z_array)
overlap += wf_out.d[1:-1] * wf_in.c[1:-1] / (1j * qrt_inside) * (exp(1j * qrt_inside * dz) - 1.0)*exp(1j*qrt_inside*z_array)
self.overlap = overlap
overlap_BA = 1.0 / (1j * self.qz) * (exp(1j * self.qz * dz) - 1.0) * exp(1j*self.qz*z_array)
self.overlap_BA = overlap_BA
gisans = sum(sum(overlap * array(self.dFTs)[:,:,:,newaxis], axis=0), axis=0) # first over layers, then Qx
# now if you want to add specular back in...
if add_specular == True:
specular = complex128(2)*pi/self.Lx * normgauss(qx, FWHM_to_sigma(2.0*pi/self.Lx), x0=0.0)
specular *= complex128(2)*pi/self.Ly * normgauss(self.qy[newaxis,:,newaxis], FWHM_to_sigma(2.0*pi/self.Ly), x0=0.0)
specular *= 2.0*1j*kz_in_0*wf_in.r[newaxis,newaxis,:]*self.Lx*self.Ly
specular = sum(specular, axis=0)/self.qx.shape[0] # sum over Qx, taking average
self.specular = specular
gisans += specular
gisans_BA = sum(sum(overlap_BA * array(self.FTs)[:,:,:,newaxis], axis=0), axis=0)
extent = [self.qy.min(), self.qy.max(), self.qz.min(), self.qz.max()]
self.alpha_in = alpha_in
self.gisans = gisans
self.gisans_BA = gisans_BA
if show_plot == True:
from pylab import imshow, figure, colorbar
zmax = max(log10(abs(gisans)**2).max(), log10(abs(gisans_BA)**2).max())
zmin = min(log10(abs(gisans)**2).min(), log10(abs(gisans_BA)**2).min())
figure()
imshow(log10(abs(gisans)**2).T, origin='lower', extent=extent, aspect='auto', vmax=zmax, vmin=zmin)
colorbar()
figure()
imshow(log10(abs(gisans_BA)**2).T, origin='lower', extent=extent, aspect='auto', vmax=zmax, vmin=zmin)
colorbar()
