def _transfer_ray_4x4_1(field,
wavenumbers,
layer,
dmat1,
dmat2,
beta=0,
phi=0,
nsteps=1,
betamax=BETAMAX,
out=None):
d, epsv, epsa = layer
kd = wavenumbers * d
alpha, f = alphaf(beta, phi, epsv, epsa)
p = phasem(alpha, kd[..., None, None])
e = E_mat(f, mode=None)
ei = inv(e)
for j in range(nsteps):
field = dotmf(dmat1, field, out=out)
field = ifft2(field, out=field)
field = dotmdmf(e, p, ei, field, out=field)
field = fft2(field, out=field)
field = dotmf(dmat2, field, out=out)
return field
def _transfer_ray_4x4_1_windows(windows, field, wavenumbers, layer, dmat1, dmat2, betas, phis,
nsteps = 1, out = None,
betamax = BETAMAX):
d, epsv, epsa = layer
kd = wavenumbers*d
if out is None:
out = np.zeros_like(field)
for j in range(nsteps):
field = dotmf(dmat1,field)
for window, beta, phi in zip(windows, betas, phis):
alpha, f = alphaf(beta,phi,epsv,epsa)
p = phasem(alpha,kd[...,None,None])
e = E_mat(f, mode = None)
ei = inv(e)
f = field * window
f = ifft2(f, out = f)
f = dotmdmf(e,p,ei,f, out = f)
f = fft2(field, out = f)
out += f
out = dotmf(dmat2,out, out = out)
return out
def Epn_correction_matrix(beta,
phi,
ks,
d=1.,
epsv=(1, 1, 1),
epsa=(0, 0, 0.),
out=None):
alpha, f = alphaf(beta, phi, epsv, epsa)
kd = -np.asarray(ks) * d
pmat = phase_mat(alpha, kd[..., None, None])
e = E_mat(f, mode=None)
ei = inv(e)
return dotmdm(e, pmat, ei, out=out)
def first_Epn_diffraction_matrix(shape,
ks,
d=1.,
epsv=(1, 1, 1),
epsa=(0, 0, 0.),
betamax=BETAMAX,
out=None):
ks = np.asarray(ks, dtype=FDTYPE)
epsv = np.asarray(epsv, dtype=CDTYPE)
epsa = np.asarray(epsa, dtype=FDTYPE)
alpha, f, fi = diffraction_alphaffi(shape,
ks,
epsv=epsv,
epsa=epsa,
betamax=betamax)
kd = ks * d
e = E_mat(f, mode=None)
pmat = phase_mat(alpha, kd[..., None, None])
return dotmdm(e, pmat, fi, out=out)
def _transfer_ray_4x4_2(field,
wavenumbers,
layer,
beta=0,
phi=0,
nsteps=1,
dmatpn=None,
out=None,
tmpdata=None):
_out = {} if tmpdata is None else tmpdata
d, epsv, epsa = layer
if dmatpn is None:
kd = wavenumbers * d
else:
dmatp, dmatn = dmatpn
kd = wavenumbers * d / 2
alpha, f, fi = alphaffi(beta, phi, epsv, epsa, out=_out.get("affi"))
p = phasem(alpha, kd[..., None, None], out=_out.get("p"))
if tmpdata is not None:
tmpdata["affi"] = (alpha, f, fi)
tmpdata["p"] = p
if dmatpn is not None:
e = E_mat(f, mode=None)
ei = inv(e, out=_out.get("ei"))
if tmpdata is not None:
tmpdata["ei"] = ei
for j in range(nsteps):
if dmatpn is None:
field = dotmdmf(f, p, fi, field, out=out)
else:
field = dotmdmf(e, p, fi, field, out=out)
diffract(field[..., 0::2, :, :], dmatp, out=field[..., 0::2, :, :])
diffract(field[..., 1::2, :, :], dmatn, out=field[..., 1::2, :, :])
field = dotmdmf(f, p, ei, field, out=field)
return field
def propagate_2x2_full(field,
wavenumbers,
layer,
input_layer=None,
nsteps=1,
mode=+1,
reflection=True,
betamax=BETAMAX,
refl=None,
bulk=None,
out=None):
shape = field.shape[-2:]
d, epsv, epsa = layer
if input_layer is not None:
d_in, epsv_in, epsa_in = input_layer
kd = wavenumbers * d / nsteps
if out is None:
out = np.empty_like(field)
ii, jj = np.meshgrid(range(shape[0]),
range(shape[1]),
copy=False,
indexing="ij")
for step in range(nsteps):
for i in range(len(wavenumbers)):
ffield = fft2(field[..., i, :, :, :])
ofield = np.zeros_like(out[..., i, :, :, :])
b, p = betaphi(shape, wavenumbers[i])
mask = b < betamax
amplitude = ffield[..., mask]
betas = b[mask]
phis = p[mask]
iind = ii[mask]
jind = jj[mask]
if bulk is not None:
obulk = bulk[..., i, :, :, :]
if refl is not None:
tampl = fft2(refl[..., i, :, :, :])[..., mask]
orefl = refl[..., i, :, :, :]
orefl[...] = 0.
for bp in sorted(zip(range(len(betas)), betas, phis, iind, jind),
key=lambda el: el[1],
reverse=False):
#for j,bp in enumerate(zip(betas,phis,iind,jind)):
j, beta, phi, ieig, jeig = bp
out_af = alphaf(beta, phi, epsv, epsa)
alpha, fmat_out = out_af
e = E_mat(fmat_out, mode=mode)
ei0 = inv(e)
ei = ei0
pm = phase_mat(alpha, kd[i, None, None], mode=mode)
w = eigenwave(amplitude.shape[:-1] + shape,
ieig,
jeig,
amplitude=amplitude[..., j])
if step == 0 and reflection != False:
alphain, fmat_in = alphaf(beta, phi, epsv_in, epsa_in)
if refl is not None:
ei, eri = Etri_mat(fmat_in, fmat_out, mode=mode)
ein = E_mat(fmat_in, mode=-1 * mode)
t = eigenwave(amplitude.shape[:-1] + shape,
ieig,
jeig,
amplitude=tampl[..., j])
r = dotmf(eri, w)
r = dotmf(ein, r, out=r)
np.add(orefl, r, orefl)
w = dotmf(ei, w, out=w)
t = dotmf(ei0, t, out=t)
w = np.add(t, w, out=w)
else:
ei = Eti_mat(fmat_in, fmat_out, mode=mode)
w = dotmf(ei, w, out=w)
w = dotmf(dotmd(e, pm), w, out=w)
np.add(ofield, w, ofield)
else:
w = dotmdmf(e, pm, ei, w, out=w)
np.add(ofield, w, ofield)
if bulk is not None:
e2h = E2H_mat(fmat_out, mode=mode)
obulk[..., 1::2, :, :] += dotmf(e2h, w)
obulk[..., ::2, :, :] += w
out[..., i, :, :, :] = ofield
field = out
return out, refl
def _transfer_ray_2x2_1(fft_field,
wavenumbers,
layer,
effective_layer_in,
effective_layer_out,
dmat1,
dmat2,
beta=0,
phi=0,
nsteps=1,
mode=+1,
reflection=True,
betamax=BETAMAX,
refl=None,
bulk=None,
out=None,
tmpdata=None):
_out = {} if tmpdata is None else tmpdata
#fft_field = fft2(fft_field, out = out)
shape = fft_field.shape[-2:]
d_in, epsv_in, epsa_in = effective_layer_in
d_out, epsv_out, epsa_out = effective_layer_out
if reflection:
tmat, rmat = E_tr_matrix(shape,
wavenumbers,
epsv_in=epsv_in,
epsa_in=epsa_in,
epsv_out=epsv_out,
epsa_out=epsa_out,
mode=mode,
betamax=betamax)
d, epsv, epsa = layer
alpha, fmat = alphaf(beta, phi, epsv, epsa, out=_out.get("alphaf"))
e = E_mat(fmat, mode=mode, copy=False) #2x2 E-only view of fmat
ei = inv(e, out=_out.get("ei"))
#
kd = wavenumbers * d
p = phase_mat(alpha, kd[..., None, None], mode=mode, out=_out.get("p"))
if tmpdata is not None:
_out["alphaf"] = alpha, fmat
_out["ei"] = ei
_out["p"] = p
for j in range(nsteps):
if j == 0 and reflection:
#reflect only at the beginning
if refl is not None:
trans = refl.copy()
refl = dotmf(rmat, fft_field, out=refl)
fft_field = dotmf(tmat, fft_field, out=out)
fft_field = np.add(fft_field, trans, out=fft_field)
if mode == -1 and bulk is not None:
field = ifft2(fft_field)
e2h = E2H_mat(fmat, mode=mode)
bulk[..., ::2, :, :] += field
bulk[..., 1::2, :, :] += dotmf(e2h, field, out=field)
fft_field = dotmf(dmat1, fft_field, out=fft_field)
out = fft_field
else:
fft_field = dotmf(tmat, fft_field, out=out)
fft_field = dotmf(dmat1, fft_field, out=fft_field)
out = fft_field
else:
if dmat1 is not None:
fft_field = dotmf(dmat1, fft_field, out=out)
out = fft_field
field = ifft2(fft_field, out=out)
field = dotmdmf(e, p, ei, field, out=field)
fft_field = fft2(field, out=field)
if dmat2 is not None:
fft_field = dotmf(dmat2, fft_field, out=fft_field)
#return fft_field, refl
#out = ifft2(fft_field, out = out)
if mode == +1 and bulk is not None:
field = ifft2(fft_field)
e2h = E2H_mat(fmat, mode=mode)
bulk[..., 1::2, :, :] += dotmf(e2h, field)
bulk[..., ::2, :, :] += field
return fft_field, refl
def _transfer_ray_2x2_2(field,
wavenumbers,
in_layer,
out_layer,
dmat=None,
beta=0,
phi=0,
nsteps=1,
mode=+1,
reflection=True,
betamax=BETAMAX,
refl=None,
bulk=None,
out=None,
tmpdata=None):
_out = {} if tmpdata is None else tmpdata
if in_layer is not None:
d, epsv, epsa = in_layer
alpha, fmat_in = alphaf(beta, phi, epsv, epsa, out=_out.get("afin"))
if tmpdata is not None:
_out["afin"] = alpha, fmat_in
d, epsv, epsa = out_layer
alpha, fmat = alphaf(beta, phi, epsv, epsa, out=_out.get("afout"))
e = E_mat(fmat, mode=mode, copy=False) #2x2 E-only view of fmat
# if refl is not None:
# ein = E_mat(fmat_in, mode = mode * (-1)) #reverse direction
#
# if reflection == 0:
# kd = wavenumbers * d
# else:
kd = wavenumbers * d / 2
p = phase_mat(alpha, kd[..., None, None], mode=mode, out=_out.get("p"))
ei0 = inv(e, out=_out.get("ei0"))
ei = ei0
if tmpdata is not None:
_out["afout"] = alpha, fmat
_out["ei0"] = ei
_out["p"] = p
for j in range(nsteps):
#reflect only at the beginning
if j == 0 and reflection != 0:
#if we need to track reflections (multipass)
if refl is not None:
#ei,eri = Etri_mat(fmat_in, fmat, mode = mode, out = _out.get("eieri"))
tmat, rmat = tr_mat(fmat_in,
fmat,
mode=mode,
out=_out.get("eieri"))
if tmpdata is not None:
#_out["eieri"] = ei,eri
_out["eieri"] = tmat, rmat
trans = refl.copy()
#refl = dotmf(eri, field, out = refl)
refl = dotmf(rmat, field, out=refl)
#field = dotmf(ei,field, out = out)
field = dotmf(tmat, field, out=out)
field = np.add(field, trans, out=field)
if mode == -1 and bulk is not None:
#tmp_field = dotmf(e,field)
tmp_field = field
e2h = E2H_mat(fmat, mode=mode)
bulk[..., ::2, :, :] += tmp_field
bulk[..., 1::2, :, :] += dotmf(e2h, tmp_field)
field = dotmf(ei, field, out=field)
if d != 0.:
field = dotmf(dotmd(e, p), field, out=field)
else:
field = dotmf(e, field, out=field)
out = field
# rmat = dotmm(ein, eri, out = eri)
# trans = refl.copy()
# refl = dotmf(rmat, field, out = refl)
# ei0 = inv(e)
# field = dotmf(ei,field, out = out)
# field = dotmf(e,field) + trans
# if d != 0.:
# field = dotmdmf(e,p,ei0,field, out = out)
ei = ei0
else:
ei = Eti_mat(fmat_in, fmat, mode=mode, out=_out.get("eti"))
field = dotmdmf(e, p, ei, field, out=out)
out = field
if tmpdata is not None:
_out["eti"] = ei
ei = ei0
else:
#no need to compute if d == 0!.. identity
if d != 0.:
field = dotmdmf(e, p, ei, field, out=out)
out = field
if dmat is not None:
field = diffract(field, dmat, out=out)
out = field
#no need to compute if d == 0!.. identity
if d != 0.:
field = dotmdmf(e, p, ei, field, out=out)
if mode == +1 and bulk is not None:
e2h = E2H_mat(fmat, mode=mode)
bulk[..., 1::2, :, :] += dotmf(e2h, field)
bulk[..., ::2, :, :] += field
return field, refl