def bpm_p(r1, dn1, r2=None, dn2=None, lam=.5, n0=1.):
if dn2 is None:
dn2 = dn1
if r2 is None:
r2 = r1
r1 = .5 * r2
Nz, Nx = 256, 256
dx = .1
dn0 = zeros((Nz, Nx, Nx), float32)
add_coated_sphere(dn0, [Nz / 2, Nx / 2, Nx / 2],
r1=int(r1 / dx),
r2=int(r2 / dx),
dn1=dn1,
dn2=dn2)
u, _, p, g = bpm_3d((Nx, Nx, Nz),
units=(dx, ) * 3,
lam=lam,
n0=n0,
dn=dn0,
return_scattering=True,
return_g=True)
return p, dn0, g
def test_focus(size, units, NA = .3, n0 = 1.):
""" propagates a focused wave freely to the center
"""
Nx, Ny, Nz = size
dx, dy , dz = .1, .1, .1
lam = .5
_, u_debye, _, _ = psf(size, units, n0= n0, lam=lam, NA=NA, return_field = True)
u0 = u_debye[0]
u0 = psf_u0(size[:2],units[:2],
zfoc = .5*units[-1]*(size[-1]-1),
n0 = n0,
lam = lam,
NA = NA)
u = bpm_3d(size,units= units, lam = lam,
n0 = n0,
u0 = u0,
absorbing_width = 0)
return u, u_debye
def bpm_sca(r1, dn1, r2=None, dn2=None, lam=.5, n0=1., return_g=False):
if dn2 is None:
dn2 = dn1
if r2 is None:
r2 = r1
r1 = .5 * r2
Nz, Nx = 256, 256
dx = .1
dn0 = zeros((Nz, Nx, Nx), float32)
add_coated_sphere(dn0, [Nz / 2, Nx / 2, Nx / 2],
r1=int(r1 / dx),
r2=int(r2 / dx),
dn1=dn1,
dn2=dn2)
res = bpm_3d((Nx, Nx, Nz),
units=(dx, ) * 3,
lam=lam,
n0=n0,
dn=dn0,
return_scattering=True,
return_g=return_g)
if return_g:
p, g = res[-2:]
return p[-1] / r**2 / pi, g[-1]
else:
p = res[-1]
return p[-1] / r**2 / pi
def test_focus(size, units, NA=.3, n0=1.):
""" propagates a focused wave freely to the center
"""
Nx, Ny, Nz = size
dx, dy, dz = .1, .1, .1
lam = .5
_, u_debye, _, _ = psf(size,
units,
n0=n0,
lam=lam,
NA=NA,
return_field=True)
u0 = u_debye[0]
u0 = psf_u0(size[:2],
units[:2],
zfoc=.5 * units[-1] * (size[-1] - 1),
n0=n0,
lam=lam,
NA=NA)
u = bpm_3d(size, units=units, lam=lam, n0=n0, u0=u0, absorbing_width=0)
return u, u_debye
def bpm_sca(r1,dn1,r2 = None,dn2 = None, lam= .5, n0 = 1., return_g = False):
if dn2 is None:
dn2 = dn1
if r2 is None:
r2 = r1
r1 = .5*r2
Nz, Nx = 256,256
dx = .1
dn0 = zeros((Nz,Nx,Nx),float32)
add_coated_sphere(dn0,[Nz/2,Nx/2,Nx/2],r1=int(r1/dx),r2 = int(r2/dx),dn1 = dn1,dn2 = dn2)
res = bpm_3d((Nx,Nx,Nz),units= (dx,)*3,
lam = lam,
n0 = n0,
dn = dn0,
return_scattering = True,
return_g = return_g
)
if return_g:
p, g = res[-2:]
return p[-1]/r**2/pi, g[-1]
else:
p = res[-1]
return p[-1]/r**2/pi
def test_plane(size = (256,)*3, n_x_comp = 0, n0 = 1., n = None):
""" propagates a plane wave freely
n_x_comp is the tilt in x
"""
Nx, Ny, Nz = size
dx, dz = .05, 0.05
if n is None:
n = n0
lam = .5
units = (dx,dx,dz)
x = dx*np.arange(Nx)
y = dx*np.arange(Ny)
z = dz*np.arange(Nz)
Z,Y,X = np.meshgrid(z,y,x,indexing="ij")
k_x = 1.*n_x_comp/(dx*(Nx-1.))
k_y = k_x
k_z = np.sqrt(1.*n**2/lam**2-k_x**2-k_y**2)
print (k_x,k_z), np.sqrt(k_x**2+k_y**2+k_z**2)
u_plane = np.exp(-2.j*np.pi*(k_z*Z+k_y*Y+k_x*X))
u = 0
dn = (n-n0)*np.ones_like(Z)
u = bpm_3d((Nx,Ny,Nz),units= units, lam = lam,
n0 = n0,
dn = dn,
n_volumes = 1,
absorbing_width=0,
u0 = u_plane[0,...])
print "L2 difference = %.4f"%np.mean(np.abs(u_plane-u)**2)
#npt.assert_almost_equal(np.mean(np.abs(u_plane-u)**2),0,decimal = 2)
return u, u_plane
def test_plane(size=(256, ) * 3, n_x_comp=0, n0=1., n=None):
""" propagates a plane wave freely
n_x_comp is the tilt in x
"""
Nx, Ny, Nz = size
dx, dz = .05, 0.05
if n is None:
n = n0
lam = .5
units = (dx, dx, dz)
x = dx * np.arange(Nx)
y = dx * np.arange(Ny)
z = dz * np.arange(Nz)
Z, Y, X = np.meshgrid(z, y, x, indexing="ij")
k_x = 1. * n_x_comp / (dx * (Nx - 1.))
k_y = k_x
k_z = np.sqrt(1. * n**2 / lam**2 - k_x**2 - k_y**2)
print(k_x, k_z), np.sqrt(k_x**2 + k_y**2 + k_z**2)
u_plane = np.exp(-2.j * np.pi * (k_z * Z + k_y * Y + k_x * X))
u = 0
dn = (n - n0) * np.ones_like(Z)
u = bpm_3d((Nx, Ny, Nz),
units=units,
lam=lam,
n0=n0,
dn=dn,
n_volumes=1,
absorbing_width=0,
u0=u_plane[0, ...])
print "L2 difference = %.4f" % np.mean(np.abs(u_plane - u)**2)
#npt.assert_almost_equal(np.mean(np.abs(u_plane-u)**2),0,decimal = 2)
return u, u_plane
def bpm_p(r1, dn1, r2=None, dn2=None, lam=0.5, n0=1.0):
if dn2 is None:
dn2 = dn1
if r2 is None:
r2 = r1
r1 = 0.5 * r2
Nz, Nx = 256, 256
dx = 0.1
dn0 = zeros((Nz, Nx, Nx), float32)
add_coated_sphere(dn0, [Nz / 2, Nx / 2, Nx / 2], r1=int(r1 / dx), r2=int(r2 / dx), dn1=dn1, dn2=dn2)
u, _, p, g = bpm_3d((Nx, Nx, Nz), units=(dx,) * 3, lam=lam, n0=n0, dn=dn0, return_scattering=True, return_g=True)
m = Bpm3d((Nx, Nx, Nz), units=(dx,) * 3, lam=lam, n0=n0)
return u, p, dn0, g, m
def test_plane_complex(n_x_comp = 0, n0 = 1., n = None):
""" propagates a plane wave freely
n_x_comp is the tilt in x
"""
Nx, Nz = 128,128
dx, dz = .05, 0.05
if n is None:
n = n0
n -= 0.01j
lam = .5
units = (dx,dx,dz)
x = dx*np.arange(Nx)
y = dx*np.arange(Nx)
z = dz*np.arange(Nz)
Z,Y,X = np.meshgrid(z,y,x,indexing="ij")
k_x = 1.*n_x_comp/(dx*(Nx-1.))
k_z = np.sqrt(1.*n**2/lam**2-k_x**2)
print np.sqrt(k_x**2+k_z**2)
u_plane = np.exp(-2.j*np.pi*(k_z*Z+k_x*X))
u = 0
dn = (n-n0)*np.ones_like(Z)
print n,n0, np.mean(dn)
u, dn = bpm_3d((Nx,Nx,Nz),units= units, lam = lam,
n0 = n0,
dn = dn,
subsample = 2,
u0 = u_plane[0,...])
print "difference", np.mean(np.abs(u_plane-u)**2)
npt.assert_almost_equal(np.mean(np.abs(u_plane-u)**2),0,decimal = 2)
return u_plane, u
def test_gaussian(size, units, NA = .4, tilt =0.):
""" propagates a gaussian wave freely to the center
"""
Nx, Ny, Nz = size
dx, dy, dz = units
lam = .5
x = dx*(np.arange(-Nx/2, Nx/2)+.5)
y = dy*(np.arange(-Ny/2, Ny/2)+.5)
z = dz*(np.arange(-Nz/2, Nz/2)+.5)
Z,Y,X = np.meshgrid(z,y,x,indexing="ij")
u0 = gaussian_tilt(X,Y,Z,lam = lam, NA= NA, tilt = 0)
u = bpm_3d(size, units=units, lam=lam,
n0=n0,
u0=u0[0],
#use_fresnel_approx=True
)
return u, u0
dx, dz = .05, 0.05
lam = .5
units = (dx, dx, dz)
x = dx * np.arange(-Nx / 2, Nx / 2)
y = dx * np.arange(-Ny / 2, Ny / 2)
z = dz * np.arange(-Nz / 2, Nz / 2)
Z, Y, X = np.meshgrid(z, y, x, indexing="ij")
R = np.sqrt(X**2 + Y**2 + Z**2)
dn = .05 * (R < 1.)
u1 = bpm_3d((Nx, Ny, Nz),
units=units,
lam=lam,
dn=dn,
n_volumes=2,
return_field=True)
u1 = abs(u1)**2
u2 = bpm_3d((Nx, Ny, Nz),
units=units,
lam=lam,
dn=dn,
n_volumes=2,
return_field=False)
is_close = np.allclose(u1, u2)
print is_close
assert is_close
Nx, Ny, Nz = 256,256,512
dx, dz = .05, 0.05
lam = .5
units = (dx,dx,dz)
x = dx*np.arange(-Nx/2,Nx/2)
y = dx*np.arange(-Ny/2,Ny/2)
z = dz*np.arange(-Nz/2,Nz/2)
Z,Y,X = np.meshgrid(z,y,x,indexing="ij")
R = np.sqrt(X**2+Y**2+Z**2)
dn = .05*(R<1.)
u1 = bpm_3d((Nx,Ny,Nz),units= units, lam = lam,
dn = dn,
n_volumes = 2,
return_field=True)
u1 = abs(u1)**2
u2 = bpm_3d((Nx,Ny,Nz),units= units, lam = lam,
dn = dn,
n_volumes = 2,
return_field=False)
is_close = np.allclose(u1,u2)
print is_close
assert is_close
"""
check whether we conserve energy along z
"""
import bpm
import numpy as np
import pylab
if __name__ == '__main__':
N = 256
dn = .1*np.random.uniform(-1,1,(N,)*3)
#plane wave through empty space and through dn
u0 = bpm.bpm_3d((N,)*3,(.1,)*3)
u = bpm.bpm_3d((N,)*3,(.1,)*3,dn = dn)
pylab.ioff()
pylab.plot(np.mean(np.abs(u0),(1,2)))
pylab.plot(np.mean(np.abs(u),(1,2)))
pylab.show()
y = dx * (np.arange(-Nx / 2, Nx / 2) + .5)
z = dx * (np.arange(-Nz / 2, Nz / 2) + .5)
Z, Y, X = np.meshgrid(z, y, x, indexing="ij")
Z, X = np.cos(w) * Z - np.sin(w) * X, np.cos(w) * X + np.sin(w) * Z
dn = dn0 * (Z > 0)
u0 = psf_u0((Nx, Nx),
units=(dx, ) * 2,
zfoc=dx * (Nz - 1.) / 2.,
lam=lam,
NA=NA)
u = bpm_3d((Nx, Nx, Nz), units=(dx, ) * 3, lam=lam, dn=dn, u0=u0)
u1 = np.abs(u[:Nz / 2, ...])[::-1, ...]**2
u2 = gputools.rotate(abs(u[Nz / 2:, ...])**2,
center=(0, Nx / 2, Nx / 2),
axis=(0., 1., 0),
angle=phi(dn0, w),
mode="linear")
pylab.figure(1)
pylab.clf()
pylab.plot(u1[Nz / 10, Nx / 2, :])
pylab.plot(u2[Nz / 10, Nx / 2, :])
# return u, u0
#
from bpm import bpm_3d, focus_field_debye, psf_focus_u0
if __name__ == '__main__':
# u1,u2 = test_plane(n_x_comp=1, n0 = 1.1)
Nx = 256
Nz = 512
NA = .7
_,u1, _, _ = focus_field_debye((Nx, Nx, 2 * Nz), (.1,) * 3, lam = .5, NAs = [0., NA])
u1 = u1[Nz:]
u2 = bpm_3d((Nx,Nx,Nz),(.1,)*3,u0 = u1[0])
u3 = bpm_3d((Nx,Nx,Nz),(.1,)*3,u0 = u1[0],dn = np.zeros((Nz,Nx,Nx)),
absorbing_width=10)
import pylab
pylab.figure()
pylab.clf()
for i,u in enumerate([u1,u2,u3]):
pylab.subplot(1,3,i+1)
pylab.imshow(abs(u[...,Nx/2])**.6,cmap = "hot")
pylab.axis("off")
pylab.show()
w = .8
dn0 = 0.1
x = dx*(np.arange(-Nx/2, Nx/2)+.5)
y = dx*(np.arange(-Nx/2, Nx/2)+.5)
z = dx*(np.arange(-Nz/2, Nz/2)+.5)
Z,Y,X = np.meshgrid(z,y,x,indexing="ij")
Z,X = np.cos(w)*Z-np.sin(w)*X, np.cos(w)*X+np.sin(w)*Z
dn = dn0*(Z>0)
u0 = psf_u0((Nx,Nx), units = (dx,)*2,zfoc = dx*(Nz-1.)/2.,lam = lam, NA= NA)
u = bpm_3d((Nx,Nx,Nz), units=(dx,)*3, lam=lam, dn =dn,
u0=u0)
u1 = np.abs(u[:Nz/2,...])[::-1,...]**2
u2 = gputools.rotate(abs(u[Nz/2:,...])**2, center = (0,Nx/2,Nx/2),
axis = (0.,1.,0),
angle = phi(dn0,w),
mode = "linear")
pylab.figure(1)
pylab.clf()
pylab.plot(u1[Nz/10,Nx/2,:])
pylab.plot(u2[Nz/10,Nx/2,:])
# return u, u0
#
#
if __name__ == '__main__':
# u1,u2 = test_plane(n_x_comp=1, n0 = 1.1)
Nx = 256
Nz = 512
NA = .7
_, u1, _, _ = focus_field_debye((Nx, Nx, 2 * Nz), (.1, ) * 3,
lam=.5,
NAs=[0., NA])
u1 = u1[Nz:]
u2 = bpm_3d((Nx, Nx, Nz), (.1, ) * 3, u0=u1[0])
u3 = bpm_3d((Nx, Nx, Nz), (.1, ) * 3,
u0=u1[0],
dn=np.zeros((Nz, Nx, Nx)),
absorbing_width=10)
import pylab
pylab.figure()
pylab.clf()
for i, u in enumerate([u1, u2, u3]):
pylab.subplot(1, 3, i + 1)
pylab.imshow(abs(u[..., Nx / 2])**.6, cmap="hot")
pylab.axis("off")
