def propagate_2D_fresnel_convolution(wavefront, propagation_distance,shift_half_pixel=1):
"""
2D Fresnel propagator using convolution via Fourier transform
:param wavefront:
:param propagation_distance: propagation distance
:param shift_half_pixel: set to 1 to shift half pixel (recommended using an even number of pixels) Set as default.
:return: a new 2D wavefront object with propagated wavefront
"""
from scipy.signal import fftconvolve
wavelength = wavefront.get_wavelength()
X = wavefront.get_mesh_x()
Y = wavefront.get_mesh_y()
if shift_half_pixel:
x = wavefront.get_coordinate_x()
y = wavefront.get_coordinate_y()
X += 0.5 * numpy.abs( x[0] - x[1] )
Y += 0.5 * numpy.abs( y[0] - y[1] )
kernel = numpy.exp(1j*2*numpy.pi/wavefront.get_wavelength() *
(X**2 + Y**2) / 2 / propagation_distance)
kernel *= numpy.exp(1j*2*numpy.pi/wavefront.get_wavelength() * propagation_distance)
kernel /= 1j * wavefront.get_wavelength() * propagation_distance
tmp = fftconvolve(wavefront.get_complex_amplitude(),kernel,mode='same')
wf_propagated = Wavefront2D.initialize_wavefront_from_arrays(wavefront.get_coordinate_x(),
wavefront.get_coordinate_y(),
tmp,
wavelength=wavelength)
return wf_propagated
def test_polarization_interpolation(self):
print("# ")
print("# Tests polarization with interpolation ")
print("# ")
#
# from arrays
#
x = numpy.linspace(-100, 100, 50)
y = numpy.linspace(-50, 50, 200)
X = numpy.outer(x, numpy.ones_like(y))
Y = numpy.outer(numpy.ones_like(x), y)
sigma = 10
Z = numpy.exp(-(X**2 + Y**2) / 2 / sigma**2) * 1j
Zp = 0.3333 * numpy.exp(-(X**2 + Y**2) / 2 / sigma**2) * 1j
wf2 = Wavefront2D.initialize_wavefront_from_arrays(x, y, Z, Zp)
ca1 = wf2.get_complex_amplitude(polarization=Polarization.SIGMA)
ca2 = wf2.get_interpolated_complex_amplitude(
X + 1e-3, Y + 1e-4, polarization=Polarization.SIGMA)
assert_array_almost_equal(ca1, ca2, 4)
ca1pi = wf2.get_complex_amplitude(polarization=Polarization.PI)
ca2pi = wf2.get_interpolated_complex_amplitude(
X + 1e-3, Y + 1e-4, polarization=Polarization.PI)
assert_array_almost_equal(ca1pi, ca2pi, 4)
def propagate_2D_fraunhofer(wavefront, propagation_distance=1.0,shift_half_pixel=1):
"""
2D Fraunhofer propagator using convolution via Fourier transform
:param wavefront:
:param propagation_distance: propagation distance. If set to zero, the abscissas
of the returned wavefront are in angle (rad)
:param shift_half_pixel: set to 1 to shift half pixel (recommended using an even number of pixels) Set as default.
:return: a new 2D wavefront object with propagated wavefront
"""
wavelength = wavefront.get_wavelength()
#
# check validity
#
x = wavefront.get_coordinate_x()
y = wavefront.get_coordinate_y()
half_max_aperture = 0.5 * numpy.array( (x[-1]-x[0],y[-1]-y[0])).max()
far_field_distance = half_max_aperture**2/wavelength
if propagation_distance < far_field_distance:
print("WARNING: Fraunhoffer diffraction valid for distances > > half_max_aperture^2/lambda = %f m (propagating at %4.1f)"%
(far_field_distance,propagation_distance))
#
#compute Fourier transform
#
F1 = numpy.fft.fft2(wavefront.get_complex_amplitude()) # Take the fourier transform of the image.
# Now shift the quadrants around so that low spatial frequencies are in
# the center of the 2D fourier transformed image.
F2 = numpy.fft.fftshift( F1 )
# frequency for axis 1
shape = wavefront.size()
delta = wavefront.delta()
pixelsize = delta[0] # p_x[1] - p_x[0]
npixels = shape[0]
freq_nyquist = 0.5/pixelsize
freq_n = numpy.linspace(-1.0,1.0,npixels)
freq_x = freq_n * freq_nyquist
freq_x *= wavelength
# frequency for axis 2
pixelsize = delta[1]
npixels = shape[1]
freq_nyquist = 0.5/pixelsize
freq_n = numpy.linspace(-1.0,1.0,npixels)
freq_y = freq_n * freq_nyquist
freq_y *= wavelength
if shift_half_pixel:
freq_x = freq_x - 0.5 * numpy.abs(freq_x[1] - freq_x[0])
freq_y = freq_y - 0.5 * numpy.abs(freq_y[1] - freq_y[0])
if propagation_distance != 1.0:
freq_x *= propagation_distance
freq_y *= propagation_distance
wf_propagated = Wavefront2D.initialize_wavefront_from_arrays(freq_x,freq_y,F2,wavelength=wavelength)
return wf_propagated
def propagate_2D_fresnel_convolution(wavefront,
propagation_distance,
shift_half_pixel=1):
"""
2D Fresnel propagator using convolution via Fourier transform
:param wavefront:
:param propagation_distance: propagation distance
:param shift_half_pixel: set to 1 to shift half pixel (recommended using an even number of pixels) Set as default.
:return: a new 2D wavefront object with propagated wavefront
"""
from scipy.signal import fftconvolve
wavelength = wavefront.get_wavelength()
X = wavefront.get_mesh_x()
Y = wavefront.get_mesh_y()
if shift_half_pixel:
x = wavefront.get_coordinate_x()
y = wavefront.get_coordinate_y()
X += 0.5 * numpy.abs(x[0] - x[1])
Y += 0.5 * numpy.abs(y[0] - y[1])
kernel = numpy.exp(1j * 2 * numpy.pi / wavefront.get_wavelength() *
(X**2 + Y**2) / 2 / propagation_distance)
kernel *= numpy.exp(1j * 2 * numpy.pi / wavefront.get_wavelength() *
propagation_distance)
kernel /= 1j * wavefront.get_wavelength() * propagation_distance
tmp = fftconvolve(wavefront.get_complex_amplitude(), kernel, mode='same')
# tmp = convolve(wavefront.get_complex_amplitude(), kernel, mode='full',method='auto')
# print(">>>>>>>>>>>> kernel: ",kernel.shape)
# print(">>>>>>>>>>>> wavefront: ", wavefront.get_complex_amplitude().shape)
# print(">>>>>>>>>>>> result: ", tmp.shape,numpy.arange(0, tmp.shape[1]).shape)
wf_propagated = Wavefront2D.initialize_wavefront_from_arrays(
wavefront.get_coordinate_x(),
wavefront.get_coordinate_y(),
tmp,
wavelength=wavelength)
# start = 0.75 * (tmp.shape)[0]
# start = int(start)
# end = start + (tmp.shape)[0]
#
# tmp2 = (numpy.copy(tmp))[start:end,start:end]
#
# print(">>>>>>>>>>> tmp2,start,end",tmp2.shape,start,end)
#
#
# wf_propagated = Wavefront2D.initialize_wavefront_from_arrays(numpy.arange(0,tmp2.shape[0]),
# numpy.arange(0, tmp2.shape[1]),
# tmp2,
# wavelength=wavelength)
return wf_propagated
def propagate_2D_fresnel(wavefront, propagation_distance, shift_half_pixel=1):
"""
2D Fresnel propagator using convolution via Fourier transform
:param wavefront:
:param propagation_distance: propagation distance
:param shift_half_pixel: set to 1 to shift half pixel (recommended using an even number of pixels) Set as default.
:return: a new 2D wavefront object with propagated wavefront
"""
wavelength = wavefront.get_wavelength()
#
# convolving with the Fresnel kernel via FFT multiplication
#
fft = numpy.fft.fft2(wavefront.get_complex_amplitude())
# frequency for axis 1
shape = wavefront.size()
delta = wavefront.delta()
pixelsize = delta[0] # p_x[1] - p_x[0]
npixels = shape[0]
freq_nyquist = 0.5 / pixelsize
freq_n = numpy.linspace(-1.0, 1.0, npixels)
freq_x = freq_n * freq_nyquist
# frequency for axis 2
pixelsize = delta[1]
npixels = shape[1]
freq_nyquist = 0.5 / pixelsize
freq_n = numpy.linspace(-1.0, 1.0, npixels)
freq_y = freq_n * freq_nyquist
if shift_half_pixel:
freq_x = freq_x - 0.5 * numpy.abs(freq_x[1] - freq_x[0])
freq_y = freq_y - 0.5 * numpy.abs(freq_y[1] - freq_y[0])
freq_xy = numpy.array(numpy.meshgrid(freq_y, freq_x))
fft *= numpy.exp(
(-1.0j) * numpy.pi * wavelength * propagation_distance *
numpy.fft.fftshift(freq_xy[0] * freq_xy[0] + freq_xy[1] * freq_xy[1]))
ifft = numpy.fft.ifft2(fft)
wf_propagated = Wavefront2D.initialize_wavefront_from_arrays(
wavefront.get_coordinate_x(),
wavefront.get_coordinate_y(),
ifft,
wavelength=wavelength)
return wf_propagated
def propagate_2D_fresnel(wavefront, propagation_distance,shift_half_pixel=1):
"""
2D Fresnel propagator using convolution via Fourier transform
:param wavefront:
:param propagation_distance: propagation distance
:param shift_half_pixel: set to 1 to shift half pixel (recommended using an even number of pixels) Set as default.
:return: a new 2D wavefront object with propagated wavefront
"""
wavelength = wavefront.get_wavelength()
#
# convolving with the Fresnel kernel via FFT multiplication
#
fft = numpy.fft.fft2(wavefront.get_complex_amplitude())
# frequency for axis 1
shape = wavefront.size()
delta = wavefront.delta()
pixelsize = delta[0] # p_x[1] - p_x[0]
npixels = shape[0]
freq_nyquist = 0.5/pixelsize
freq_n = numpy.linspace(-1.0,1.0,npixels)
freq_x = freq_n * freq_nyquist
# frequency for axis 2
pixelsize = delta[1]
npixels = shape[1]
freq_nyquist = 0.5/pixelsize
freq_n = numpy.linspace(-1.0,1.0,npixels)
freq_y = freq_n * freq_nyquist
if shift_half_pixel:
freq_x = freq_x - 0.5 * numpy.abs(freq_x[1] - freq_x[0])
freq_y = freq_y - 0.5 * numpy.abs(freq_y[1] - freq_y[0])
freq_xy = numpy.array(numpy.meshgrid(freq_y,freq_x))
fft *= numpy.exp((-1.0j) * numpy.pi * wavelength * propagation_distance *
numpy.fft.fftshift(freq_xy[0]*freq_xy[0] + freq_xy[1]*freq_xy[1]) )
ifft = numpy.fft.ifft2(fft)
wf_propagated = Wavefront2D.initialize_wavefront_from_arrays(wavefront.get_coordinate_x(),
wavefront.get_coordinate_y(),
ifft,
wavelength=wavelength)
return wf_propagated
def test_initializers(self,do_plot=do_plot):
print("# ")
print("# Tests for initializars (2D) ")
print("# ")
x = numpy.linspace(-100,100,50)
y = numpy.linspace(-50,50,200)
XY = numpy.meshgrid(x,y)
X = XY[0].T
Y = XY[1].T
sigma = 10
Z = numpy.exp(- (X**2 + Y**2)/2/sigma**2) * 1j
print("Shapes x,y,z: ",x.shape,y.shape,Z.shape)
wf0 = Wavefront2D.initialize_wavefront_from_steps(x[0],numpy.abs(x[1]-x[0]),y[0],numpy.abs(y[1]-y[0]),number_of_points=Z.shape)
wf0.set_complex_amplitude(Z)
wf1 = Wavefront2D.initialize_wavefront_from_range(x[0],x[-1],y[0],y[-1],number_of_points=Z.shape)
wf1.set_complex_amplitude(Z)
wf2 = Wavefront2D.initialize_wavefront_from_arrays(x,y,Z)
if do_plot:
from srxraylib.plot.gol import plot_image
plot_image(wf0.get_intensity(),wf0.get_coordinate_x(),wf0.get_coordinate_y(),
title="initialize_wavefront_from_steps",show=0)
plot_image(wf1.get_intensity(),wf1.get_coordinate_x(),wf1.get_coordinate_y(),
title="initialize_wavefront_from_range",show=0)
plot_image(wf2.get_intensity(),wf2.get_coordinate_x(),wf2.get_coordinate_y(),
title="initialize_wavefront_from_arrays",show=1)
numpy.testing.assert_almost_equal(numpy.abs(Z)**2,wf0.get_intensity(),11)
numpy.testing.assert_almost_equal(numpy.abs(Z)**2,wf1.get_intensity(),11)
numpy.testing.assert_almost_equal(numpy.abs(Z)**2,wf2.get_intensity(),11)
numpy.testing.assert_almost_equal(x,wf0.get_coordinate_x(),11)
numpy.testing.assert_almost_equal(x,wf1.get_coordinate_x(),11)
numpy.testing.assert_almost_equal(x,wf2.get_coordinate_x(),11)
numpy.testing.assert_almost_equal(y,wf0.get_coordinate_y(),11)
numpy.testing.assert_almost_equal(y,wf1.get_coordinate_y(),11)
numpy.testing.assert_almost_equal(y,wf2.get_coordinate_y(),11)
def get_wavefront2d(self,i_mode,wavelength):
return Wavefront2D.initialize_wavefront_from_arrays(self.x_coordinates(),self.y_coordinates(),
self.mode(i_mode),wavelength=wavelength)
def propagate_2D_integral(wavefront, propagation_distance,
shuffle_interval=0,calculate_grid_only=1):
"""
2D Fresnel-Kirchhoff propagator via simplified integral
NOTE: this propagator is experimental and much less performant than the ones using Fourier Optics
Therefore, it is not recommended to use.
:param wavefront:
:param propagation_distance: propagation distance
:param shuffle_interval: it is known that this method replicates the central diffraction spot
The distace of the replica is proportional to 1/pixelsize
To avoid that, it is possible to change a bit (randomly) the coordinates
of the wavefront. shuffle_interval controls this shift: 0=No shift. A typical
value can be 1e5.
The result shows a diffraction pattern without replica but with much noise.
:param calculate_grid_only: if set, it calculates only the horizontal and vertical profiles, but returns the
full image with the other pixels to zero. This is useful when calculating large arrays,
so it is set as the default.
:return: a new 2D wavefront object with propagated wavefront
"""
#
# Fresnel-Kirchhoff integral (neglecting inclination factor)
#
if calculate_grid_only == 0:
#
# calculation over the whole detector area
#
p_x = wavefront.get_coordinate_x()
p_y = wavefront.get_coordinate_y()
wavelength = wavefront.get_wavelength()
amplitude = wavefront.get_complex_amplitude()
det_x = p_x.copy()
det_y = p_y.copy()
p_X = wavefront.get_mesh_x()
p_Y = wavefront.get_mesh_y()
det_X = p_X
det_Y = p_Y
amplitude_propagated = numpy.zeros_like(amplitude,dtype='complex')
wavenumber = 2 * numpy.pi / wavelength
for i in range(det_x.size):
for j in range(det_y.size):
if shuffle_interval == 0:
rd_x = 0.0
rd_y = 0.0
else:
rd_x = (numpy.random.rand(p_x.size,p_y.size)-0.5)*shuffle_interval
rd_y = (numpy.random.rand(p_x.size,p_y.size)-0.5)*shuffle_interval
r = numpy.sqrt( numpy.power(p_X + rd_x - det_X[i,j],2) +
numpy.power(p_Y + rd_y - det_Y[i,j],2) +
numpy.power(propagation_distance,2) )
amplitude_propagated[i,j] = (amplitude / r * numpy.exp(1.j * wavenumber * r)).sum()
wavefront2 = Wavefront2D.initialize_wavefront_from_arrays(det_x,det_y,amplitude_propagated)
else:
x = wavefront.get_coordinate_x()
y = wavefront.get_coordinate_y()
X = wavefront.get_mesh_x()
Y = wavefront.get_mesh_y()
wavenumber = 2 * numpy.pi / wavefront.get_wavelength()
amplitude = wavefront.get_complex_amplitude()
used_indices = wavefront.get_mask_grid(width_in_pixels=(1,1),number_of_lines=(1,1))
indices_x = wavefront.get_mesh_indices_x()
indices_y = wavefront.get_mesh_indices_y()
indices_x_flatten = indices_x[numpy.where(used_indices == 1)].flatten()
indices_y_flatten = indices_y[numpy.where(used_indices == 1)].flatten()
X_flatten = X[numpy.where(used_indices == 1)].flatten()
Y_flatten = Y[numpy.where(used_indices == 1)].flatten()
complex_amplitude_propagated = amplitude*0
print("propagate_2D_integral: Calculating %d points from a total of %d x %d = %d"%(
X_flatten.size,amplitude.shape[0],amplitude.shape[1],amplitude.shape[0]*amplitude.shape[1]))
for i in range(X_flatten.size):
r = numpy.sqrt( numpy.power(wavefront.get_mesh_x() - X_flatten[i],2) +
numpy.power(wavefront.get_mesh_y() - Y_flatten[i],2) +
numpy.power(propagation_distance,2) )
complex_amplitude_propagated[indices_x_flatten[i],indices_y_flatten[i]] = (amplitude / r * numpy.exp(1.j * wavenumber * r)).sum()
wavefront2 = Wavefront2D.initialize_wavefront_from_arrays(x,y,complex_amplitude_propagated,wavefront.get_wavelength())
return wavefront2
def propagate_2D_fraunhofer(wavefront,
propagation_distance=1.0,
shift_half_pixel=0): #todo: modificato da giovanni
"""
2D Fraunhofer propagator using convolution via Fourier transform
:param wavefront:
:param propagation_distance: propagation distance. If set to zero, the abscissas
of the returned wavefront are in angle (rad)
:param shift_half_pixel: set to 1 to shift half pixel (recommended using an even number of pixels) Set as default.
:return: a new 2D wavefront object with propagated wavefront
"""
wavelength = wavefront.get_wavelength()
#
# check validity
#
x = wavefront.get_coordinate_x()
y = wavefront.get_coordinate_y()
half_max_aperture = 0.5 * numpy.array((x[-1] - x[0], y[-1] - y[0])).max()
far_field_distance = half_max_aperture**2 / wavelength
if propagation_distance < far_field_distance:
print(
"WARNING: Fraunhoffer diffraction valid for distances > > half_max_aperture^2/lambda = %f m (propagating at %4.1f)"
% (far_field_distance, propagation_distance))
#
#compute Fourier transform
#
# frequency for axis 1
shape = wavefront.size()
delta = wavefront.delta()
wavenumber = wavefront.get_wavenumber()
pixelsize = delta[0] # p_x[1] - p_x[0]
npixels = shape[0]
fft_scale = numpy.fft.fftfreq(npixels, d=pixelsize)
fft_scale = numpy.fft.fftshift(fft_scale)
x2 = fft_scale * propagation_distance * wavelength
# frequency for axis 2
pixelsize = delta[1]
npixels = shape[1]
fft_scale = numpy.fft.fftfreq(npixels, d=pixelsize)
fft_scale = numpy.fft.fftshift(fft_scale)
y2 = fft_scale * propagation_distance * wavelength
f_x, f_y = numpy.meshgrid(x2, y2, indexing='ij')
fsq = numpy.fft.fftshift(f_x**2 + f_y**2)
P1 = numpy.exp(1.0j * wavenumber * propagation_distance)
P2 = numpy.exp(1.0j * wavenumber / 2 / propagation_distance * fsq)
P3 = 1.0j * wavelength * propagation_distance
F1 = numpy.fft.fft2(wavefront.get_complex_amplitude()
) # Take the fourier transform of the image.
# Now shift the quadrants around so that low spatial frequencies are in
# the center of the 2D fourier transformed image.
F1 *= P1
F1 *= P2
F1 /= P3
F2 = numpy.fft.fftshift(F1)
if shift_half_pixel:
x2 = x2 - 0.5 * numpy.abs(x2[1] - x2[0])
y2 = y2 - 0.5 * numpy.abs(y2[1] - y2[0])
wf_propagated = Wavefront2D.initialize_wavefront_from_arrays(
x2, y2, F2, wavelength=wavelength)
return wf_propagated
def propagate_2D_integral(wavefront,
propagation_distance,
shuffle_interval=0,
calculate_grid_only=1):
"""
2D Fresnel-Kirchhoff propagator via simplified integral
NOTE: this propagator is experimental and much less performant than the ones using Fourier Optics
Therefore, it is not recommended to use.
:param wavefront:
:param propagation_distance: propagation distance
:param shuffle_interval: it is known that this method replicates the central diffraction spot
The distace of the replica is proportional to 1/pixelsize
To avoid that, it is possible to change a bit (randomly) the coordinates
of the wavefront. shuffle_interval controls this shift: 0=No shift. A typical
value can be 1e5.
The result shows a diffraction pattern without replica but with much noise.
:param calculate_grid_only: if set, it calculates only the horizontal and vertical profiles, but returns the
full image with the other pixels to zero. This is useful when calculating large arrays,
so it is set as the default.
:return: a new 2D wavefront object with propagated wavefront
"""
#
# Fresnel-Kirchhoff integral (neglecting inclination factor)
#
if calculate_grid_only == 0:
#
# calculation over the whole detector area
#
p_x = wavefront.get_coordinate_x()
p_y = wavefront.get_coordinate_y()
wavelength = wavefront.get_wavelength()
amplitude = wavefront.get_complex_amplitude()
det_x = p_x.copy()
det_y = p_y.copy()
p_X = wavefront.get_mesh_x()
p_Y = wavefront.get_mesh_y()
det_X = p_X
det_Y = p_Y
amplitude_propagated = numpy.zeros_like(amplitude, dtype='complex')
wavenumber = 2 * numpy.pi / wavelength
for i in range(det_x.size):
for j in range(det_y.size):
if shuffle_interval == 0:
rd_x = 0.0
rd_y = 0.0
else:
rd_x = (numpy.random.rand(p_x.size, p_y.size) -
0.5) * shuffle_interval
rd_y = (numpy.random.rand(p_x.size, p_y.size) -
0.5) * shuffle_interval
r = numpy.sqrt(
numpy.power(p_X + rd_x - det_X[i, j], 2) +
numpy.power(p_Y + rd_y - det_Y[i, j], 2) +
numpy.power(propagation_distance, 2))
amplitude_propagated[i, j] = (
amplitude / r * numpy.exp(1.j * wavenumber * r)).sum()
wavefront2 = Wavefront2D.initialize_wavefront_from_arrays(
det_x, det_y, amplitude_propagated)
else:
x = wavefront.get_coordinate_x()
y = wavefront.get_coordinate_y()
X = wavefront.get_mesh_x()
Y = wavefront.get_mesh_y()
wavenumber = 2 * numpy.pi / wavefront.get_wavelength()
amplitude = wavefront.get_complex_amplitude()
used_indices = wavefront.get_mask_grid(width_in_pixels=(1, 1),
number_of_lines=(1, 1))
indices_x = wavefront.get_mesh_indices_x()
indices_y = wavefront.get_mesh_indices_y()
indices_x_flatten = indices_x[numpy.where(used_indices == 1)].flatten()
indices_y_flatten = indices_y[numpy.where(used_indices == 1)].flatten()
X_flatten = X[numpy.where(used_indices == 1)].flatten()
Y_flatten = Y[numpy.where(used_indices == 1)].flatten()
complex_amplitude_propagated = amplitude * 0
print(
"propagate_2D_integral: Calculating %d points from a total of %d x %d = %d"
% (X_flatten.size, amplitude.shape[0], amplitude.shape[1],
amplitude.shape[0] * amplitude.shape[1]))
for i in range(X_flatten.size):
r = numpy.sqrt(
numpy.power(wavefront.get_mesh_x() - X_flatten[i], 2) +
numpy.power(wavefront.get_mesh_y() - Y_flatten[i], 2) +
numpy.power(propagation_distance, 2))
complex_amplitude_propagated[indices_x_flatten[i],
indices_y_flatten[i]] = (
amplitude / r * numpy.exp(
1.j * wavenumber * r)).sum()
wavefront2 = Wavefront2D.initialize_wavefront_from_arrays(
x, y, complex_amplitude_propagated, wavefront.get_wavelength())
return wavefront2
def propagator2d_fourier_rescaling_xy(wf,
propagation_distance,
shift_half_pixel=1,
m_x=1,
m_y=1):
wavefront = wf.duplicate()
wavenumber = wavefront.get_wavenumber()
wavelength = wavefront.get_wavelength()
# frequency for axis 1
shape = wavefront.size()
delta = wavefront.delta()
pixelsize = delta[0] # p_x[1] - p_x[0]
npixels = shape[0]
freq_nyquist = 0.5 / pixelsize
freq_n = numpy.linspace(-1.0, 1.0, npixels)
freq_x = freq_n * freq_nyquist
# frequency for axis 2
pixelsize = delta[1]
npixels = shape[1]
freq_nyquist = 0.5 / pixelsize
freq_n = numpy.linspace(-1.0, 1.0, npixels)
freq_y = freq_n * freq_nyquist
if shift_half_pixel:
freq_x = freq_x - 0.5 * numpy.abs(freq_x[1] - freq_x[0])
freq_y = freq_y - 0.5 * numpy.abs(freq_y[1] - freq_y[0])
f_x, f_y = numpy.meshgrid(freq_x, freq_y, indexing='ij')
fsq = numpy.fft.fftshift(f_x**2 / m_x + f_y**2 / m_y)
x = wavefront.get_mesh_x()
y = wavefront.get_mesh_y()
x_rescaling = wavefront.get_mesh_x() * m_x
y_rescaling = wavefront.get_mesh_y() * m_y
r1sq = x**2 * (1 - m_x) + y**2 * (1 - m_y)
r2sq = x_rescaling**2 * (m_x - 1 / m_x) + y_rescaling**2 * (m_y - 1 / m_y)
Q1 = wavenumber / 2 / propagation_distance * r1sq
Q2 = numpy.exp(-1.0j * numpy.pi * wavelength * propagation_distance * fsq)
Q3 = numpy.exp(1.0j * wavenumber / 2 / propagation_distance * r2sq)
wavefront.add_phase_shift(Q1)
fft = numpy.fft.fft2(wavefront.get_complex_amplitude())
ifft = numpy.fft.ifft2(fft * Q2) * Q3 / numpy.sqrt(m_x * m_y)
wf_propagated = Wavefront2D.initialize_wavefront_from_arrays(
wavefront.get_coordinate_x() *
m_x, ####################NON SONO SICURO CHE SIA GIUSTO QUELLO CHE RETURN
wavefront.get_coordinate_y() * m_y,
ifft,
wavelength=wavelength)
return wf_propagated
def get_wavefront2d(self, i_mode, wavelength):
return Wavefront2D.initialize_wavefront_from_arrays(
self.x_coordinates(),
self.y_coordinates(),
self.mode(i_mode),
wavelength=wavelength)
def test_polarization(self, do_plot=0):
print("# ")
print("# Tests polarization ")
print("# ")
#
# from steps
#
x = numpy.linspace(-10, 10, 100)
y = numpy.linspace(-20, 20, 50)
# XY = numpy.meshgrid(y,x)
# sigma = 3.0
# Z = numpy.exp(- (XY[0]**2+XY[1]**2)/2/sigma**2)
xy = numpy.meshgrid(x, y)
X = xy[0].T
Y = xy[1].T
sigma = 3.0
Z = numpy.exp(-(X**2 + Y**2) / 2 / sigma**2)
Zp = 0.5 * numpy.exp(-(X**2 + Y**2) / 2 / sigma**2)
print("shape of Z", Z.shape)
wf = Wavefront2D.initialize_wavefront_from_steps(x[0],
x[1] - x[0],
y[0],
y[1] - y[0],
number_of_points=(100,
50))
print("wf shape: ", wf.size())
wf.set_complex_amplitude(Z, polarization=Polarization.SIGMA)
wf.set_complex_amplitude(Zp, polarization=Polarization.PI)
print("Total intensity: ",
wf.get_intensity(polarization=Polarization.TOTAL).sum())
print("Sigma intensity: ",
wf.get_intensity(polarization=Polarization.SIGMA).sum())
print("Pi intensity: ",
wf.get_intensity(polarization=Polarization.PI).sum())
self.assertAlmostEqual(wf.get_intensity(polarization=Polarization.TOTAL).sum(),
wf.get_intensity(polarization=Polarization.SIGMA).sum() +\
wf.get_intensity(polarization=Polarization.PI).sum())
#
# from range
#
x = numpy.linspace(-100, 100, 50)
y = numpy.linspace(-50, 50, 200)
X = numpy.outer(x, numpy.ones_like(y))
Y = numpy.outer(numpy.ones_like(x), y)
sigma = 10
Z = numpy.exp(-(X**2 + Y**2) / 2 / sigma**2) * 1j
Zp = 0.3333 * numpy.exp(-(X**2 + Y**2) / 2 / sigma**2) * 1j
print("Shapes x,y,z: ", x.shape, y.shape, Z.shape)
wf1 = Wavefront2D.initialize_wavefront_from_range(
x[0],
x[-1],
y[0],
y[-1],
number_of_points=Z.shape,
polarization=Polarization.SIGMA)
wf1.set_complex_amplitude(Z, polarization=Polarization.SIGMA)
wf1.set_complex_amplitude(Zp, polarization=Polarization.PI)
print("Total intensity: ",
wf1.get_intensity(polarization=Polarization.TOTAL).sum())
print("Sigma intensity: ",
wf1.get_intensity(polarization=Polarization.SIGMA).sum())
print("Pi intensity: ",
wf1.get_intensity(polarization=Polarization.PI).sum())
self.assertAlmostEqual(wf1.get_intensity(polarization=Polarization.TOTAL).sum(),
wf1.get_intensity(polarization=Polarization.SIGMA).sum() +\
wf1.get_intensity(polarization=Polarization.PI).sum())
#
# from arrays
#
wf2 = Wavefront2D.initialize_wavefront_from_arrays(x, y, Z, Zp)
self.assertAlmostEqual(wf2.get_intensity(polarization=Polarization.TOTAL).sum(),
wf2.get_intensity(polarization=Polarization.SIGMA).sum() +\
wf2.get_intensity(polarization=Polarization.PI).sum())
def test_initializers(self, do_plot=do_plot):
print("# ")
print("# Tests for initializars (2D) ")
print("# ")
x = numpy.linspace(-100, 100, 50)
y = numpy.linspace(-50, 50, 200)
XY = numpy.meshgrid(x, y)
X = XY[0].T
Y = XY[1].T
sigma = 10
Z = numpy.exp(-(X**2 + Y**2) / 2 / sigma**2) * 1j
print("Shapes x,y,z: ", x.shape, y.shape, Z.shape)
wf0 = Wavefront2D.initialize_wavefront_from_steps(
x[0],
numpy.abs(x[1] - x[0]),
y[0],
numpy.abs(y[1] - y[0]),
number_of_points=Z.shape)
wf0.set_complex_amplitude(Z)
wf1 = Wavefront2D.initialize_wavefront_from_range(
x[0], x[-1], y[0], y[-1], number_of_points=Z.shape)
wf1.set_complex_amplitude(Z)
wf2 = Wavefront2D.initialize_wavefront_from_arrays(x, y, Z)
if do_plot:
from srxraylib.plot.gol import plot_image
plot_image(wf0.get_intensity(),
wf0.get_coordinate_x(),
wf0.get_coordinate_y(),
title="initialize_wavefront_from_steps",
show=0)
plot_image(wf1.get_intensity(),
wf1.get_coordinate_x(),
wf1.get_coordinate_y(),
title="initialize_wavefront_from_range",
show=0)
plot_image(wf2.get_intensity(),
wf2.get_coordinate_x(),
wf2.get_coordinate_y(),
title="initialize_wavefront_from_arrays",
show=1)
numpy.testing.assert_almost_equal(
numpy.abs(Z)**2, wf0.get_intensity(), 11)
numpy.testing.assert_almost_equal(
numpy.abs(Z)**2, wf1.get_intensity(), 11)
numpy.testing.assert_almost_equal(
numpy.abs(Z)**2, wf2.get_intensity(), 11)
numpy.testing.assert_almost_equal(x, wf0.get_coordinate_x(), 11)
numpy.testing.assert_almost_equal(x, wf1.get_coordinate_x(), 11)
numpy.testing.assert_almost_equal(x, wf2.get_coordinate_x(), 11)
numpy.testing.assert_almost_equal(y, wf0.get_coordinate_y(), 11)
numpy.testing.assert_almost_equal(y, wf1.get_coordinate_y(), 11)
numpy.testing.assert_almost_equal(y, wf2.get_coordinate_y(), 11)
