def propagate_1D_fraunhofer(wavefront, propagation_distance=0.0, shift_half_pixel=1):
"""
1D 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)
:return: a new 1D wavefront object with propagated wavefront
"""
fft = numpy.fft.fft(wavefront.get_complex_amplitude())
fft2 = numpy.fft.fftshift(fft)
# frequency for axis 1
freq_nyquist = 0.5/wavefront.delta()
freq_n = numpy.linspace(-1.0,1.0,wavefront.size())
freq_x = freq_n * freq_nyquist
freq_x *= wavefront.get_wavelength()
if shift_half_pixel:
freq_x = freq_x - 0.5 * numpy.abs(freq_x[1] - freq_x[0])
if propagation_distance == 0:
wf = Wavefront1D.initialize_wavefront_from_arrays(freq_x,fft2,wavelength=wavefront.get_wavelength())
return wf
else:
wf = Wavefront1D.initialize_wavefront_from_arrays(freq_x*propagation_distance,fft2,wavelength=wavefront.get_wavelength())
return wf
def test_initializers(self,do_plot=do_plot):
print("# ")
print("# Tests for initializars (1D) ")
print("# ")
x = numpy.linspace(-100,100,50)
y = numpy.abs(x)**1.5 + 1j*numpy.abs(x)**1.8
wf0 = Wavefront1D.initialize_wavefront_from_steps(x[0],numpy.abs(x[1]-x[0]),y.size)
wf0.set_complex_amplitude(y)
wf1 = Wavefront1D.initialize_wavefront_from_range(x[0],x[-1],y.size)
wf1.set_complex_amplitude(y)
wf2 = Wavefront1D.initialize_wavefront_from_arrays(x,y)
print("wavefront sizes: ",wf1.size(),wf1.size(),wf2.size())
if do_plot:
from srxraylib.plot.gol import plot
plot(wf0.get_abscissas(),wf0.get_intensity(),
title="initialize_wavefront_from_steps",show=0)
plot(wf1.get_abscissas(),wf1.get_intensity(),
title="initialize_wavefront_from_range",show=0)
plot(wf2.get_abscissas(),wf2.get_intensity(),
title="initialize_wavefront_from_arrays",show=1)
numpy.testing.assert_almost_equal(wf0.get_intensity(),numpy.abs(y)**2,5)
numpy.testing.assert_almost_equal(wf1.get_intensity(),numpy.abs(y)**2,5)
numpy.testing.assert_almost_equal(x,wf1.get_abscissas(),11)
numpy.testing.assert_almost_equal(x,wf2.get_abscissas(),11)
def propagate_1D_fraunhofer(
wavefront,
propagation_distance=0.0,
shift_half_pixel=0): # todo: modificato da giovanni
"""
1D Fraunhofer propagator using convolution via Fourier transform
:param shift_half_pixel:
:param shift_half_pixel:
:param wavefront:
:param propagation_distance: propagation distance. If set to zero, the abscissas
of the returned wavefront are in angle (rad)
:return: a new 1D wavefront object with propagated wavefront
"""
shape = wavefront.size()
delta = wavefront.delta()
wavenumber = wavefront.get_wavenumber()
wavelength = wavefront.get_wavelength()
fft_scale = numpy.fft.fftfreq(shape, d=delta)
fft_scale = numpy.fft.fftshift(fft_scale)
x2 = fft_scale * propagation_distance * wavelength
# freq_nyquist = 0.5 / delta
# freq_n = numpy.linspace(-1.0, 1.0, shape)
# freq_x = freq_n * freq_nyquist
# freq_x *= wavelength * propagation_distance
# x2 = freq_x
P1 = numpy.exp(1.0j * wavenumber * propagation_distance)
P2 = numpy.exp(1.0j * wavenumber / (2 * propagation_distance) * x2**2)
P3 = 1.0j * wavelength * propagation_distance
fft = numpy.fft.fft(wavefront.get_complex_amplitude())
fft *= P1
fft *= P2
fft /= P3
# fft *= P4
fft2 = numpy.fft.fftshift(fft)
if shift_half_pixel:
x2 = x2 - 0.5 * numpy.abs(x2[1] - x2[0])
return Wavefront1D.initialize_wavefront_from_arrays(
x2, fft2, wavelength=wavefront.get_wavelength())
def test_initializers(self, do_plot=do_plot):
print("# ")
print("# Tests for initializars (1D) ")
print("# ")
x = numpy.linspace(-100, 100, 50)
y = numpy.abs(x)**1.5 + 1j * numpy.abs(x)**1.8
wf0 = Wavefront1D.initialize_wavefront_from_steps(
x[0], numpy.abs(x[1] - x[0]), y.size)
wf0.set_complex_amplitude(y)
wf1 = Wavefront1D.initialize_wavefront_from_range(x[0], x[-1], y.size)
wf1.set_complex_amplitude(y)
wf2 = Wavefront1D.initialize_wavefront_from_arrays(x, y)
print("wavefront sizes: ", wf1.size(), wf1.size(), wf2.size())
if do_plot:
from srxraylib.plot.gol import plot
plot(wf0.get_abscissas(),
wf0.get_intensity(),
title="initialize_wavefront_from_steps",
show=0)
plot(wf1.get_abscissas(),
wf1.get_intensity(),
title="initialize_wavefront_from_range",
show=0)
plot(wf2.get_abscissas(),
wf2.get_intensity(),
title="initialize_wavefront_from_arrays",
show=1)
numpy.testing.assert_almost_equal(wf0.get_intensity(),
numpy.abs(y)**2, 5)
numpy.testing.assert_almost_equal(wf1.get_intensity(),
numpy.abs(y)**2, 5)
numpy.testing.assert_almost_equal(x, wf1.get_abscissas(), 11)
numpy.testing.assert_almost_equal(x, wf2.get_abscissas(), 11)
