def test_1d_gaussian_slope_error(self):
mirror_length=200.0
step=1.0
rms_slopes=1.3e-7
rms_heights = 1e-7
correlation_length = 10.0
x, f = simulate_profile_1D_gaussian(step=step, \
mirror_length=mirror_length, \
rms_heights=rms_heights, \
correlation_length=correlation_length,\
renormalize_to_slopes_sd=None)
slopes = numpy.gradient(f, x[1]-x[0])
print("test_1d_gaussian: test function: %s, Stdev (not normalized): HEIGHTS=%g.SLOPES=%g"%("test_1d_gaussian_slope_error",f.std(),slopes.std()))
x, f = simulate_profile_1D_gaussian(step=step, \
mirror_length=mirror_length, \
rms_heights=rms_heights, \
correlation_length=correlation_length,\
renormalize_to_slopes_sd=rms_slopes)
slopes = numpy.gradient(f, x[1]-x[0])
print("test_1d_gaussian: test function: %s, SLOPES Stdev (normalized to %g)=%g"%("test_1d_gaussian_slope_error",rms_slopes,slopes.std()))
assert numpy.abs( rms_slopes - slopes.std() ) < 0.01 * numpy.abs(rms_slopes)
if do_plot:
from srxraylib.plot.gol import plot
plot(x,slopes,title="test_1d_gaussian_slope_error",xtitle="Y",ytitle="slopes Z'")
def propagate_1D(self,do_plot=do_plot,method='fft',
wavelength=1.24e-10,aperture_type='square',aperture_diameter=40e-6,
wavefront_length=100e-6,npoints=500,
propagation_distance = 30.0,show=1):
print("\n# ")
print("# far field 1D (fraunhofer) diffraction from a %s aperture "%aperture_type)
print("# ")
wf = Wavefront1D.initialize_wavefront_from_range(x_min=-wavefront_length/2, x_max=wavefront_length/2,
number_of_points=npoints,wavelength=wavelength)
wf.set_plane_wave_from_complex_amplitude((2.0+1.0j)) # an arbitraty value
if aperture_type == 'square':
wf.apply_slit(-aperture_diameter/2, aperture_diameter/2)
elif aperture_type == 'gaussian':
X = wf.get_mesh_x()
Y = wf.get_mesh_y()
window = numpy.exp(- (X*X + Y*Y)/2/(aperture_diameter/2.35)**2)
wf.rescale_amplitudes(window)
else:
raise Exception("Not implemented! (accepted: circle, square, gaussian)")
if method == 'fft':
wf1 = propagate_1D_fresnel(wf, propagation_distance)
elif method == 'convolution':
wf1 = propagate_1D_fresnel_convolution(wf, propagation_distance)
elif method == 'integral':
wf1 = propagate_1D_integral(wf, propagation_distance)
elif method == 'fraunhofer':
wf1 = propagate_1D_fraunhofer(wf, propagation_distance)
else:
raise Exception("Not implemented method: %s"%method)
# get the theoretical value
angle_x = wf1.get_abscissas() / propagation_distance
intensity_theory = get_theoretical_diffraction_pattern(angle_x,aperture_type=aperture_type,aperture_diameter=aperture_diameter,
wavelength=wavelength,normalization=True)
intensity_calculated = wf1.get_intensity()
intensity_calculated /= intensity_calculated.max()
if do_plot:
from srxraylib.plot.gol import plot
plot(wf1.get_abscissas()*1e6/propagation_distance,intensity_calculated,
angle_x*1e6,intensity_theory,
legend=["%s "%method,"Theoretical (far field)"],
legend_position=(0.95, 0.95),
title="1D (%s) diffraction from a %s aperture of %3.1f um at wavelength of %3.1f A"%
(method,aperture_type,aperture_diameter*1e6,wavelength*1e10),
xtitle="X (urad)", ytitle="Intensity",xrange=[-20,20],
show=show)
return wf1.get_abscissas()/propagation_distance,intensity_calculated,intensity_theory
def showModeDistribution(self):
try:
from srxraylib.plot.gol import plot
y = (self.modeDistribution()).real
x = np.arange(y.shape[0])
plot(x, y, title = "Mode distribution", xtitle = "Mode index", ytitle = "Occupancy")
except:
pass
def propagation_to_image(wf,do_plot=do_plot,plot_title="Before lens",method='fft',
propagation_distance=30.0,defocus_factor=1.0,propagation_steps=1,show=1):
method_label = "fresnel (%s)"%method
print("\n# ")
print("# near field fresnel (%s) diffraction and focusing "%(method_label))
print("# ")
# \ | /
# * | | | *
# / | \
# <------- d ---------------><--------- d ------->
# d is propagation_distance
print("Incident intensity: ",wf.get_intensity().sum())
# propagation downstream the lens to image plane
for i in range(propagation_steps):
if propagation_steps > 1:
print(">>> Propagating step %d of %d; propagation_distance=%g m"%(i+1,propagation_steps,
propagation_distance*defocus_factor/propagation_steps))
if method == 'fft':
wf = propagate_2D_fresnel(wf, propagation_distance*defocus_factor/propagation_steps)
elif method == 'convolution':
wf = propagate_2D_fresnel_convolution(wf, propagation_distance*defocus_factor/propagation_steps)
elif method == 'srw':
wf = propagate_2D_fresnel_srw(wf, propagation_distance*defocus_factor/propagation_steps)
elif method == 'fraunhofer':
wf = propagate_2D_fraunhofer(wf, propagation_distance*defocus_factor/propagation_steps)
else:
raise Exception("Not implemented method: %s"%method)
horizontal_profile = wf.get_intensity()[:,wf.size()[1]/2]
horizontal_profile /= horizontal_profile.max()
print("FWHM of the horizontal profile: %g um"%(1e6*line_fwhm(horizontal_profile)*wf.delta()[0]))
vertical_profile = wf.get_intensity()[wf.size()[0]/2,:]
vertical_profile /= vertical_profile.max()
print("FWHM of the vertical profile: %g um"%(1e6*line_fwhm(vertical_profile)*wf.delta()[1]))
if do_plot:
from srxraylib.plot.gol import plot,plot_image
plot_image(wf.get_intensity(),1e6*wf.get_coordinate_x(),1e6*wf.get_coordinate_y(),
xtitle="X um",ytitle="Y um",title='intensity (%s)'%method,show=0)
# plot_image(wf.get_amplitude(),wf.get_coordinate_x(),wf.get_coordinate_y(),title='amplitude (%s)'%method,show=0)
plot_image(wf.get_phase(),1e6*wf.get_coordinate_x(),1e6*wf.get_coordinate_y(),
xtitle="X um",ytitle="Y um",title='phase (%s)'%method,show=0)
plot(wf.get_coordinate_x(),horizontal_profile,
wf.get_coordinate_y(),vertical_profile,
legend=['Horizontal profile','Vertical profile'],title="%s %s"%(plot_title,method),show=show)
print("Output intensity: ",wf.get_intensity().sum())
return wf,wf.get_coordinate_x(),horizontal_profile
def test_plane_wave(self,do_plot=do_plot):
#
# plane wave
#
print("# ")
print("# Tests for a 1D plane wave ")
print("# ")
wavelength = 1.24e-10
wavefront_length_x = 400e-6
npixels_x = 1024
wavefront_x = numpy.linspace(-0.5*wavefront_length_x,0.5*wavefront_length_x,npixels_x)
wavefront = Wavefront1D.initialize_wavefront_from_steps(
x_start=wavefront_x[0],x_step=numpy.abs(wavefront_x[1]-wavefront_x[0]),
number_of_points=npixels_x,wavelength=wavelength)
numpy.testing.assert_almost_equal(wavefront_x,wavefront.get_abscissas(),9)
# possible modifications
wavefront.set_plane_wave_from_amplitude_and_phase(5.0,numpy.pi/2)
numpy.testing.assert_almost_equal(wavefront.get_intensity(),25,5)
wavefront.set_plane_wave_from_complex_amplitude(2.0+3j)
numpy.testing.assert_almost_equal(wavefront.get_intensity(),13,5)
phase_before = wavefront.get_phase()
wavefront.add_phase_shift(numpy.pi/2)
phase_after = wavefront.get_phase()
numpy.testing.assert_almost_equal(phase_before+numpy.pi/2,phase_after,5)
intensity_before = wavefront.get_intensity()
wavefront.rescale_amplitude(10.0)
intensity_after = wavefront.get_intensity()
numpy.testing.assert_almost_equal(intensity_before*100,intensity_after,5)
# interpolation
wavefront.set_plane_wave_from_complex_amplitude(2.0+3j)
test_value1 = wavefront.get_interpolated_complex_amplitude(0.01)
self.assertAlmostEqual( (2.0+3j).real, test_value1.real, 5)
self.assertAlmostEqual( (2.0+3j).imag, test_value1.imag, 5)
if do_plot:
from srxraylib.plot.gol import plot
plot(wavefront.get_abscissas(),wavefront.get_intensity(),title="Intensity (plane wave)",show=0)
plot(wavefront.get_abscissas(),wavefront.get_phase(),title="Phase (plane wave)",show=1)
def test_1d_fractal_slope_error(self):
mirror_length=200.0
step=1.0
rms=3e-6
x, f = simulate_profile_1D_fractal(step=step,mirror_length=mirror_length,
renormalize_to_slopes_sd=rms)
slopes = numpy.gradient(f, x[1]-x[0])
print("%s, SLOPES Stdev: input=%g, obtained=%g"%("test_1d_fractal_slope_error",rms,slopes.std()))
assert numpy.abs( rms - slopes.std() ) < 0.01 * numpy.abs(rms)
if do_plot:
from srxraylib.plot.gol import plot
plot(x,slopes,title="test_1d_fractal_slope_error",xtitle="Y",ytitle="slopes Z'")
def test_1d_fractal_figure_error(self):
mirror_length=200.0
step=1.0
rms=1.25e-7
x, f = simulate_profile_1D_fractal(step=step,mirror_length=mirror_length,
renormalize_to_heights_sd=rms)
print("%s, HEIGHTS Stdev: input=%g, obtained=%g"%("test_1d_fractal_figure_error",rms,f.std()))
assert numpy.abs( rms - f.std() ) < 0.01 * numpy.abs(rms)
if do_plot:
from srxraylib.plot.gol import plot
plot(x,f,title="test_1d_fractal_figure_error",xtitle="Y",ytitle="heights profile Z")
def test_1d_aps_figure_error(self):
mirror_length=200.0
step=1.0
random_seed=898882
rms=1e-7
# units mm
wName_x,wName = create_simulated_1D_file_APS(mirror_length=mirror_length,step=step, random_seed=random_seed,
error_type=FIGURE_ERROR, rms=rms)
print("%s, HEIGHTS Stdev: input=%g, obtained=%g"%("test_1d_aps_figure_error",rms,wName.std()))
assert numpy.abs( rms - wName.std() ) < 0.01 * numpy.abs(rms)
if do_plot:
from srxraylib.plot.gol import plot
plot(wName_x,wName,title="test_1d_aps_figure_error",xtitle="Y",ytitle="heights profile Z")
def test_1d_aps_slope_error(self):
mirror_length=200.0
step=1.0
random_seed=898882
rms=1e-7
# units mm
wName_x,wName = create_simulated_1D_file_APS(mirror_length=mirror_length,step=step, random_seed=random_seed,
error_type=SLOPE_ERROR, rms=rms)
slopes = numpy.gradient(wName, wName_x[1]-wName_x[0])
print("test_1d: test function: %s, SLOPES Stdev: input=%g, obtained=%g"%("test_1d_aps_figure_error",rms,slopes.std()))
assert numpy.abs( rms - slopes.std() ) < 0.01 * numpy.abs(rms)
if do_plot:
from srxraylib.plot.gol import plot
plot(wName_x,slopes,title="test_1d_aps_slope_error",xtitle="Y",ytitle="slopes Z'")
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 test_interpolator(self,do_plot=do_plot):
#
# interpolator
#
print("# ")
print("# Tests for 1D interpolator ")
print("# ")
x = numpy.linspace(-10,10,100)
sigma = 3.0
Z = numpy.exp(-1.0*x**2/2/sigma**2)
print("shape of Z",Z.shape)
wf = Wavefront1D.initialize_wavefront_from_steps(x[0],numpy.abs(x[1]-x[0]),number_of_points=100)
print("wf shape: ",wf.size())
wf.set_complex_amplitude( Z )
x1 = 3.2
z1 = numpy.exp(x1**2/-2/sigma**2)
print("complex ampl at (%g): %g+%gi (exact=%g)"%(x1,
wf.get_interpolated_complex_amplitude(x1).real,
wf.get_interpolated_complex_amplitude(x1).imag,
z1))
self.assertAlmostEqual(wf.get_interpolated_complex_amplitude(x1).real,z1,4)
print("intensity at (%g): %g (exact=%g)"%(x1,wf.get_interpolated_intensity(x1),z1**2))
self.assertAlmostEqual(wf.get_interpolated_intensity(x1),z1**2,4)
if do_plot:
from srxraylib.plot.gol import plot
plot(wf.get_abscissas(),wf.get_intensity(),title="Original",show=1)
xx = wf.get_abscissas()
yy = wf.get_interpolated_intensities(wf.get_abscissas()-1e-5)
plot(xx,yy,title="interpolated on same grid",show=1)
def test_spherical_wave(self,do_plot=do_plot):
#
# plane wave
#
print("# ")
print("# Tests for a 1D spherical wave ")
print("# ")
wavelength = 1.24e-10
wavefront_length_x = 400e-6
npixels_x = 1024
wavefront_x = numpy.linspace(-0.5*wavefront_length_x,0.5*wavefront_length_x,npixels_x)
wf1 = Wavefront1D.initialize_wavefront_from_steps(
x_start=wavefront_x[0],x_step=numpy.abs(wavefront_x[1]-wavefront_x[0]),
number_of_points=npixels_x,wavelength=wavelength)
wf2 = Wavefront1D.initialize_wavefront_from_steps(
x_start=wavefront_x[0],x_step=numpy.abs(wavefront_x[1]-wavefront_x[0]),
number_of_points=npixels_x,wavelength=wavelength)
# an spherical wavefront is obtained 1) by creation, 2) focusing a planewave
wf1.set_spherical_wave(-5.0, 3+0j)
wf1.apply_slit(-50e-6,10e-6)
wf2.set_plane_wave_from_complex_amplitude(3+0j)
wf2.apply_ideal_lens(5.0)
wf2.apply_slit(-50e-6,10e-6)
if do_plot:
from srxraylib.plot.gol import plot
plot(wf1.get_abscissas(),wf1.get_phase(),title="Phase of spherical wavefront",show=0)
plot(wf2.get_abscissas(),wf2.get_phase(),title="Phase of focused plane wavefront",show=0)
plot(wf1.get_abscissas(),wf1.get_phase(from_minimum_intensity=0.1),title="Phase of spherical wavefront (for intensity > 0.1)",show=0)
plot(wf2.get_abscissas(),wf2.get_phase(from_minimum_intensity=0.1),title="Phase of focused plane wavefront (for intensity > 0.1)",show=1)
numpy.testing.assert_almost_equal(wf1.get_phase(),wf2.get_phase(),5)
def test_plane_wave(do_plot=0):
import copy
#
# plane wave
#
value_amplitude = 5.0
value_phase = numpy.pi
wavefront = Wavefront1D.initialize_wavefront_from_range(
wavelength=1e-2, number_of_points=1000000, x_min=-1, x_max=1
)
wavefront.set_plane_wave_from_amplitude_and_phase(value_amplitude, value_phase)
wavefront.apply_slit(-0.4, 0.4)
wavefront_focused = copy.deepcopy(wavefront)
wavefront_focused.apply_ideal_lens(100)
#
# some tests
#
test_value1 = wavefront.get_interpolated_amplitude(0.01) - value_amplitude
assert numpy.abs(test_value1) < 1e-6
test_value2 = wavefront.get_interpolated_amplitudes(-4)
assert numpy.abs(test_value2) < 1e-6
if do_plot:
from srxraylib.plot.gol import plot
plot(
wavefront.get_abscissas(),
wavefront.get_intensity(),
show=0,
title="Plane wave defined in [-1,1] and clipped by a [-.4,.4] slit",
xtitle="X (m)",
ytitle="Intensity",
)
plot(
wavefront.get_abscissas(),
wavefront.get_amplitude(),
show=0,
title="Plane wave defined in [-1,1] and clipped by a [-.4,.4] slit",
xtitle="X (m)",
ytitle="Amplitude",
)
plot(
wavefront.get_abscissas(),
wavefront.get_phase(),
show=0,
title="Plane wave defined in [-1,1] and clipped by a [-.4,.4] slit",
xtitle="X (m)",
ytitle="Phase [rad]",
)
plot(
wavefront.get_abscissas(),
wavefront_focused.get_phase(),
show=1,
title="Plane wave after ideal lens",
xtitle="X (m)",
ytitle="Phase [rad]",
)
#
# plot profiles
#
horizontal_intensity_profile = wf_prop.get_intensity()[:,wf_prop.size()[1]/2]
horizontal_intensity_profile /= horizontal_intensity_profile.max()
vertical_intensity_profile = wf_prop.get_intensity()[wf_prop.size()[0]/2,:]
vertical_intensity_profile /= vertical_intensity_profile.max()
horizontal_intensity_profile_srw = wf_prop_srw.get_intensity()[:,wf_prop_srw.size()[1]/2]
horizontal_intensity_profile_srw /= horizontal_intensity_profile_srw.max()
vertical_intensity_profile_srw = wf_prop_srw.get_intensity()[wf_prop_srw.size()[0]/2,:]
vertical_intensity_profile_srw /= vertical_intensity_profile_srw.max()
plot( 1e6*wf_prop.get_coordinate_x(), horizontal_intensity_profile,
1e6*wf_prop_srw.get_coordinate_x(), horizontal_intensity_profile_srw,
show=0,
legend=["in-python","SRW"],color=["red","black"],
title="Horizontal profile of diffracted intensity",xtitle='X [um]',ytitle='Diffracted intensity [a.u.]')
plot( 1e6*wf_prop.get_coordinate_y(), vertical_intensity_profile,
1e6*wf_prop_srw.get_coordinate_y(), vertical_intensity_profile_srw,
show=0,
legend=["in-python","SRW"],color=["red","black"],
title="Vertical profile of diffracted intensity",xtitle='X [um]',ytitle='Diffracted intensity [a.u.]')
plot_show()
#
# sample rays fro SHADOW
def test_ScaledArray(self,do_plot=do_plot):
#
# ScaledArray.initialize + set_scale_from_steps
#
test_array = numpy.arange(15.0, 18.8, 0.2)
print("\nTesting ScaledArray.initialize + set_scale_from_steps...")
scaled_array = ScaledArray.initialize(test_array)
scaled_array.set_scale_from_steps(test_array[0],0.2)
print("Using array: ",test_array)
print("Stored array: ",scaled_array.get_values())
print("Using array: ",test_array)
print("Stored abscissas: ",scaled_array.get_abscissas())
numpy.testing.assert_almost_equal(test_array,scaled_array.get_values(),11)
numpy.testing.assert_almost_equal(test_array,scaled_array.get_abscissas(),11)
self.assertAlmostEqual(0.2,scaled_array.delta(),11)
self.assertAlmostEqual(15.0,scaled_array.offset(),11)
x_in = (18.80,16.22,22.35)
x_good = (18.80,16.22,18.8)
for i,x in enumerate(x_in):
print("interpolated at %3.2f is: %3.2f (must give %3.2f)"%( x,scaled_array.interpolate_value(x), x_good[i] ))
self.assertAlmostEqual(scaled_array.interpolate_value(x), x_good[i], 2)
#
# ScaledArray.initialize + set_scale_from_range ; interpolate vectorized
#
print("\nTesting ScaledArray.initialize + set_scale_from_range ; interpolate vectorized...")
scaled_array = ScaledArray.initialize(test_array)
scaled_array.set_scale_from_range(test_array[0],test_array[-1])
x_in = (18.80,16.22,22.35)
x_good = (18.80,16.22,18.8)
for i,x in enumerate(x_in):
print("interpolated at %3.2f is: %3.2f (must give %3.2f)"%( x,scaled_array.interpolate_value(x), x_good[i] ))
self.assertAlmostEqual(scaled_array.interpolate_value(x), x_good[i], 2)
#
# ScaledArray.initialize_from_steps
#
print("\nTesting ScaledArray.initialize_from_steps...")
scaled_array = ScaledArray.initialize_from_steps(test_array, test_array[0], 0.2)
x_in = (18.80,16.22,22.35)
x_good = (18.80,16.22,18.8)
for i,x in enumerate(x_in):
print("interpolated at %3.2f is: %3.2f (must give %3.2f)"%( x,scaled_array.interpolate_value(x), x_good[i] ))
self.assertAlmostEqual(scaled_array.interpolate_value(x), x_good[i], 2)
#
# ScaledArray.initialize_from_steps
#
print("\nTesting ScaledArray.initialize_from_range...")
scaled_array = ScaledArray.initialize_from_range(test_array,test_array[0], test_array[-1])
x_in = (18.80,16.22,22.35)
x_good = (18.80,16.22,18.8)
for i,x in enumerate(x_in):
print("interpolated at %3.2f is: %3.2f (must give %3.2f)"%( x,scaled_array.interpolate_value(x), x_good[i] ))
self.assertAlmostEqual(scaled_array.interpolate_value(x), x_good[i], 2)
#
# interpolator
#
print("\nTesting interpolator...")
x = numpy.arange(-5.0, 18.8, 3)
y = x**2
scaled_array = ScaledArray.initialize_from_range(y,x[0],x[-1])
print("for interpolation; x=",x)
print("for interpolation; offset, delta:=",scaled_array.offset(),scaled_array.delta())
print("for interpolation; abscissas:=",scaled_array.get_abscissas())
x1 = numpy.concatenate( ( numpy.arange(-6, -4, 0.1) , [0], numpy.arange(11, 20.0, 0.1) ) )
y1 = scaled_array.interpolate_values(x1)
if do_plot:
from srxraylib.plot.gol import plot
plot(x,y,x1,y1,legend=["Data",'Interpolated'],legend_position=[0.4,0.8],
marker=['','o'],linestyle=['-',''],xrange=[-6,21],yrange=[-5,375])
for i in range(len(x1)):
y2 = x1[i]**2
if x1[i] <= x[0]:
y2 = y[0]
if x1[i] >= x[-1]:
y2 = y[-1]
print(" interpolated at x=%g is: %g (expected: %g)"%(x1[i],y1[i],y2))
self.assertAlmostEqual(1e-3*y1[i], 1e-3*y2, 2)
# interpolate on same grid
print("\nTesting interpolation on the same grid...")
y1 = scaled_array.interpolate_values(scaled_array.get_abscissas())
if do_plot:
from srxraylib.plot.gol import plot
plot(scaled_array.get_abscissas(),scaled_array.get_values(),
scaled_array.get_abscissas(),y1,legend=["Data",'Interpolated on same grid'],legend_position=[0.4,0.8],
marker=['','o'],linestyle=['-',''])
numpy.testing.assert_almost_equal(scaled_array.get_values(),y1,5)
def propagate_2D_fresnel(self,do_plot=do_plot,method='fft',
wavelength=1.24e-10,aperture_type='square',aperture_diameter=40e-6,
pixelsize_x=1e-6,pixelsize_y=1e-6,npixels_x=1024,npixels_y=1024,
propagation_distance = 30.0,show=1):
method_label = "fresnel (%s)"%method
print("\n# ")
print("# 2D near field fresnel (%s) diffraction from a %s aperture "%(method_label,aperture_type))
print("# ")
# wf = Wavefront2D.initialize_wavefront_from_steps(x_start=-pixelsize_x*npixels_x/2,
# x_step=pixelsize_x,
# y_start=-pixelsize_y*npixels_y/2,
# y_step=pixelsize_y,
# wavelength=wavelength,
# number_of_points=(npixels_x,npixels_y))
wf = Wavefront2D.initialize_wavefront_from_range(x_min=-pixelsize_x*npixels_x/2,x_max=pixelsize_x*npixels_x/2,
y_min=-pixelsize_y*npixels_y/2,y_max=pixelsize_y*npixels_y/2,
number_of_points=(npixels_x,npixels_y),wavelength=wavelength)
wf.set_plane_wave_from_complex_amplitude((1.0+0j))
if aperture_type == 'circle':
wf.apply_pinhole(aperture_diameter/2)
elif aperture_type == 'square':
wf.apply_slit(-aperture_diameter/2, aperture_diameter/2,-aperture_diameter/2, aperture_diameter/2)
elif aperture_type == 'gaussian':
X = wf.get_mesh_x()
Y = wf.get_mesh_y()
window = numpy.exp(- (X*X + Y*Y)/2/(aperture_diameter/2.35)**2)
wf.rescale_amplitudes(window)
else:
raise Exception("Not implemented! (accepted: circle, square, gaussian)")
if method == 'fft':
wf1 = propagate_2D_fresnel(wf, propagation_distance)
elif method == 'convolution':
wf1 = propagate_2D_fresnel_convolution(wf, propagation_distance)
elif method == 'srw':
wf1 = propagate_2D_fresnel_srw(wf, propagation_distance)
elif method == 'integral':
wf1 = propagate_2D_integral(wf, propagation_distance)
else:
raise Exception("Not implemented method: %s"%method)
if do_plot:
from srxraylib.plot.gol import plot_image
plot_image(wf.get_intensity(),1e6*wf.get_coordinate_x(),1e6*wf.get_coordinate_y(),
title="aperture intensity (%s), Diameter=%5.1f um"%
(aperture_type,1e6*aperture_diameter),xtitle="X [um]",ytitle="Y [um]",
show=0)
plot_image(wf1.get_intensity(),
1e6*wf1.get_coordinate_x()/propagation_distance,
1e6*wf1.get_coordinate_y()/propagation_distance,
title="Diffracted intensity (%s) by a %s slit of aperture %3.1f um"%
(aperture_type,method_label,1e6*aperture_diameter),
xtitle="X [urad]",ytitle="Y [urad]",
show=0)
# get the theoretical value
angle_x = wf1.get_coordinate_x() / propagation_distance
intensity_theory = get_theoretical_diffraction_pattern(angle_x,aperture_type=aperture_type,aperture_diameter=aperture_diameter,
wavelength=wavelength,normalization=True)
intensity_calculated = wf1.get_intensity()[:,wf1.size()[1]/2]
intensity_calculated /= intensity_calculated.max()
if do_plot:
from srxraylib.plot.gol import plot
plot(wf1.get_coordinate_x()*1e6/propagation_distance,intensity_calculated,
angle_x*1e6,intensity_theory,
legend=["%s H profile"%method_label,"Theoretical (far field)"],
legend_position=(0.95, 0.95),
title="%s diffraction of a %s slit of %3.1f um at wavelength of %3.1f A"%
(method_label,aperture_type,aperture_diameter*1e6,wavelength*1e10),
xtitle="X (urad)", ytitle="Intensity",xrange=[-20,20],
show=show)
return wf1.get_coordinate_x()/propagation_distance,intensity_calculated,angle_x,intensity_theory
def propagation_with_lens(self,do_plot=do_plot,method='fft',
wavelength=1.24e-10,
pixelsize_x=1e-6,npixels_x=2000,pixelsize_y=1e-6,npixels_y=2000,
propagation_distance=30.0,defocus_factor=1.0,propagation_steps=1,show=1):
method_label = "fresnel (%s)"%method
print("\n# ")
print("# near field fresnel (%s) diffraction and focusing "%(method_label))
print("# ")
# \ | /
# * | | | *
# / | \
# <------- d ---------------><--------- d ------->
# d is propagation_distance
# wf = Wavefront2D.initialize_wavefront_from_steps(x_start=-pixelsize_x*npixels_x/2,
# x_step=pixelsize_x,
# y_start=-pixelsize_y*npixels_y/2,
# y_step=pixelsize_y,
# wavelength=wavelength,
# number_of_points=(npixels_x,npixels_y))
wf = Wavefront2D.initialize_wavefront_from_range(x_min=-pixelsize_x*npixels_x/2,x_max=pixelsize_x*npixels_x/2,
y_min=-pixelsize_y*npixels_y/2,y_max=pixelsize_y*npixels_y/2,
number_of_points=(npixels_x,npixels_y),wavelength=wavelength)
spherical_or_plane_and_lens = 0
if spherical_or_plane_and_lens == 0:
# set spherical wave at the lens entrance (radius=distance)
wf.set_spherical_wave(complex_amplitude=1.0,radius=-propagation_distance)
else:
# apply lens that will focus at propagation_distance downstream the lens.
# Note that the vertical is a bit defocused
wf.set_plane_wave_from_complex_amplitude(1.0+0j)
focal_length = propagation_distance # / 2
wf.apply_ideal_lens(focal_length,focal_length)
print("Incident intensity: ",wf.get_intensity().sum())
# propagation downstream the lens to image plane
for i in range(propagation_steps):
if propagation_steps > 1:
print(">>> Propagating step %d of %d; propagation_distance=%g m"%(i+1,propagation_steps,
propagation_distance*defocus_factor/propagation_steps))
if method == 'fft':
wf = propagate_2D_fresnel(wf, propagation_distance*defocus_factor/propagation_steps)
elif method == 'convolution':
wf = propagate_2D_fresnel_convolution(wf, propagation_distance*defocus_factor/propagation_steps)
elif method == 'srw':
wf = propagate_2D_fresnel_srw(wf, propagation_distance*defocus_factor/propagation_steps)
elif method == 'fraunhofer':
wf = propagate_2D_fraunhofer(wf, propagation_distance*defocus_factor/propagation_steps)
else:
raise Exception("Not implemented method: %s"%method)
horizontal_profile = wf.get_intensity()[:,wf.size()[1]/2]
horizontal_profile /= horizontal_profile.max()
print("FWHM of the horizontal profile: %g um"%(1e6*line_fwhm(horizontal_profile)*wf.delta()[0]))
vertical_profile = wf.get_intensity()[wf.size()[0]/2,:]
vertical_profile /= vertical_profile.max()
print("FWHM of the vertical profile: %g um"%(1e6*line_fwhm(vertical_profile)*wf.delta()[1]))
if do_plot:
from srxraylib.plot.gol import plot,plot_image
plot_image(wf.get_intensity(),wf.get_coordinate_x(),wf.get_coordinate_y(),title='intensity (%s)'%method,show=0)
# plot_image(wf.get_amplitude(),wf.get_coordinate_x(),wf.get_coordinate_y(),title='amplitude (%s)'%method,show=0)
plot_image(wf.get_phase(),wf.get_coordinate_x(),wf.get_coordinate_y(),title='phase (%s)'%method,show=0)
plot(wf.get_coordinate_x(),horizontal_profile,
wf.get_coordinate_y(),vertical_profile,
legend=['Horizontal profile','Vertical profile'],title="%s"%method,show=show)
print("Output intensity: ",wf.get_intensity().sum())
return wf.get_coordinate_x(),horizontal_profile
def test_propagate_2D_fraunhofer(self,do_plot=do_plot,aperture_type='square',aperture_diameter=40e-6,
pixelsize_x=1e-6,pixelsize_y=1e-6,npixels_x=1024,npixels_y=1024,wavelength=1.24e-10):
"""
:param do_plot: 0=No plot, 1=Do plot
:param aperture_type: 'circle' 'square' 'gaussian' (Gaussian sigma = aperture_diameter/2.35)
:param aperture_diameter:
:param pixelsize_x:
:param pixelsize_y:
:param npixels_x:
:param npixels_y:
:param wavelength:
:return:
"""
print("\n# ")
print("# far field 2D (fraunhofer) diffraction from a square aperture ")
print("# ")
method = "fraunhofer"
print("Fraunhoffer diffraction valid for distances > > a^2/lambda = %f m"%((aperture_diameter/2)**2/wavelength))
# wf = Wavefront2D.initialize_wavefront_from_steps(x_start=-pixelsize_x*npixels_x/2,
# x_step=pixelsize_x,
# y_start=-pixelsize_y*npixels_y/2,
# y_step=pixelsize_y,
# wavelength=wavelength,
# number_of_points=(npixels_x,npixels_y))
wf = Wavefront2D.initialize_wavefront_from_range(x_min=-pixelsize_x*npixels_x/2,x_max=pixelsize_x*npixels_x/2,
y_min=-pixelsize_y*npixels_y/2,y_max=pixelsize_y*npixels_y/2,
number_of_points=(npixels_x,npixels_y),wavelength=wavelength)
wf.set_plane_wave_from_complex_amplitude((1.0+0j))
if aperture_type == 'circle':
wf.apply_pinhole(aperture_diameter/2)
elif aperture_type == 'square':
wf.apply_slit(-aperture_diameter/2, aperture_diameter/2,-aperture_diameter/2, aperture_diameter/2)
elif aperture_type == 'gaussian':
X = wf.get_mesh_x()
Y = wf.get_mesh_y()
window = numpy.exp(- (X*X + Y*Y)/2/(aperture_diameter/2.35)**2)
wf.rescale_amplitudes(window)
else:
raise Exception("Not implemented! (accepted: circle, square, gaussian)")
wf1 = propagate_2D_fraunhofer(wf, propagation_distance=1.0) # propagating at 1 m means the result is like in angles
if do_plot:
plot_image(wf.get_intensity(),1e6*wf.get_coordinate_x(),1e6*wf.get_coordinate_y(),
title="aperture intensity (%s), Diameter=%5.1f um"%
(aperture_type,1e6*aperture_diameter),xtitle="X [um]",ytitle="Y [um]",
show=0)
plot_image(wf1.get_intensity(),1e6*wf1.get_coordinate_x(),1e6*wf1.get_coordinate_y(),
title="2D Diffracted intensity (%s) by a %s slit of aperture %3.1f um"%
(aperture_type,method,1e6*aperture_diameter),
xtitle="X [urad]",ytitle="Y [urad]",
show=0)
angle_x = wf1.get_coordinate_x() # + 0.5*wf1.delta()[0] # shifted of half-pixel!!!
intensity_theory = get_theoretical_diffraction_pattern(angle_x,
aperture_type=aperture_type,aperture_diameter=aperture_diameter,
wavelength=wavelength,normalization=True)
intensity_calculated = wf1.get_intensity()[:,wf1.size()[1]/2]
intensity_calculated /= intensity_calculated.max()
if do_plot:
plot(wf1.get_coordinate_x()*1e6,intensity_calculated,
angle_x*1e6,intensity_theory,
legend=["Calculated (FT) H profile","Theoretical"],legend_position=(0.95, 0.95),
title="2D Fraunhofer Diffraction of a %s slit of %3.1f um at wavelength of %3.1f A"%
(aperture_type,aperture_diameter*1e6,wavelength*1e10),
xtitle="X (urad)", ytitle="Intensity",xrange=[-80,80])
numpy.testing.assert_almost_equal(intensity_calculated,intensity_theory,1)
h5w = H5SimpleWriter.initialize_file(h5_file,creator="xoppy_undulators.py")
else:
h5w = H5SimpleWriter(h5_file,None)
h5w.create_entry(h5_entry_name,nx_default=None)
h5w.add_stack(e,h,v,p,stack_name="Radiation",entry_name=h5_entry_name,
title_0="Photon energy [eV]",
title_1="X gap [mm]",
title_2="Y gap [mm]")
h5w.create_entry("parameters",root_entry=h5_entry_name,nx_default=None)
for key in h5_parameters.keys():
h5w.add_key(key,h5_parameters[key], entry_name=h5_entry_name+"/parameters")
print("File written to disk: %s"%h5_file)
except:
print("ERROR initializing h5 file")
return e, h, v, p, code
if __name__ == "__main__":
from srxraylib.plot.gol import plot,plot_image
e, f, spectral_power, cumulated_power = xoppy_calc_undulator_spectrum()
plot(e,f)
h, v, p, code = xoppy_calc_undulator_power_density(h5_file="test.h5",h5_initialize=True)
plot_image(p,h,v)
e, h, v, p, code = xoppy_calc_undulator_radiation(ELECTRONENERGY=6.0, h5_file="test.h5",h5_entry_name="first_entry",h5_initialize=True)
e, h, v, p, code = xoppy_calc_undulator_radiation(ELECTRONENERGY=7.0, h5_file="test.h5",h5_entry_name="second_entry",h5_initialize=False)
