def test_Circular_Aperture_PTP_long(display=False,
npix=512,
display_proper=False):
""" Tests plane-to-plane propagation at large distances.
Confirm that magnitude of central spike from diffraction
due to a circular aperture agrees with expectation.
The comparison is against a worked example presented as
Figure 6.15 in Anderson and Enmark, Integrated Modeling of Telescopes.
Values are also compared against a simulation of the same
case using PROPER.
Note this tests only the Plane-to-Plane propagation method,
since the propagation distance z < z_rayleigh ~ 360 km
See https://github.com/mperrin/poppy/issues/106 for further
discussion of this test case.
"""
# for npix, n.b. ~512 is minimum to accurately recover the central diffraction spike
z = 5e3 * u.m
# the following points were traced/digitized using GraphClick from
# the published figure 6.15 by Anderson and Enmark. Beware of limited precision!
ref_x = [-0.505, -0.412, -0.368, -0.323, -0.302, -0.027, 0]
ref_y = [0.233, 1.446, 0.757, 1.264, 0.784, 1.520, 3.134]
proper_x = [0]
proper_y = [3.30790] # from high res sim: 16384**2 pix, beam ratio=0.125
# The test condition here is subtle, as the exact peak value expected
# here depends on the sampling. A high resolution simulation with
# PROPER yields peak=3.30790 for this case but we will only get roughly
# close to that with lower sampling. we do not want to add too high a
# computation load to the unit test system, so we have to tolerate some
# imprecision here.
#
# Therefore tune the expected tolerance based on empirical past results.
# N.B. this is only approximate and the test may still fail depending
# on particular choice of npix, without indicating anything
# fundamentally wrong rather than just the inherent limits of discrete
# transformations of samplings of continuous functions.
if npix < 512:
raise ValueError('npix too low for reasonable accuracy')
elif npix >= 512 and npix < 1024:
tolerance = 0.02
elif npix >= 1024 and npix < 2048:
# for some strange reason, 1024 pix does relatively worse than 512, assuming oversample=4
tolerance = 0.035
else:
tolerance = 0.03
# Note there is a slight error in the text of Anderson and Enmark; the
# paragraph just before Fig 6.15 says "diameter D=0.5 m", but the
# figure actually depicts a case with radius r=0.5 m, as is immediately
# and obviously the case based on the x axis of the figure.
gw = fresnel.FresnelWavefront(beam_radius=0.5 * u.m,
wavelength=2200e-9,
npix=npix,
oversample=4)
gw *= optics.CircularAperture(radius=0.5, oversample=gw.oversample)
gw.propagate_fresnel(z)
inten = gw.intensity
y, x = gw.coordinates()
if display:
plt.figure()
gw.display('both', colorbar=True)
plt.figure(figsize=(12, 6))
plt.plot(x[0, :], inten[inten.shape[1] / 2, :], label='POPPY')
plt.title(
"z={:0.2e} , compare to Anderson and Enmark fig.6.15".format(z))
plt.gca().set_xlim(-1, 1)
plt.text(
0.1, 2, "Max value: {0:.4f}\nExpected: {1:.4f}".format(
np.max(inten), max(proper_y)))
if display_proper:
# This needs a data file output from PROPER, which we don't
# bother with including for automated unit testing.
proper_result = fits.getdata('proper_circle_5e3_cut.fits')
plt.plot(proper_result[0],
proper_result[1],
linestyle='-',
color='red',
alpha=0.5,
label="PROPER")
plt.plot(ref_x, ref_y, 'o', label="Anderson & Enmark")
plt.legend(loc='upper right', frameon=False)
_log.debug("test_Circular_Aperture_PTP peak flux comparison: " +
str(np.abs(max(proper_y) - np.max(inten))))
_log.debug(" allowed tolerance for {0} is {1}".format(npix, tolerance))
#assert(np.round(3.3633280006866424,9) == np.round(np.max(gw.intensity),9))
assert (np.abs(max(proper_y) - np.max(inten)) < tolerance)
# also let's test that the output is centered on the array as expected.
# the peak pixel should be at the coordinates (0,0)
assert inten[np.where((y == 0) & (x == 0))] == inten.max()
# and the image should be symmetric if you flip in X or Y
# (approximately but not perfectly to machine precision
# due to the minor asymmetry from having the FFT center pixel
# not precisely centered in the array.)
cen = inten.shape[0] / 2
cutsize = 10
center_cut_x = inten[cen - cutsize:cen + cutsize + 1, cen]
assert (np.all((center_cut_x - center_cut_x[::-1]) / center_cut_x < 0.001))
center_cut_y = inten[cen, cen - cutsize:cen + cutsize + 1]
assert (np.all((center_cut_y - center_cut_y[::-1]) / center_cut_y < 0.001))
def test_Circular_Aperture_PTP_long(display=False, npix=512, display_proper=False):
""" Tests plane-to-plane propagation at large distances.
Confirm that magnitude of central spike from diffraction
due to a circular aperture agrees with expectation.
The comparison is against a worked example presented as
Figure 6.15 in Anderson and Enmark, Integrated Modeling of Telescopes.
Values are also compared against a simulation of the same
case using PROPER.
Note this tests only the Plane-to-Plane propagation method,
since the propagation distance z < z_rayleigh ~ 360 km
See https://github.com/mperrin/poppy/issues/106 for further
discussion of this test case.
"""
# for npix, n.b. ~512 is minimum to accurately recover the central diffraction spike
z = 5e3*u.m
# the following points were traced/digitized using GraphClick from
# the published figure 6.15 by Anderson and Enmark. Beware of limited precision!
ref_x = [-0.505, -0.412, -0.368, -0.323, -0.302, -0.027, 0]
ref_y = [ 0.233, 1.446, 0.757, 1.264, 0.784, 1.520, 3.134]
proper_x = [0]
proper_y = [3.30790] # from high res sim: 16384**2 pix, beam ratio=0.125
# The test condition here is subtle, as the exact peak value expected
# here depends on the sampling. A high resolution simulation with
# PROPER yields peak=3.30790 for this case but we will only get roughly
# close to that with lower sampling. we do not want to add too high a
# computation load to the unit test system, so we have to tolerate some
# imprecision here.
#
# Therefore tune the expected tolerance based on empirical past results.
# N.B. this is only approximate and the test may still fail depending
# on particular choice of npix, without indicating anything
# fundamentally wrong rather than just the inherent limits of discrete
# transformations of samplings of continuous functions.
if npix< 512:
raise ValueError('npix too low for reasonable accuracy')
elif npix>=512 and npix < 1024:
tolerance=0.02
elif npix>=1024 and npix<2048:
# for some strange reason, 1024 pix does relatively worse than 512, assuming oversample=4
tolerance = 0.035
else:
tolerance=0.03
# Note there is a slight error in the text of Anderson and Enmark; the
# paragraph just before Fig 6.15 says "diameter D=0.5 m", but the
# figure actually depicts a case with radius r=0.5 m, as is immediately
# and obviously the case based on the x axis of the figure.
gw = fresnel.FresnelWavefront(beam_radius=0.5*u.m,wavelength=2200e-9,npix=npix,oversample=4)
gw *= optics.CircularAperture(radius=0.5,oversample=gw.oversample)
gw.propagate_fresnel(z)
inten = gw.intensity
y, x = gw.coordinates()
if display:
plt.figure()
gw.display('both',colorbar=True)
plt.figure(figsize=(12,6))
plt.plot(x[0,:], inten[inten.shape[1]/2,:], label='POPPY')
plt.title("z={:0.2e} , compare to Anderson and Enmark fig.6.15".format(z))
plt.gca().set_xlim(-1, 1)
plt.text(0.1,2, "Max value: {0:.4f}\nExpected: {1:.4f}".format(np.max(inten), max(proper_y)))
if display_proper:
# This needs a data file output from PROPER, which we don't
# bother with including for automated unit testing.
proper_result = fits.getdata('proper_circle_5e3_cut.fits')
plt.plot(proper_result[0], proper_result[1], linestyle='-', color='red', alpha=0.5, label="PROPER")
plt.plot( ref_x, ref_y, 'o', label="Anderson & Enmark")
plt.legend(loc='upper right', frameon=False)
_log.debug("test_Circular_Aperture_PTP peak flux comparison: "+str(np.abs(max(proper_y) - np.max(inten))))
_log.debug(" allowed tolerance for {0} is {1}".format(npix, tolerance))
#assert(np.round(3.3633280006866424,9) == np.round(np.max(gw.intensity),9))
assert (np.abs(max(proper_y) - np.max(inten)) < tolerance)
# also let's test that the output is centered on the array as expected.
# the peak pixel should be at the coordinates (0,0)
assert inten[np.where((y==0) & (x==0))] == inten.max()
# and the image should be symmetric if you flip in X or Y
# (approximately but not perfectly to machine precision
# due to the minor asymmetry from having the FFT center pixel
# not precisely centered in the array.)
cen = inten.shape[0]/2
cutsize=10
center_cut_x = inten[cen-cutsize:cen+cutsize+1, cen]
assert(np.all((center_cut_x- center_cut_x[::-1])/center_cut_x < 0.001))
center_cut_y = inten[cen, cen-cutsize:cen+cutsize+1]
assert(np.all((center_cut_y- center_cut_y[::-1])/center_cut_y < 0.001))