def ptf(array_shape=(256, 256), dx=1., lam_over_diam=2., defocus=0., astig1=0., astig2=0., coma1=0.,
coma2=0., trefoil1=0., trefoil2=0., spher=0., circular_pupil=True, obscuration=0.,
nstruts=0, strut_thick=0.05, strut_angle=0.*galsim.degrees):
"""Return NumPy array containing the PTF [radians] of a circular (default) or square pupil with
low-order aberrations.
PTF array element ordering follows the DFT standard of kxky(array_shape), and has
ptf[0, 0] = 0. by default.
To ensure properly Nyquist sampled output any user should set lam_over_diam >= 2. * dx.
Output double NumPy array is C-contiguous.
@param array_shape the NumPy array shape desired for the output array.
@param dx grid spacing of PSF in real space units
@param lam_over_diam lambda / telescope diameter in the physical units adopted for dx
(user responsible for consistency).
@param defocus defocus in units of incident light wavelength.
@param astig1 astigmatism (like e2) in units of incident light wavelength.
@param astig2 astigmatism (like e1) in units of incident light wavelength.
@param coma1 coma along y in units of incident light wavelength.
@param coma2 coma along x in units of incident light wavelength.
@param trefoil1 trefoil (one of the arrows along y) in units of incident light
wavelength.
@param trefoil2 trefoil (one of the arrows along x) in units of incident light
wavelength.
@param spher spherical aberration in units of incident light wavelength.
@param circular_pupil adopt a circular pupil?
@param obscuration linear dimension of central obscuration as fraction of pupil linear
dimension, [0., 1.)
@param nstruts Number of radial support struts to add to the central obscuration
[default `nstruts = 0`].
@param strut_thick Thickness of support struts as a fraction of pupil diameter
[default `strut_thick = 0.05`].
@param strut_angle Angle made between the vertical and the strut starting closest to it,
defined to be positive in the counter-clockwise direction; must be a
galsim.Angle instance [default `strut_angle = 0. * galsim.degrees`].
"""
kx, ky = utilities.kxky(array_shape)
k2 = (kx**2 + ky**2)
ptf = np.zeros(array_shape)
kmax_internal = dx * 2. * np.pi / lam_over_diam # INTERNAL kmax in units of array grid spacing
# Try to handle where both real and imag tend to zero...
ptf[k2 < kmax_internal**2] = np.angle(otf(
array_shape=array_shape, dx=dx, lam_over_diam=lam_over_diam, defocus=defocus, astig1=astig1,
astig2=astig2, coma1=coma1, coma2=coma2, trefoil1=trefoil1, trefoil2=trefoil2, spher=spher,
circular_pupil=circular_pupil, obscuration=obscuration, nstruts=nstruts,
strut_thick=strut_thick, strut_angle=strut_angle)[k2 < kmax_internal**2])
return ptf
def generate_pupil_plane(array_shape=(256, 256),
dx=1.,
lam_over_diam=2.,
circular_pupil=True,
obscuration=0.):
"""Generate a pupil plane, including a central obscuration such as caused by a secondary mirror.
@param array_shape the NumPy array shape desired for the output array.
@param dx grid spacing of PSF in real space units.
@param lam_over_diam lambda / telescope diameter in the physical units adopted for dx
(user responsible for consistency).
@param circular_pupil adopt a circular pupil?
@param obscuration linear dimension of central obscuration as fraction of pupil linear
dimension, [0., 1.)
Returns a tuple (rho, theta, in_pupil), the first two of which are the coordinates of the
pupil in unit disc-scaled coordinates for use by Zernike polynomials for describing the
wavefront across the pupil plane. The array in_pupil is a vector of Bools used to specify
where in the pupil plane described by rho, theta is illuminated. See also optics.wavefront.
"""
kmax_internal = dx * 2. * np.pi / lam_over_diam # INTERNAL kmax in units of array grid spacing
# Build kx, ky coords
kx, ky = utilities.kxky(array_shape)
# Then define unit disc rho and theta pupil coords for Zernike polynomials
rho = np.sqrt((kx**2 + ky**2) / (.5 * kmax_internal)**2)
theta = np.arctan2(ky, kx)
# Cut out circular pupil if desired (default, square pupil optionally supported) and include
# central obscuration
if obscuration >= 1.:
raise ValueError("Pupil fully obscured! obscuration =" +
str(obscuration) + " (>= 1)")
if circular_pupil:
in_pupil = (rho < 1.)
if obscuration > 0.:
in_pupil = in_pupil * (rho >= obscuration
) # * acts like "and" for boolean arrays
else:
in_pupil = (np.abs(kx) < .5 * kmax_internal) * (np.abs(ky) <
.5 * kmax_internal)
if obscuration > 0.:
in_pupil = in_pupil * (
(np.abs(kx) >= .5 * obscuration * kmax_internal) *
(np.abs(ky) >= .5 * obscuration * kmax_internal))
return rho, theta, in_pupil
def ptf(array_shape=(256, 256), dx=1., lam_over_diam=2., defocus=0., astig1=0., astig2=0., coma1=0.,
coma2=0., trefoil1=0., trefoil2=0., spher=0., circular_pupil=True, obscuration=0.):
"""Return NumPy array containing the PTF [radians] of a circular (default) or square pupil with
low-order aberrations.
PTF array element ordering follows the DFT standard of kxky(array_shape), and has
ptf[0, 0] = 0. by default.
To ensure properly Nyquist sampled output any user should set lam_over_diam >= 2. * dx.
Output double NumPy array is C-contiguous.
@param array_shape the NumPy array shape desired for the output array.
@param dx grid spacing of PSF in real space units
@param lam_over_diam lambda / telescope diameter in the physical units adopted for dx
(user responsible for consistency).
@param defocus defocus in units of incident light wavelength.
@param astig1 astigmatism (like e2) in units of incident light wavelength.
@param astig2 astigmatism (like e1) in units of incident light wavelength.
@param coma1 coma along y in units of incident light wavelength.
@param coma2 coma along x in units of incident light wavelength.
@param trefoil1 trefoil (one of the arrows along y) in units of incident light
wavelength.
@param trefoil2 trefoil (one of the arrows along x) in units of incident light
wavelength.
@param spher spherical aberration in units of incident light wavelength.
@param circular_pupil adopt a circular pupil?
@param obscuration linear dimension of central obscuration as fraction of pupil linear
dimension, [0., 1.)
"""
kx, ky = utilities.kxky(array_shape)
k2 = (kx**2 + ky**2)
ptf = np.zeros(array_shape)
kmax_internal = dx * 2. * np.pi / lam_over_diam # INTERNAL kmax in units of array grid spacing
# Try to handle where both real and imag tend to zero...
ptf[k2 < kmax_internal**2] = np.angle(otf(
array_shape=array_shape, dx=dx, lam_over_diam=lam_over_diam, defocus=defocus, astig1=astig1,
astig2=astig2, coma1=coma1, coma2=coma2, trefoil1=trefoil1, trefoil2=trefoil2, spher=spher,
circular_pupil=circular_pupil, obscuration=obscuration)[k2 < kmax_internal**2])
return ptf
def generate_pupil_plane(array_shape=(256, 256), dx=1., lam_over_diam=2., circular_pupil=True,
obscuration=0.):
"""Generate a pupil plane, including a central obscuration such as caused by a secondary mirror.
@param array_shape the NumPy array shape desired for the output array.
@param dx grid spacing of PSF in real space units.
@param lam_over_diam lambda / telescope diameter in the physical units adopted for dx
(user responsible for consistency).
@param circular_pupil adopt a circular pupil?
@param obscuration linear dimension of central obscuration as fraction of pupil linear
dimension, [0., 1.)
Returns a tuple (rho, theta, in_pupil), the first two of which are the coordinates of the
pupil in unit disc-scaled coordinates for use by Zernike polynomials for describing the
wavefront across the pupil plane. The array in_pupil is a vector of Bools used to specify
where in the pupil plane described by rho, theta is illuminated. See also optics.wavefront.
"""
kmax_internal = dx * 2. * np.pi / lam_over_diam # INTERNAL kmax in units of array grid spacing
# Build kx, ky coords
kx, ky = utilities.kxky(array_shape)
# Then define unit disc rho and theta pupil coords for Zernike polynomials
rho = np.sqrt((kx**2 + ky**2) / (.5 * kmax_internal)**2)
theta = np.arctan2(ky, kx)
# Cut out circular pupil if desired (default, square pupil optionally supported) and include
# central obscuration
if obscuration >= 1.:
raise ValueError("Pupil fully obscured! obscuration ="+str(obscuration)+" (>= 1)")
if circular_pupil:
in_pupil = (rho < 1.)
if obscuration > 0.:
in_pupil = in_pupil * (rho >= obscuration) # * acts like "and" for boolean arrays
else:
in_pupil = (np.abs(kx) < .5 * kmax_internal) * (np.abs(ky) < .5 * kmax_internal)
if obscuration > 0.:
in_pupil = in_pupil * (
(np.abs(kx) >= .5 * obscuration * kmax_internal) *
(np.abs(ky) >= .5 * obscuration * kmax_internal))
return rho, theta, in_pupil
def generate_pupil_plane(array_shape=(256, 256), dx=1., lam_over_diam=2., circular_pupil=True,
obscuration=0., nstruts=0, strut_thick=0.05,
strut_angle=0.*galsim.degrees):
"""Generate a pupil plane, including a central obscuration such as caused by a secondary mirror.
@param array_shape the NumPy array shape desired for the output array.
@param dx grid spacing of PSF in real space units.
@param lam_over_diam lambda / telescope diameter in the physical units adopted for dx
(user responsible for consistency).
@param circular_pupil adopt a circular pupil?
@param obscuration linear dimension of central obscuration as fraction of pupil linear
dimension, [0., 1.).
@param nstruts Number of radial support struts to add to the central obscuration
[default `nstruts = 0`].
@param strut_thick Thickness of support struts as a fraction of pupil diameter
[default `strut_thick = 0.05`].
@param strut_angle Angle made between the vertical and the strut starting closest to it,
defined to be positive in the counter-clockwise direction; must be a
galsim.Angle instance [default `strut_angle = 0. * galsim.degrees`].
Returns a tuple (rho, in_pupil), the first of which is the coordinates of the pupil
in unit disc-scaled coordinates for use by Zernike polynomials (as a complex number)
for describing the wavefront across the pupil plane. The array in_pupil is a vector of
Bools used to specify where in the pupil plane described by rho is illuminated. See also
optics.wavefront.
"""
kmax_internal = dx * 2. * np.pi / lam_over_diam # INTERNAL kmax in units of array grid spacing
# Build kx, ky coords
kx, ky = utilities.kxky(array_shape)
# Then define unit disc rho pupil coords for Zernike polynomials
rho = (kx + 1j * ky) / (.5 * kmax_internal)
rhosq = np.abs(rho)**2
# Amazingly, the above line is faster than the following. (~ 35% faster)
# See the longer comment about this in psf function.
#rhosq = rho.real**2 + rho.imag**2
# Cut out circular pupil if desired (default, square pupil optionally supported) and include
# central obscuration
if obscuration >= 1.:
raise ValueError("Pupil fully obscured! obscuration ="+str(obscuration)+" (>= 1)")
if circular_pupil:
in_pupil = (rhosq < 1.)
if obscuration > 0.:
in_pupil *= rhosq >= obscuration**2 # * acts like "and" for boolean arrays
else:
in_pupil = (np.abs(kx) < .5 * kmax_internal) * (np.abs(ky) < .5 * kmax_internal)
if obscuration > 0.:
in_pupil *= ( (np.abs(kx) >= .5 * obscuration * kmax_internal) *
(np.abs(ky) >= .5 * obscuration * kmax_internal) )
if nstruts > 0:
if not isinstance(strut_angle, galsim.Angle):
raise TypeError("Input kwarg strut_angle must be a galsim.Angle instance.")
# Add the initial rotation if requested, converting to radians
if strut_angle.rad != 0.:
kxs, kys = utilities.rotate_xy(kx, ky, -strut_angle) # strut rotation +=ve, so coords
# rotation -ve!
else:
kxs, kys = kx, ky
# Define the angle between struts for successive use below
rotang = 360. * galsim.degrees / float(nstruts)
# Then loop through struts setting to zero in the pupil regions which lie under the strut
in_pupil *= (
(np.abs(kxs) >= .5 * strut_thick * kmax_internal) +
((kys < 0.) * (np.abs(kxs) < .5 * strut_thick * kmax_internal)))
for istrut in range(nstruts)[1:]:
kxs, kys = utilities.rotate_xy(kxs, kys, -rotang)
in_pupil *= (
(np.abs(kxs) >= .5 * strut_thick * kmax_internal) +
((kys < 0.) * (np.abs(kxs) < .5 * strut_thick * kmax_internal)))
return rho, in_pupil
def ptf(array_shape=(256, 256),
dx=1.,
lam_over_diam=2.,
defocus=0.,
astig1=0.,
astig2=0.,
coma1=0.,
coma2=0.,
trefoil1=0.,
trefoil2=0.,
spher=0.,
circular_pupil=True,
obscuration=0.):
"""Return NumPy array containing the PTF [radians] of a circular (default) or square pupil with
low-order aberrations.
PTF array element ordering follows the DFT standard of kxky(array_shape), and has
ptf[0, 0] = 0. by default.
To ensure properly Nyquist sampled output any user should set lam_over_diam >= 2. * dx.
Output double NumPy array is C-contiguous.
@param array_shape the NumPy array shape desired for the output array.
@param dx grid spacing of PSF in real space units
@param lam_over_diam lambda / telescope diameter in the physical units adopted for dx
(user responsible for consistency).
@param defocus defocus in units of incident light wavelength.
@param astig1 astigmatism (like e2) in units of incident light wavelength.
@param astig2 astigmatism (like e1) in units of incident light wavelength.
@param coma1 coma along y in units of incident light wavelength.
@param coma2 coma along x in units of incident light wavelength.
@param trefoil1 trefoil (one of the arrows along y) in units of incident light
wavelength.
@param trefoil2 trefoil (one of the arrows along x) in units of incident light
wavelength.
@param spher spherical aberration in units of incident light wavelength.
@param circular_pupil adopt a circular pupil?
@param obscuration linear dimension of central obscuration as fraction of pupil linear
dimension, [0., 1.)
"""
kx, ky = utilities.kxky(array_shape)
k2 = (kx**2 + ky**2)
ptf = np.zeros(array_shape)
kmax_internal = dx * 2. * np.pi / lam_over_diam # INTERNAL kmax in units of array grid spacing
# Try to handle where both real and imag tend to zero...
ptf[k2 < kmax_internal**2] = np.angle(
otf(array_shape=array_shape,
dx=dx,
lam_over_diam=lam_over_diam,
defocus=defocus,
astig1=astig1,
astig2=astig2,
coma1=coma1,
coma2=coma2,
trefoil1=trefoil1,
trefoil2=trefoil2,
spher=spher,
circular_pupil=circular_pupil,
obscuration=obscuration)[k2 < kmax_internal**2])
return ptf
