def compute_Calias_element_YY(xx, yy, fc, d, nsub, tabx, taby, xoff=0, yoff=0):
"""
Compute the element of the aliasing covariance matrix
:parameters:
Ca: (np.ndarray(ndim=2, dtype=np.float32)): aliasing covariance matrix to fill
xx: (np.ndarray(ndim=2, dtype=np.float32)): X positions of the WFS subap
yy: (np.ndarray(ndim=2, dtype=np.float32)): Y positions of the WFS subap
fc: (float): cut-off frequency for structure function
d: (float): subap diameter
nsub: (int): number of subap
tabx: (np.ndarray(ndim=1, dtype=np.float32)): X tabulation for dphi
taby: (np.ndarray(ndim=1, dtype=np.float32)): Y tabulation for dphi
xoff: (float) : (optionnal) offset to apply on the WFS xpos (units of d)
yoff: (float) : (optionnal) offset to apply on the WFS ypos (units of d)
"""
xx = xx - xx.T #+ xoff * d
yy = yy - yy.T #+ yoff * d
#xx = np.triu(xx) - np.triu(xx, -1).T
#yy = np.triu(yy) - np.triu(yy, -1).T
Ca = np.zeros((2 * nsub, 2 * nsub))
# YY covariance
CD = np.linalg.norm([xx + xoff, yy], axis=0)
Cd = np.linalg.norm([xx + xoff, yy - d], axis=0)
cD = np.linalg.norm([xx + xoff, yy + d], axis=0)
cd = CD
Ca[nsub:, nsub:] += starlord.dphi_highpass(
Cd, fc, tabx, taby) + starlord.dphi_highpass(
cD, fc, tabx,
taby) - 2 * starlord.dphi_highpass(CD, fc, tabx, taby)
return Ca
def compute_Calias_element_XY(xx, yy, fc, d, nsub, tabx, taby, xoff=0, yoff=0):
"""
Compute the element of the aliasing covariance matrix
:parameters:
Ca: (np.ndarray(ndim=2, dtype=np.float32)): aliasing covariance matrix to fill
xx: (np.ndarray(ndim=2, dtype=np.float32)): X positions of the WFS subap
yy: (np.ndarray(ndim=2, dtype=np.float32)): Y positions of the WFS subap
fc: (float): cut-off frequency for struture function
d: (float): subap diameter
nsub: (int): number of subap
tabx: (np.ndarray(ndim=1, dtype=np.float32)): X tabulation for dphi
taby: (np.ndarray(ndim=1, dtype=np.float32)): Y tabulation for dphi
xoff: (float) : (optionnal) offset to apply on the WFS xpos (units of d)
yoff: (float) : (optionnal) offset to apply on the WFS ypos (units of d)
"""
xx = xx - xx.T + xoff * d
yy = yy - yy.T + yoff * d
Ca = np.zeros((2 * nsub, 2 * nsub))
# YY covariance
aD = np.linalg.norm([xx + d / 2, yy + d / 2], axis=0)
ad = np.linalg.norm([xx + d / 2, yy - d / 2], axis=0)
Ad = np.linalg.norm([xx - d / 2, yy - d / 2], axis=0)
AD = np.linalg.norm([xx - d / 2, yy + d / 2], axis=0)
Ca[nsub:, :nsub] = 0.25 * (starlord.dphi_highpass(Ad, d, tabx, taby) +
starlord.dphi_highpass(aD, d, tabx, taby) -
starlord.dphi_highpass(AD, d, tabx, taby) -
starlord.dphi_highpass(ad, d, tabx, taby))
Ca[:nsub, nsub:] = Ca[nsub:, :nsub].copy()
return Ca
def compute_Calias_element(xx, yy, fc, d, nsub, tabx, taby, xoff=0, yoff=0):
"""
Compute the element of the aliasing covariance matrix
:parameters:
Ca: (np.ndarray(ndim=2, dtype=np.float32)): aliasing covariance matrix to fill
xx: (np.ndarray(ndim=2, dtype=np.float32)): X positions of the WFS subap
yy: (np.ndarray(ndim=2, dtype=np.float32)): Y positions of the WFS subap
fc: (float): cut-off frequency for structure function
d: (float): subap diameter
nsub: (int): number of subap
tabx: (np.ndarray(ndim=1, dtype=np.float32)): X tabulation for dphi
taby: (np.ndarray(ndim=1, dtype=np.float32)): Y tabulation for dphi
xoff: (float) : (optionnal) offset to apply on the WFS xpos (units of d)
yoff: (float) : (optionnal) offset to apply on the WFS ypos (units of d)
"""
xx = xx - xx.T + xoff * d
yy = yy - yy.T + yoff * d
Ca = np.zeros((2 * nsub, 2 * nsub))
# XX covariance
AB = np.linalg.norm([xx, yy], axis=0)
Ab = np.linalg.norm([xx - d, yy], axis=0)
aB = np.linalg.norm([xx + d, yy], axis=0)
ab = AB
Ca[:nsub, :nsub] += starlord.dphi_highpass(
Ab, fc, tabx, taby) + starlord.dphi_highpass(
aB, fc, tabx,
taby) - 2 * starlord.dphi_highpass(AB, fc, tabx, taby)
# YY covariance
CD = AB
Cd = np.linalg.norm([xx, yy - d], axis=0)
cD = np.linalg.norm([xx, yy + d], axis=0)
cd = CD
Ca[nsub:, nsub:] += starlord.dphi_highpass(
Cd, fc, tabx, taby) + starlord.dphi_highpass(
cD, fc, tabx,
taby) - 2 * starlord.dphi_highpass(CD, fc, tabx, taby)
# XY covariance
# aD = np.linalg.norm([xx + d/2, yy + d/2], axis=0)
# ad = np.linalg.norm([xx + d/2, yy - d/2], axis=0)
# Ad = np.linalg.norm([xx - d/2, yy - d/2], axis=0)
# AD = np.linalg.norm([xx - d/2, yy + d/2], axis=0)
#
# Ca[nsub:,:nsub] = 0.25 * (starlord.dphi_highpass(Ad, d, tabx, taby)
# + starlord.dphi_highpass(aD, d, tabx, taby)
# - starlord.dphi_highpass(AD, d, tabx, taby)
# - starlord.dphi_highpass(ad, d, tabx, taby)) * (1 / r0)**(5. / 3.)
# Ca[:nsub,nsub:] = Ca[nsub:,:nsub].copy()
return Ca
def compute_OTF_fitting(filename, otftel):
"""
Modelize the OTF due to the fitting using dphi_highpass
:parameters:
filename: (str) : ROKET hdf5 file path
otftel: (np.ndarray) : Telescope OTF
:return:
otf_fit: (np.ndarray) : Fitting OTF
psf_fit (np.ndarray) : Fitting PSF
"""
f = h5py.File(filename, 'r')
r0 = f.attrs["_Param_atmos__r0"] * (f.attrs["_Param_target__Lambda"][0] /
0.5)**(6. / 5.)
ratio_lambda = 2 * np.pi / f.attrs["_Param_target__Lambda"][0]
# Telescope OTF
spup = drax.get_pup(filename)
mradix = 2
fft_size = mradix**int((np.log(2 * spup.shape[0]) / np.log(mradix)) + 1)
mask = np.ones((fft_size, fft_size))
mask[np.where(otftel < 1e-5)] = 0
x = np.arange(fft_size) - fft_size / 2
pixsize = f.attrs["_Param_tel__diam"] / f.attrs["_Param_geom__pupdiam"]
x = x * pixsize
r = np.sqrt(x[:, None] * x[:, None] + x[None, :] * x[None, :])
tabx, taby = starlord.tabulateIj0()
dphi = np.fft.fftshift(
starlord.dphi_highpass(
r, f.attrs["_Param_tel__diam"] /
(f.attrs["_Param_dm__nact"][0] - 1), tabx, taby) *
(1 / r0)**(5 / 3.)) # * den * ratio_lambda**2 * mask
otf_fit = np.exp(-0.5 * dphi) * mask
otf_fit = otf_fit / otf_fit.max()
psf_fit = np.fft.fftshift(np.real(np.fft.ifft2(otftel * otf_fit)))
psf_fit *= (fft_size * fft_size / float(np.where(spup)[0].shape[0]))
f.close()
return otf_fit, psf_fit