def test_normalisations_complex(self):
log = logging.getLogger('TestZern.test_normalisations_complex')
n_beta = 6
L, K = 400, 393
# polar grid
pol = CZern(n_beta)
fitBeta = FitZern(pol, L, K)
t1 = time()
pol.make_pol_grid(fitBeta.rho_j, fitBeta.theta_i)
t2 = time()
log.debug('make pol grid {:.6f}'.format(t2 - t1))
# cartesian grid
cart = CZern(n_beta)
dd = np.linspace(-1.0, 1.0, max(L, K))
xx, yy = np.meshgrid(dd, dd)
t1 = time()
cart.make_cart_grid(xx, yy)
t2 = time()
log.debug('make cart grid {:.6f}'.format(t2 - t1))
smap = np.isfinite(cart.eval_grid(np.zeros(cart.nk)))
scale = (1.0 / np.sum(smap))
log.debug('')
log.debug('{} modes, {} x {} grid'.format(n_beta, L, K))
for i in range(pol.nk):
a = np.zeros(pol.nk)
a[i] = 1.0
Phi_a = cart.eval_grid(a)
for j in range(pol.nk):
b = np.zeros(pol.nk)
b[j] = 1.0
Phi_b = cart.eval_grid(b)
ip = scale * np.sum(Phi_a[smap] * (Phi_b[smap].conj()))
if i == j:
eip = 1.0
else:
eip = 0.0
iperr = abs(ip - eip)
log.debug('<{:02},{:02}> = {:+e} {:+e}'.format(
i + 1, j + 1, ip, iperr))
self.assertTrue(iperr < self.max_ip_err)
def __init__(self, unparsed):
super().__init__()
args = self.do_cmdline(unparsed)
# plot objects
phaseplot = PhasePlot(n=args.n_alpha) # to plot beta and the PSF
betaplot = BetaPlot(args) # to plot the phase
# complex-valued Zernike polynomials for the GPF
ip = FitZern(CZern(args.n_beta), args.fit_L, args.fit_K)
# real-valued Zernike polynomials for the phase
phase_pol = RZern(args.n_alpha)
phase_pol.make_pol_grid(ip.rho_j, ip.theta_i) # make a polar grid
# real-valued Zernike coefficients
alpha = np.zeros(phase_pol.nk)
# set the alpha coefficients randomly
if args.random:
alpha1 = normal(size=alpha.size - 1)
alpha1 = (args.rms / norm(alpha1)) * alpha1
alpha[1:] = alpha1
del alpha1
self.rms = args.rms
self.alpha = alpha
self.phase_pol = phase_pol
self.ip = ip
self.betaplot = betaplot
self.phaseplot = phaseplot
# fit beta coefficients from alpha coefficients
self.alpha2beta()
# make gui
self.make_gui()
def test_fit_real_numpy(self):
log = logging.getLogger('TestFitZern.test_fit_real_numpy')
z = RZern(4)
F = FitZern(z, self.L, self.K)
theta_i = F.theta_i
rho_j = F.rho_j
c = normal(size=z.nk)
Phi = [z.eval_a(c, rh, th) for rh in rho_j for th in theta_i]
time1 = time()
ce = F._fit_slow(Phi)
time2 = time()
log.debug('elapsed FIT_LIST {:.6f}'.format(time2 - time1))
time1 = time()
ce2 = F.fit(np.array(Phi, order='F'))
time2 = time()
log.debug('elapsed FIT_NUMPY {:.6f}'.format(time2 - time1))
enorm = norm(ce2 - np.array(ce, order='F'))
log.debug('enorm {:e}'.format(enorm))
self.assertTrue(enorm < self.max_enorm)
def test_fit_real(self):
log = logging.getLogger('TestFitZern.test_fit_real')
z = RZern(4)
F = FitZern(z, self.L, self.K)
theta_i = F.theta_i
rho_j = F.rho_j
c = normal(size=z.nk)
time1 = time()
Phi = [z.eval_a(c, rh, th) for rh in rho_j for th in theta_i]
time2 = time()
log.debug('eval Phi {:.4f}'.format(time2 - time1))
time1 = time()
ce = F._fit_slow(Phi)
time2 = time()
log.debug('elapsed time {:.4f}'.format(time2 - time1))
err1 = norm(np.array(c) - np.array(ce))
max1 = max([abs(c[i] - ce[i]) for i in range(z.nk)])
log.debug('err1 {:e} max1 {:e}'.format(err1, max1))
self.assertTrue(err1 < self.max_fit_norm)
def do_test(cls, complex_a):
z = cls(4)
F = FitZern(z, self.L, self.K)
theta_i = F.theta_i
rho_j = F.rho_j
z.make_pol_grid(rho_j, theta_i)
if complex_a:
c = normal(size=z.nk) + 1j * normal(size=z.nk)
else:
c = normal(size=z.nk)
PhiN = np.array(
[z.eval_a(c, rh, th) for rh in rho_j for th in theta_i],
order='F')
ce1 = F.fit(PhiN)
# create tmp path
tmpfile = NamedTemporaryFile()
tmppath = tmpfile.name
tmpfile.close()
F.save(tmppath)
F2 = FitZern.load(tmppath)
PhiN1 = np.array(
[F.z.eval_a(c, rh, th) for rh in rho_j for th in theta_i],
order='F')
PhiN2 = np.array(
[F2.z.eval_a(c, rh, th) for rh in rho_j for th in theta_i],
order='F')
self.assertTrue(isinstance(F, FitZern))
self.assertTrue(isinstance(F2, FitZern))
if complex_a:
self.assertTrue(isinstance(F.z, CZern))
self.assertTrue(isinstance(F2.z, CZern))
else:
self.assertTrue(isinstance(F.z, RZern))
self.assertTrue(isinstance(F2.z, RZern))
self.assertTrue(norm(PhiN - PhiN1) == 0)
self.assertTrue(norm(PhiN - PhiN2) == 0)
self.assertTrue(norm(F.z.coefnorm - F2.z.coefnorm) == 0)
self.assertTrue(norm(F.z.ntab - F2.z.ntab) == 0)
self.assertTrue(norm(F.z.mtab - F2.z.mtab) == 0)
self.assertTrue(F.z.n == F2.z.n)
self.assertTrue(F.z.nk == F2.z.nk)
self.assertTrue(F.z.normalise == F2.z.normalise)
self.assertTrue(norm(F.z.rhoitab - F2.z.rhoitab) == 0)
self.assertTrue(norm(F.z.rhotab - F2.z.rhotab) == 0)
self.assertTrue(F.z.numpy_dtype == F2.z.numpy_dtype)
self.assertTrue(norm(F.z.ZZ - F2.z.ZZ) == 0)
self.assertTrue(norm(F.A - F2.A) == 0)
self.assertTrue(norm(F.I_cosm - F2.I_cosm) == 0)
self.assertTrue(norm(F.I_sinm - F2.I_sinm) == 0)
self.assertTrue(norm(F.I_Rnmrho - F2.I_Rnmrho) == 0)
self.assertTrue(F.K == F2.K)
self.assertTrue(F.L == F2.L)
self.assertTrue(norm(F.rho_a - F2.rho_a) == 0)
self.assertTrue(norm(F.rho_b - F2.rho_b) == 0)
self.assertTrue(norm(F.rho_j - F2.rho_j) == 0)
self.assertTrue(norm(F.theta_a - F2.theta_a) == 0)
self.assertTrue(norm(F.theta_b - F2.theta_b) == 0)
self.assertTrue(norm(F.theta_i - F2.theta_i) == 0)
ce2 = F2.fit(PhiN)
self.assertTrue(norm(ce2 - ce1) < self.max_enorm)
os.unlink(tmppath)
del z, F, F2, c, ce1, ce2, PhiN, PhiN1, PhiN2
.. [A2015] Jacopo Antonello and Michel Verhaegen, "Modal-based phase retrieval
for adaptive optics," J. Opt. Soc. Am. A 32, 1160-1170 (2015) . `url
<http://dx.doi.org/10.1364/JOSAA.32.001160>`__.
"""
if __name__ == '__main__':
# grid sizes
L, K = 95, 105
# complex-valued Zernike polynomials up to the 4-th radial order
gpf_pol = CZern(4) # to approximate the GPF
# FitZern computes the approximate inner products, see Eq. (B4) in [A2015]
ip = FitZern(gpf_pol, L, K)
gpf_pol.make_pol_grid(ip.rho_j, ip.theta_i) # make a polar grid
# random vector of Zernike coefficients to be estimated
beta_true = normal(size=gpf_pol.nk) + 1j * normal(size=gpf_pol.nk)
# random generalised pupil function P
P = gpf_pol.eval_grid(beta_true)
# estimate the random vector from the GPF grid
beta_hat = ip.fit(P)
# plot the results
p.figure(2)
# real part of the Zernike coefficients of beta_true and beta_hat
'--rms', type=float, default=1.0,
help='Rms of the alpha aberration.')
parser.add_argument(
'--random', action='store_true',
help='Make a random alpha aberration.')
parser.add_argument(
'--fit-L', type=int, default=95, metavar='L',
help='Grid size for the inner products.')
parser.add_argument(
'--fit-K', type=int, default=105, metavar='K',
help='Grid size for the inner products.')
args = parser.parse_args()
# complex-valued Zernike polynomials for the GPF
ip = FitZern(CZern(args.n_beta), args.fit_L, args.fit_K)
# real-valued Zernike polynomials for the phase
phase_pol = RZern(args.n_alpha)
phase_pol.make_pol_grid(ip.rho_j, ip.theta_i) # make a polar grid
# real-valued Zernike coefficients
alpha = np.zeros(phase_pol.nk)
# nm to linear index conversion
nmlist = list(zip(phase_pol.ntab, phase_pol.mtab))
# set an alpha coefficient using the (n, m) indeces
if args.nm[0] != -1 and args.nm[0] != -1:
try:
k = nmlist.index(tuple(args.nm))
def make(self, wavelength, aperture_radius, focal_length, pixel_size,
image_width, image_height, n_alpha, n_beta, fit_L, fit_K,
focus_positions):
self.wavelength = wavelength
self.aperture_radius = aperture_radius
self.focal_length = focal_length
self.image_width = image_width
self.image_height = image_height
self.pixel_size = pixel_size
self.n_alpha, self.n_beta = n_alpha, n_beta
self.fit_L, self.fit_K = fit_L, fit_K
self.focus_positions = np.array(focus_positions)
fu = enz.get_field_unit(wavelength, aperture_radius, focal_length)
def make_space(w, p, fu):
if w % 2 == 0:
return np.linspace(-(w / 2 - 0.5), w / 2 - 0.5, w) * p / fu
else:
return np.linspace(-(w - 1) / 2, (w - 1) / 2, w) * p / fu
# image side space
xspace = make_space(image_width, pixel_size, fu)
yspace = make_space(image_height, pixel_size, fu)
self.xspace, self.yspace = xspace, yspace
# phase
self.phase_grid = RZern(n_alpha)
self.phase_fit = FitZern(self.phase_grid, self.fit_L, self.fit_K)
print('phase: n_alpha = {}, N_alpha = {}'.format(
self.n_alpha, self.phase_grid.nk))
# complex psf
self.cpsf = CPsf(n_beta)
self.gpf_fit = FitZern(self.cpsf.czern, self.fit_L, self.fit_K)
print('cpsf: n_beta = {}, N_beta = {}, N_f = {}'.format(
n_beta, self.cpsf.czern.nk, self.focus_positions.size))
# make phase polar grid
t1 = time.time()
self.phase_grid.make_pol_grid(self.phase_fit.rho_j,
self.phase_fit.theta_i)
t2 = time.time()
print('make phase pol grid {:.6f}'.format(t2 - t1))
# make gpf polar grid (Zernike approximation)
t1 = time.time()
self.cpsf.czern.make_pol_grid(self.phase_fit.rho_j,
self.phase_fit.theta_i)
t2 = time.time()
print('make gpf pol grid {:.6f}'.format(t2 - t1))
# make cpsf cart grid
t1 = time.time()
self.cpsf.make_cart_grid(x_sp=xspace,
y_sp=yspace,
f_sp=focus_positions)
t2 = time.time()
print('make cpsf cart grid {:.6f}'.format(t2 - t1))
"""
if __name__ == '__main__':
# plotting stuff
phaseplot = PhasePlot()
# grid sizes
L, K = 95, 105
# real-valued Zernike polynomials up to the 6-th radial order
phase_pol = RZern(6)
# FitZern computes the approximate inner products, see Eq. (B2) in [A2015]
ip = FitZern(phase_pol, L, K)
phase_pol.make_pol_grid(ip.rho_j, ip.theta_i) # make a polar grid
# random vector of Zernike coefficients to be estimated
alpha_true = normal(size=phase_pol.nk)
# phase grid
Phi = phase_pol.eval_grid(alpha_true)
# estimate the random vector from the phase grid
alpha_hat = ip.fit(Phi)
# plot the results
p.figure(2)
# Zernike coefficients of alpha_true and alpha_hat
