def test_normalisations_real(self):
log = logging.getLogger('TestZern.test_normalisations_real')
n_alpha = 6
L, K = 400, 357
# polar grid
pol = RZern(n_alpha)
fitAlpha = FitZern(pol, L, K)
t1 = time()
pol.make_pol_grid(fitAlpha.rho_j, fitAlpha.theta_i)
t2 = time()
log.debug('make pol grid {:.6f}'.format(t2 - t1))
# cartesian grid
cart = RZern(n_alpha)
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_alpha, 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])
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, n=6, L=200, K=250):
# real-valued Zernike polynomials up to the n-th radial order
rzern = RZern(n)
# make a cartesian grid (unit disk pupil coordinates)
ddx = np.linspace(-1.0, 1.0, K)
ddy = np.linspace(-1.0, 1.0, L)
xv, yv = np.meshgrid(ddx, ddy)
rzern.make_cart_grid(xv, yv)
self.rzern = rzern
self.grid_size = (L, K)
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 setUp(self):
self.pupil = RZern(4)
self.max_enorm = 1e-9
self.max_ip_err = 5e-2
'--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))
alpha[k] = args.rms
except BaseException:
print('Cannot find indeces ' + str(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))
.. [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__':
# 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
