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()
alpha1 = normal(size=alpha.size-1)
alpha1 = (args.rms/norm(alpha1))*alpha1
alpha[1:] = alpha1
del alpha1
# evaluate the phase corresponding to alpha
Phi = phase_pol.eval_grid(alpha)
# evaluate the generalised pupil function P corresponding to alpha
P = np.exp(1j*Phi)
# estimate the beta coefficients from P
beta_hat = ip.fit(P)
# plot the results
phaseplot = PhasePlot(n=args.n_alpha) # to plot beta and the PSF
betaplot = BetaPlot(args) # to plot the phase
# plot alpha
p.figure(10)
p.subplot2grid((1, 3), (0, 0), colspan=2)
h1 = p.plot(range(1, phase_pol.nk + 1), alpha, marker='o')
p.legend(h1, [r'$\alpha$'])
p.ylabel('[rad]')
p.xlabel('$k$')
p.subplot2grid((1, 3), (0, 2))
phaseplot.plot_alpha(alpha)
p.title(r'$\alpha$')
p.colorbar()
# plot beta
alpha1 = normal(size=alpha.size-1)
alpha1 = (args.rms/norm(alpha1))*alpha1
alpha[1:] = alpha1
del alpha1
# evaluate the phase corresponding to alpha
Phi = phase_pol.eval_grid(alpha)
# evaluate the generalised pupil function P corresponding to alpha
P = np.exp(1j*Phi)
# estimate the beta coefficients from P
beta_hat = ip.fit(P)
# plot the results
phaseplot = PhasePlot(n=args.n_alpha) # to plot beta and the PSF
betaplot = BetaPlot(args) # to plot the phase
# plot alpha
p.figure(10)
p.subplot2grid((1, 3), (0, 0), colspan=2)
h1 = p.plot(range(1, phase_pol.nk + 1), alpha, marker='o')
p.legend(h1, [r'$\alpha$'])
p.ylabel('[rad]')
p.xlabel('$k$')
p.subplot2grid((1, 3), (0, 2))
phaseplot.plot_alpha(alpha)
p.title(r'$\alpha$')
p.colorbar()
# plot beta
Estimate a vector of real-valued Zernike coefficients from a phase grid by
taking inner products.
References
----------
.. [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
from sage.all_cmdline import *
from phi4 import Simulation
from phase_plot import PhasePlot
plt = PhasePlot(32, 32, equilibrate=1512, iterations=1512, observable=Simulation.abs_phi)
plt.mass_squared = srange(-1.5, 0, 0.1)
plt.coupling_constant = srange(0.1, 1, 0.1)
gfx = \
plt.plot3d() + \
text3d(r'lambda', [0, 0.75, 1]) + \
text3d(r'mu squared', [-0.5, 0, 0.2]) + \
text3d(r'abs(phi)', [-1.5, 0, 2])
gfx.show()
Estimate a vector of real-valued Zernike coefficients from a phase grid by
taking inner products.
References
----------
.. [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
