# 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
betaplot.plot_beta(beta_hat)
p.show()
h1 = ax.plot(range(1, phase_pol.nk + 1), alpha_true, marker='o')
h2 = ax.plot(range(1, phase_pol.nk + 1), alpha_hat, marker='x')
p.legend(h1 + h2, [r'$\alpha$', r'$\hat{\alpha}$'])
p.ylabel('[rad]')
p.xlabel('$k$')
# Zernike coefficients error between alpha_true and alpha_hat
ax = p.subplot2grid((3, 3), (1, 0), colspan=3)
err = alpha_true - alpha_hat
ax.bar(range(1, phase_pol.nk + 1), np.abs(err))
p.title('error {:g} rms rad'.format(norm(err[1:])))
p.ylabel('[rad]')
p.xlabel('$k$')
ax = p.subplot2grid((3, 3), (2, 0))
phaseplot.plot_alpha(alpha_true)
p.title(r'$\alpha$')
p.colorbar()
ax = p.subplot2grid((3, 3), (2, 1))
phaseplot.plot_alpha(alpha_hat)
p.title(r'$\hat{\alpha}$')
p.colorbar()
ax = p.subplot2grid((3, 3), (2, 2))
phaseplot.plot_alpha(alpha_true - alpha_hat)
p.title(r'$\alpha - \hat{\alpha}$')
p.colorbar()
p.tight_layout()
p.show()
# 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
betaplot.plot_beta(beta_hat)
p.show()
h1 = ax.plot(range(1, phase_pol.nk + 1), alpha_true, marker='o')
h2 = ax.plot(range(1, phase_pol.nk + 1), alpha_hat, marker='x')
p.legend(h1 + h2, [r'$\alpha$', r'$\hat{\alpha}$'])
p.ylabel('[rad]')
p.xlabel('$k$')
# Zernike coefficients error between alpha_true and alpha_hat
ax = p.subplot2grid((3, 3), (1, 0), colspan=3)
err = alpha_true - alpha_hat
ax.bar(range(1, phase_pol.nk + 1), np.abs(err))
p.title('error {:g} rms rad'.format(norm(err[1:])))
p.ylabel('[rad]')
p.xlabel('$k$')
ax = p.subplot2grid((3, 3), (2, 0))
phaseplot.plot_alpha(alpha_true)
p.title(r'$\alpha$')
p.colorbar()
ax = p.subplot2grid((3, 3), (2, 1))
phaseplot.plot_alpha(alpha_hat)
p.title(r'$\hat{\alpha}$')
p.colorbar()
ax = p.subplot2grid((3, 3), (2, 2))
phaseplot.plot_alpha(alpha_true - alpha_hat)
p.title(r'$\alpha - \hat{\alpha}$')
p.colorbar()
p.tight_layout()
p.show()
