res_factor=1.0,
n_hat=platform['n_hat'])
# Apply polar format algorithm to phase history data
# (Other options not available since platform position is unknown)
img_pf = imgTools.polar_format(phs_corr, platform, img_plane, taylor=30)
# Degrade image with random 10th order polynomial phase
coeff = (np.random.rand(10) - 0.5) * img_pf.shape[0]
x = np.linspace(-1, 1, img_pf.shape[0])
y = np.poly1d(coeff)(x)
slope, intercept, r_value, p_value, std_err = linregress(x, y)
line = slope * x + np.mean(y)
y = y - line
ph_err = np.tile(np.array([y]).T, (1, img_pf.shape[1]))
img_err = sig.ft(sig.ift(img_pf, ax=0) * np.exp(1j * ph_err), ax=0)
# Autofocus image
print('autofocusing')
img_af, af_ph = imgTools.autoFocus2(img_err, win='auto')
# img_af, af_ph = imgTools.autoFocus2(img_err, win = 0, win_params = [500,0.8])
# Output image
plt.figure()
plt.plot(x, y, x, af_ph)
plt.legend(['true error', 'estimated error'], loc='best')
plt.ylabel('Phase (radians)')
# Output image
plt.figure()
imgTools.imshow(img_af, dB_scale=[-45, 0])
ng = np.min(np.min(G));
cg = 255 / (xg - ng);
plt.imshow(256 - cg * (G - ng)[::-1, :],
extent=(t.min() * 1e6, t.max() * 1e6, uc.min(), uc.max()), aspect='auto');
plt.xlabel('Fast-time t, $\mu$sec')
plt.ylabel('Synthetic Aperture (Slow-time) U, meters')
plt.title('Measured Spotlight SAR Signal')
#
td0 = t - 2 * sqrt(Xc ** 2 + Yc ** 2) / c;
s0 = exp(cj * wcm * td0 + cj * alpha * (td0 ** 2)) * ((td0 >= 0) & (td0 <= Tp));
s0 = s0 * exp(-cj * wc * t); # Baseband reference fast-time signal
s = sig.ft(s) * (conj(sig.ft(s0))); # Fast-time matched filtering
#
G = abs(sig.ift(s));
xg = np.max(np.max(G));
ng = np.min(np.min(G));
cg = 255 / (xg - ng);
tm = (2 * Rc / c) + dt * arange(-n / 2, n / 2); # fast-time array after matched filtering
plt.figure()
plt.imshow(256 - cg * (G - ng)[::-1, :],
extent=(tm.min() * 1e6, tm.max() * 1e6, uc.min(), uc.max()), aspect='auto');
plt.xlabel('Fast-time t, sec')
plt.ylabel('Synthetic Aperture (Slow-time) U, meters')
plt.title('SAR Signal after Fast-time Matched Filtering')
#
#############################################
# Slow-time baseband conversion for squint #
#############################################
#
extent=(t.min() * 1e6, t.max() * 1e6, uc.min(), uc.max()),
aspect='auto')
plt.xlabel('Fast-time t, $\mu$sec')
plt.ylabel('Synthetic Aperture (Slow-time) U, meters')
plt.title('Measured Spotlight SAR Signal')
#
td0 = t - 2 * sqrt(Xc**2 + Yc**2) / c
s0 = exp(cj * wcm * td0 + cj * alpha * (td0**2)) * ((td0 >= 0) & (td0 <= Tp))
s0 = s0 * exp(-cj * wc * t)
# Baseband reference fast-time signal
s = sig.ft(s) * (conj(sig.ft(s0)))
# Fast-time matched filtering
#
G = abs(sig.ift(s))
xg = np.max(np.max(G))
ng = np.min(np.min(G))
cg = 255 / (xg - ng)
tm = (2 * Rc / c) + dt * arange(-n / 2, n / 2)
# fast-time array after matched filtering
plt.figure()
plt.imshow(256 - cg * (G - ng)[::-1, :],
extent=(tm.min() * 1e6, tm.max() * 1e6, uc.min(), uc.max()),
aspect='auto')
plt.xlabel('Fast-time t, sec')
plt.ylabel('Synthetic Aperture (Slow-time) U, meters')
plt.title('SAR Signal after Fast-time Matched Filtering')
#
#############################################
# Slow-time baseband conversion for squint #
cg = 255 / (xg - ng)
plt.imshow(256 - cg * (G - ng)[::-1, :], extent=(t.min() * 1e6, t.max() * 1e6, uc.min(), uc.max()), aspect="auto")
plt.xlabel("Fast-time t, $\mu$sec")
plt.ylabel("Synthetic Aperture (Slow-time) U, meters")
plt.title("Measured Spotlight SAR Signal")
#
td0 = t - 2 * sqrt(Xc ** 2 + Yc ** 2) / c
s0 = exp(cj * wcm * td0 + cj * alpha * (td0 ** 2)) * ((td0 >= 0) & (td0 <= Tp))
s0 = s0 * exp(-cj * wc * t)
# Baseband reference fast-time signal
s = sig.ft(s) * (conj(sig.ft(s0)))
# Fast-time matched filtering
#
G = abs(sig.ift(s))
xg = np.max(np.max(G))
ng = np.min(np.min(G))
cg = 255 / (xg - ng)
tm = (2 * Rc / c) + dt * arange(-n / 2, n / 2)
# fast-time array after matched filtering
plt.figure()
plt.imshow(256 - cg * (G - ng)[::-1, :], extent=(tm.min() * 1e6, tm.max() * 1e6, uc.min(), uc.max()), aspect="auto")
plt.xlabel("Fast-time t, sec")
plt.ylabel("Synthetic Aperture (Slow-time) U, meters")
plt.title("SAR Signal after Fast-time Matched Filtering")
#
#############################################
# Slow-time baseband conversion for squint #
#############################################
#
#Import image plane dictionary from './parameters/img_plane'
img_plane = imgTools.img_plane_dict(platform,
res_factor = 1.0, n_hat = platform['n_hat'])
#Apply polar format algorithm to phase history data
#(Other options not available since platform position is unknown)
img_pf = imgTools.polar_format(phs_corr, platform, img_plane, taylor = 43)
#Degrade image with random 10th order polynomial phase
coeff = (np.random.rand(10)-0.5)*img_pf.shape[0]/4
x = np.linspace(-1,1,img_pf.shape[0])
y = np.poly1d(coeff)(x)
slope, intercept, r_value, p_value, std_err = linregress(x,y)
line = slope*x+np.mean(y)
y = y-line
ph_err = np.tile(np.array([y]).T,(1,img_pf.shape[1]))
img_err = sig.ft(sig.ift(img_pf,ax=0)*np.exp(1j*ph_err),ax=0)
#Output image
plt.imshow(np.abs(img_pf)**(0.1), cmap = cmap)
#Autofocus image
print('autofocusing')
img_af, af_ph = imgTools.autoFocus2(img_err, win = 'auto')
#img_af, af_ph = imgTools.autoFocus2(img_err, win = 0, win_params = [500,0.8])
#Output image
plt.figure()
plt.plot(x,y,x,af_ph); plt.legend(['true error','estimated error'], loc = 'best')
plt.ylabel('Phase (radians)')
