def __init__(self, sigma):
if self._erf is None:
try:
from scipy.special import erf
self.__class__._erf = erf
except (ValueError, ImportError):
raise ImportError("Gaussian PSF model requires scipy.")
x_0 = 0
y_0 = 0
amplitude = 1
constraints = {'fixed': {'x_0': True, 'y_0': True, 'sigma': True}}
super(GaussianPSF, self).__init__(param_dim=1,
sigma=sigma,
x_0=x_0,
y_0=y_0,
amplitude=amplitude,
**constraints)
# Default size is 8 * sigma
self.shape = (int(8 * sigma) + 1, int(8 * sigma) + 1)
self.fitter = fitting.NonLinearLSQFitter()
# Fix position per default
self.x_0.fixed = True
self.y_0.fixed = True
def gaussian_fit(x, y, order=0, **p0):
""" Fit a Gaussian + polynomial to the data.
Parameters
----------
x : array_like
y : array_like
order : int (optional)
The order of the Polynomial model. Defaults to constant (order=0).
**p0
Initial conditions for the model fit.
"""
if len(x) != len(y):
raise ValueError("x and y must have the sample shape!")
# TODO: when astropy.modeling allows combining models, fix this
if order > 0:
raise NotImplementedError()
#g = custom_model_1d(_gaussian_constant_model)
g = GaussianPolynomial()
default_p0 = dict(b=min(y),
m=0.,
log10_amp=np.log10(max(y)),
stddev=0.5,
mean=float(np.mean(x)))
for k, v in default_p0.items():
setattr(g, k, p0.get(k, v))
fit = fitting.NonLinearLSQFitter(g)
fit(x, y)
return g
def plotStatistcs(data):
"""
Plot statistics of the background pixels. Assumes that the input contains only
the background pixel values as a 1D array.
:return: None
"""
#search for best bandwidth
# print 'searching for the best KDE bandwidth'
# grid = GridSearchCV(KernelDensity(),
# {'bandwidth': np.linspace(0.1, 1.0, 15)}, n_jobs=-1,
# cv=20) # 20-fold cross-validation
# grid.fit(data.copy())
# print grid.best_params_
#derive KDE
print 'deriving KDE'
x_grid = np.linspace(data.min(), data.max(), 200)
#pdf = kde_sklearn(data.copy(), x_grid, bandwidth=grid.best_params_['bandwidth'])
#pdf = kde_sklearn(data.copy(), x_grid)
pdf = kde_statsmodels_u(data.copy().astype(np.float64), x_grid, bandwidth=1.5)
#plot data
fig, axarr = plt.subplots(1, 2, sharey=True)
ax1 = axarr[0]
ax2 = axarr[1]
fig.subplots_adjust(wspace=0)
ax1.set_title('Background Pixels')
ax2.set_title('Models')
d = ax1.hist(data, bins=np.linspace(data.min(), data.max()), normed=True, alpha=0.7)
ax1.plot(x_grid, pdf, 'r-', label='Gaussian KDE')
# Gaussian fit
x = [0.5 * (d[1][i] + d[1][i+1]) for i in xrange(len(d[1])-1)]
y = d[0]
g_init = models.Gaussian1D(amplitude=1., mean=np.mean(data), stddev=np.std(data))
f2 = fitting.NonLinearLSQFitter()
g = f2(g_init, x, y)
ax2.plot(x, g(x), 'b-', label='Gaussian Fit')
ax2.plot(x_grid, pdf, 'r-', label='Gaussian KDE', alpha=0.7)
ax1.set_ylabel('PDF')
ax1.set_xticks(ax1.get_xticks()[:-1])
ax2.set_xticks(ax2.get_xticks()[1:])
plt.legend(shadow=True, fancybox=True)
plt.savefig('backgroundStatistics.pdf')
plt.close()
def make_normalized_flat(self, overwrite=False):
""" Make a normalized Flat frame by fitting and dividing out
the flat lamp spectrum.
TODO: right now, this just fits a 1D polynomial. could do
a 2D fit to the image instead...
Parameters
----------
overwrite : bool (optional)
"""
# TODO: I can't get this 2D fit to work...
# x, y = np.mgrid[:shp[0], :shp[1]]
# p = models.Polynomial2DModel(degree=13)
# fit = fitting.LinearLSQFitter(p)
# fit(x, y, master_flat)
# smooth_flat = p(x,y)
cache_file = os.path.join(self.redux_path, "normalized_flat.fits")
if os.path.exists(cache_file) and overwrite:
os.remove(cache_file)
if not os.path.exists(cache_file):
# collapse the flat to 1D, fit a polynomial
master_flat_1d = np.median(self.master_flat, axis=1)
p = models.Polynomial1DModel(degree=15)
fit = fitting.NonLinearLSQFitter(p)
pix = np.arange(len(master_flat_1d))
fit(pix, master_flat_1d)
smooth_flat = p(pix)
# normalize the flat
n_flat = self.master_flat / smooth_flat[:, np.newaxis]
hdu = fits.PrimaryHDU(n_flat)
hdu.writeto(cache_file)
else:
n_flat = fits.getdata(cache_file)
return n_flat
def __init__(self, prf_array, normalize=True, subsampling=1):
# Array shape and dimension check
if subsampling == 1:
if prf_array.ndim == 2:
prf_array = np.array([[prf_array]])
if prf_array.ndim != 4:
raise TypeError('Array must have 4 dimensions.')
if prf_array.shape[:2] != (subsampling, subsampling):
raise TypeError('Incompatible subsampling and array size')
if np.isnan(prf_array).any():
raise Exception("Array contains NaN values. Can't create PRF.")
# Normalize if requested
if normalize:
for i in range(prf_array.shape[0]):
for j in range(prf_array.shape[1]):
prf_array[i, j] /= prf_array[i, j].sum()
# Set PRF asttributes
self._prf_array = prf_array
self.subsampling = subsampling
constraints = {'fixed': {'x_0': True, 'y_0': True}}
x_0 = 0
y_0 = 0
amplitude = 1
super(DiscretePRF, self).__init__(param_dim=1,
x_0=x_0,
y_0=y_0,
amplitude=amplitude,
**constraints)
self.linear = True
self.fitter = fitting.NonLinearLSQFitter()
# Fix position per default
self.x_0.fixed = True
self.y_0.fixed = True
def plotPRNU(data,
xmin=700,
xmax=1700,
ymin=3500,
ymax=4500,
order=3,
smooth=3.):
"""
Generate and plot maps of PRNU, ratios of PRNU maps, and show the PRNU as a function of wavelength.
"""
number_of_subplots = math.ceil(len(data.keys()) / 2.)
plt.figure(figsize=(8, 13))
plt.subplots_adjust(wspace=0.05,
hspace=0.15,
left=0.01,
right=0.99,
top=0.95,
bottom=0.05)
#loop over data from shortest wavelength to the longest
w = []
prnu = []
dat = {}
for i, wave in enumerate(sorted(data.keys())):
tmp = data[wave][ymin:ymax, xmin:xmax]
tmp /= np.median(tmp)
#meshgrid representing data
x, y = np.mgrid[:tmp.shape[1], :tmp.shape[0]]
#fit a polynomial 2d surface to remove the illumination profile
p_init = models.Polynomial2D(degree=order)
f = fitting.NonLinearLSQFitter()
p = f(p_init, x, y, tmp)
#normalize data
tmp /= p(x, y)
print tmp.max(), tmp.min()
#sigma clipped std to reject dead pixels etc.
prn = np.std(sigma_clip(tmp, 6.)) * 100.
print 'PRNU:', prn, 'per cent at lambda =', wave, 'nm'
w.append(int(wave))
prnu.append(prn)
if int(wave) > 750 and int(wave) < 850:
reference = tmp.copy()
dat[wave] = tmp.copy()
#Gaussian smooth to enhance structures for plotting
tmp = gaussian_filter(tmp, smooth)
ax = plt.subplot(number_of_subplots, 2, i + 1)
ax.imshow(tmp,
interpolation='none',
origin='lower',
vmin=0.995,
vmax=1.003)
ax.set_title(r'$\lambda =$ ' + str(int(wave)) + 'nm')
plt.axis('off')
#write to file
fileIO.writeFITS(tmp, str(int(wave)) + '.fits', int=False)
plt.savefig('PRNUmaps.png')
plt.close()
#ratio images
plt.figure(figsize=(8, 13))
plt.subplots_adjust(wspace=0.05,
hspace=0.15,
left=0.01,
right=0.99,
top=0.95,
bottom=0.05)
for i, wave in enumerate(sorted(dat.keys())):
tmp = dat[wave]
#divide by the reference
tmp /= reference
#Gaussian smooth to enhance structures for plotting
tmp = gaussian_filter(tmp, smooth)
ax = plt.subplot(number_of_subplots, 2, i + 1)
ax.imshow(tmp,
interpolation='none',
origin='lower',
vmin=0.995,
vmax=1.003)
ax.set_title(r'$\lambda =$ ' + str(int(wave)) + 'nm')
plt.axis('off')
plt.savefig('PRNURationmaps.png')
plt.close()
def plotWavelengthDependency(data,
xmin=700,
xmax=1700,
ymin=3500,
ymax=4500,
order=3,
samples=10):
#loop over data from shortest wavelength to the longest
dat = {}
for i, wave in enumerate(sorted(data.keys())):
tmp = data[wave][ymin:ymax, xmin:xmax]
tmp /= np.median(tmp)
#meshgrid representing data
x, y = np.mgrid[:tmp.shape[1], :tmp.shape[0]]
#fit a polynomial 2d surface to remove the illumination profile
p_init = models.Polynomial2D(degree=order)
f = fitting.NonLinearLSQFitter()
p = f(p_init, x, y, tmp)
#normalize data
tmp /= p(x, y)
#select sub regions to calculate the PRNU in
prnu = []
ydim, xdim = tmp.shape
ylen = ydim / samples
xlen = xdim / samples
for a in range(samples):
for b in range(samples):
area = tmp[a * ylen:(a + 1) * ylen, b * xlen:(b + 1) * xlen]
prn = np.std(sigma_clip(area, 6.)) * 100.
prnu.append(prn)
dat[int(wave)] = prnu
#calculate the mean for each wavelength and std
w = []
mean = []
std = []
for wave in sorted(dat.keys()):
m = np.mean(dat[wave])
s = np.std(dat[wave])
w.append(wave)
mean.append(m)
std.append(s)
print wave, m, s
#polynomial fit to PRNU datra
z2 = np.polyfit(w, mean, 2)
p2 = np.poly1d(z2)
z3 = np.polyfit(w, mean, 3)
p3 = np.poly1d(z3)
x = np.linspace(500, 950)
#wavelength dependency plot
plt.title('Wavelength Dependency of the PRNU')
plt.plot(x, p2(x), 'b-', label='2nd order fit')
plt.plot(x, p3(x), 'g--', label='3rd order fit')
plt.errorbar(w,
mean,
yerr=3 * np.asarray(std),
c='r',
fmt='o',
label='data, $3\sigma$ errors')
plt.xlabel(r'Wavelength $\lambda$ [nm]')
plt.ylabel(r'PRNU $[\%]$')
plt.xlim(500, 950)
plt.ylim(0.4, 0.8)
plt.legend(shadow=True, fancybox=True, scatterpoints=1, numpoints=1)
plt.savefig('PRNUwave.pdf')
plt.close()
def normaliseFlat(data, output, order=5, mask=True, method='boxcar'):
"""
Normalise each quadrant separately. If limit set use to to generate a mask.
"""
#split to quadrants
Q0 = data[7:2052, 57:2098].copy()
Q2 = data[2543:4592, 57:2098].copy()
Q1 = data[7:2052, 2505:4545].copy()
Q3 = data[2543:4592, 2505:4545].copy()
Qs = [Q0, Q1, Q2, Q3]
res = []
for tmp in Qs:
if mask:
print 'Using masked 2D arrays (not applied in spline fitting)...'
# median = np.median(tmp)
# msk = (tmp > median*0.88) & (tmp < 40000.)
# #note the inversion of the mask before applying, as for numpy masked arrays True means masking
# #while in my selection above True means good data
# t = np.ma.MaskedArray(tmp, mask=~msk)
t = sigma_clip(
tmp, sig=3.
) #this can be used to generate automatically a masked array
else:
print 'No 2D masking applied...'
t = tmp.copy()
if method is 'surface':
print 'Fitting a surface to model the illumination profile'
#meshgrid representing data
x, y = np.mgrid[:t.shape[0], :t.shape[1]]
#fit a polynomial 2d surface to remove the illumination profile
p_init = models.Polynomial2D(degree=order)
f = fitting.NonLinearLSQFitter()
p = f(p_init, x, y, t)
#normalize data and save it to res list
tmp /= p(x, y)
elif method is 'boxcar':
size = 15 #this is very small, so will probably smooth out some actual PRNU, but needed to remove dust specs
print 'Using a boxcar smoothed image to model the illumination profile'
#will have to convert masked array to NaN array as convolve does not support masks
t = t.filled(np.nan)
box_2D_kernel = Box2DKernel(size)
if size > 50:
model = convolve_fft(t, box_2D_kernel)
else:
model = convolve(t, box_2D_kernel) #faster for small kernels
tmp /= model
elif method is 'spline':
spacing = 27
print 'Fitting 1D splines to each row to model the illumination profile'
for i, line in enumerate(tmp):
#Initializes the instance with dummy xnodes
Spline = splineFitting.SplineFitting([
0,
])
#filter dead pixels from the data
y = line.copy()
median = np.median(y)
y = y[
y > median *
0.92] #this is pretty aggressive masking, but needed because of no dead pixel map
x = np.arange(len(y))
#Median filter the data
medianFiltered = signal.medfilt(y, 25)
#Spline nodes and initial guess for y positions from median filtered
xnods = np.arange(0, len(y), spacing)
ynods = medianFiltered[xnods]
#Updates dummy xnodes in Spline instance with real deal
Spline.xnodes = xnods
#Do the fitting
fittedYnodes, success = Spline.doFit(ynods, x, y)
#normalize the line with the fit
tmp[i, :] /= Spline.fitfunc(np.arange(len(line)), fittedYnodes)
else:
print 'No fitting method selected, will exit...'
sys.exit(-9)
res.append(tmp)
print np.mean(tmp), np.median(tmp), np.std(tmp)
#save out
out = np.zeros_like(data)
out[7:2052, 57:2098] = res[0]
out[7:2052, 2505:4545] = res[1]
out[2543:4592, 57:2098] = res[2]
out[2543:4592, 2505:4545] = res[3]
fileIO.writeFITS(out, output + 'FlatField%s.fits' % (method), int=False)
return out