def centroid_airy(data, coords, rad=30, returnFit=False):
if isinstance(data, str):
data = pyfits.getdata(data)
# Transpose x and y b/c reasons
center_y, center_x = coords
dslice = data[center_x - rad:center_x + rad, center_y - rad:center_y + rad]
# Construct a grid of coordinates
x, y = np.mgrid[0:dslice.shape[0], 0:dslice.shape[1]]
x -= dslice.shape[0] / 2.
y -= dslice.shape[1] / 2.
p_init = models.AiryDisk2D(np.max(dslice), 0, 0, rad)
p = fitter(p_init, x, y, dslice)
# Rescale coordinates to match data
px = center_y + p.y_0
py = center_x + p.x_0
if returnFit:
return px, py, p
else:
return px, py
def log_likelihoodG(theta, x, y, data, var, size=21):
"""
Logarithm of the likelihood function.
"""
#unpack the parameters
amplitude, center_x, center_y, radius, focus, width_x, width_y = theta
#1)Generate a model Airy disc
airy = models.AiryDisk2D(amplitude, center_x, center_y, radius)
adata = airy.eval(x, y, amplitude, center_x, center_y, radius).reshape((size, size))
#2)Apply Focus
f = models.Gaussian2D(1., center_x, center_y, focus, focus, 0.)
focusdata = f.eval(x, y, 1., center_x, center_y, focus, focus, 0.).reshape((size, size))
model = signal.convolve2d(adata, focusdata, mode='same')
#3)Apply CCD diffusion, approximated with a Gaussian
CCD = models.Gaussian2D(1., size/2.-0.5, size/2.-0.5, width_x, width_y, 0.)
CCDdata = CCD.eval(x, y, 1., size/2.-0.5, size/2.-0.5, width_x, width_y, 0.).reshape((size, size))
model = signal.convolve2d(model, CCDdata, mode='same').flatten()
#true for Gaussian errors, but not really true here because of mixture of Poisson and Gaussian noise
lnL = - 0.5 * np.sum((data - model)**2 / var)
return lnL
def fit_airy_2d(data, x=None, y=None):
"""Fit an AiryDisk2D model to the data."""
delta = int(len(data) / 2) # guess the center
ldata = len(data)
if not x:
x = delta
if not y:
y = delta
fixed_pars = {"x_0": True, "y_0": True} # hold these constant
yy, xx = np.mgrid[:ldata, :ldata]
# fit model to the data
fit = fitting.LevMarLSQFitter()
# AiryDisk2D(amplitude, x_0, y_0, radius)
model = models.AiryDisk2D(np.max(data),
x_0=x,
y_0=y,
radius=delta,
fixed=fixed_pars)
with warnings.catch_warnings():
# Ignore model warnings for new_plot_window
warnings.simplefilter('ignore')
results = fit(model, xx, yy, data)
return results
def _simpleExample(CCDx=10, CCDy=10):
spot = np.zeros((21, 21))
#Create the coordinates x and y
x = np.arange(0, spot.shape[1])
y = np.arange(0, spot.shape[0])
#Put the coordinates in a mesh
xx, yy = np.meshgrid(x, y)
peak, center_x, center_y, radius, focus, width_x, width_y = (200000, 10.1,
9.95, 0.5,
0.5, 0.03,
0.06)
amplitude = _amplitudeFromPeak(peak,
center_x,
center_y,
radius,
x_0=CCDx,
y_0=CCDy)
airy = models.AiryDisk2D(amplitude, center_x, center_y, radius)
adata = airy.eval(xx, yy, amplitude, center_x, center_y,
radius).reshape(spot.shape)
f = models.Gaussian2D(1., center_x, center_y, focus, focus, 0.)
focusdata = f.eval(xx, yy, 1., center_x, center_y, focus, focus,
0.).reshape(spot.shape)
foc = signal.convolve2d(adata, focusdata, mode='same')
fileIO.writeFITS(foc, 'TESTfocus.fits', int=False)
CCDdata = np.array(
[[0.0, width_y, 0.0],
[width_x, (1. - width_y - width_y - width_x - width_x), width_x],
[0.0, width_y, 0.0]])
model = signal.convolve2d(foc, CCDdata, mode='same')
#save model
fileIO.writeFITS(model, 'TESTkernel.fits', int=False)
def log_likelihoodC(theta, x, y, data, var, size=21):
"""
Logarithm of the likelihood function.
"""
#unpack the parameters
amplitude, center_x, center_y, radius, focus, width_x, width_y, width_d = theta
#1)Generate a model Airy disc
airy = models.AiryDisk2D(amplitude, center_x, center_y, radius)
adata = airy.eval(x, y, amplitude, center_x, center_y, radius).reshape((size, size))
#2)Apply Focus
f = models.Gaussian2D(1., center_x, center_y, focus, focus, 0.)
focusdata = f.eval(x, y, 1., center_x, center_y, focus, focus, 0.).reshape((size, size))
focusmodel = signal.convolve2d(adata, focusdata, mode='same')
#3)Apply CCD diffusion kernel
kernel = np.array([[width_d, width_y, width_d],
[width_x, 1., width_x],
[width_d, width_y, width_d]])
kernel /= kernel.sum()
#model = ndimage.convolve(focusmodel, kernel)
model = signal.convolve2d(focusmodel, kernel, mode='same').flatten()
#true for Gaussian errors, but not really true here because of mixture of Poisson and Gaussian noise
lnL = - 0.5 * np.sum((data - model)**2 / var)
return lnL
def model_psf(self, model, radius, psf_resolution, shape=256, **kwargs):
"""Models the PSF given the desired model function and kwargs.
Args:
model (str):
Must be either 'airydisk' or 'gaussian'.
radius (int, float, astropy.unit.Quantity):
Radius of the PSF model that is the radius of the first zero in an AiryDisk model or the standard
deviation of the Gaussian model. Scalar values will be interpreted in units of arcseconds.
psf_resolution (int, float, astropy.unit.Quantity):
Resolution of the model PSF, equivalent to the pixel scale of the array. Scalar values will be
interpreted in units of arcseconds.
shape (int, optional):
Size of the model PSF along both axes.
kwargs are forwarded to the model function.
"""
# Check input parameters
if not isinstance(model, str):
raise SpecklepyTypeError('model_psf', 'model', type(model), 'str')
if isinstance(radius, Quantity):
self.radius = radius
elif isinstance(radius, (int, float)):
logger.warning(f"Interpreting scalar type radius as {radius} arcsec")
self.radius = Quantity(f"{radius} arcsec")
elif isinstance(radius, str):
self.radius = Quantity(radius)
else:
raise SpecklepyTypeError('model_psf', 'radius', type(radius), 'Quantity')
if isinstance(psf_resolution, Quantity):
self.psf_resolution = psf_resolution
elif isinstance(psf_resolution, (int, float)):
logger.warning(f"Interpreting scalar type psf_resolution as {psf_resolution} arcsec")
self.psf_resolution = Quantity(f"{psf_resolution} arcsec")
elif isinstance(psf_resolution, str):
self.psf_resolution = Quantity(psf_resolution)
else:
raise SpecklepyTypeError('model_psf', 'psf_resolution', type(psf_resolution), 'Quantity')
if isinstance(shape, int):
center = (shape / 2, shape / 2)
shape = (shape, shape)
elif isinstance(shape, tuple):
center = (shape[0] / 2, shape[1] / 2)
else:
raise SpecklepyTypeError('model_psf', 'shape', type(shape), 'int or tuple')
if model.lower() == 'airydisk':
model = models.AiryDisk2D(x_0=center[0], y_0=center[1], radius=float(self.radius / self.psf_resolution))
elif model.lower() == 'gaussian':
stddev = float(self.radius / self.psf_resolution)
model = models.Gaussian2D(x_mean=center[0], y_mean=center[1], x_stddev=stddev, y_stddev=stddev)
else:
raise SpecklepyValueError('model_psf', 'model', model, 'either AiryDisk or Gaussian')
y, x = np.mgrid[0:shape[0], 0:shape[1]]
self.psf = model(x, y)
self.psf = self.normalize(self.psf)
def test_model_integer_indexing(int_type):
"""Regression for PR 12561; verify that compound model components
can be accessed by integer index"""
gauss = models.Gaussian2D()
airy = models.AiryDisk2D()
compound = gauss + airy
assert compound[int_type(0)] == gauss
assert compound[int_type(1)] == airy
def fit_airy_2d(data, x=None, y=None, sigma_factor=0):
"""Fit an AiryDisk2D model to the data.
Parameters
----------
data: 2D float array
should be a 2d array, the initial center is used to estimate
the fit center
x: float (optional)
xcenter location
y: float (optional)
ycenter location
sigma_factor: float (optional)
If sigma_factor > 0 then clipping will be performed
on the data during the model fit
Returns
-------
The the fit model for Airy2D function
"""
delta = int(len(data) / 2) # guess the center
ldata = len(data)
if x is None:
x = delta
if y is None:
y = delta
fixed_pars = {"x_0": True, "y_0": True} # hold these constant
yy, xx = np.mgrid[:ldata, :ldata]
# Initialize the fitter
fitter = fitting.LevMarLSQFitter()
if sigma_factor > 0:
fit = fitting.FittingWithOutlierRemoval(fitter,
sigma_clip,
niter=3,
sigma=sigma_factor)
else:
fit = fitter
# AiryDisk2D(amplitude, x_0, y_0, radius) + constant
model = (models.AiryDisk2D(
np.max(data), x_0=x, y_0=y, radius=delta, fixed=fixed_pars) +
models.Polynomial2D(c0_0=data.min(), degree=0))
with warnings.catch_warnings():
# Ignore model warnings for new_plot_window
warnings.simplefilter('ignore')
results = fit(model, xx, yy, data)
if sigma_factor > 0:
return results[1]
else:
return results
def test_model_string_indexing():
"""Regression for PR 12561; verify that compound model components
can be accessed by indexing with model name"""
gauss = models.Gaussian2D()
gauss.name = 'Model1'
airy = models.AiryDisk2D()
airy.name = 'Model2'
compound = gauss + airy
assert compound['Model1'] == gauss
assert compound['Model2'] == airy
def _peakFromTruth(theta, size=21):
"""
Derive the peak value from the parameters used for simulations.
"""
amplitude, center_x, center_y, radius, focus, width_x, width_y = theta
x = np.arange(0, size)
y = np.arange(0, size)
x, y = np.meshgrid(x, y)
airy = models.AiryDisk2D(amplitude, center_x, center_y, radius)
adata = airy.eval(x, y, amplitude, center_x, center_y, radius)
return adata.max()
def compute_airy_model(self, size=256, wavelength=None, first_zero_radius=4): """ compute_airy_model() computes a diffraction limited PSF, based on an Airy model on grid with shape = (size, size). The corresponding pixel scale (the psf_resolution) is computed radius of the first zero (first_zero_radius=12, in pix), the telescope diameter and a wavelength. Therefore, please provide the telescope instance with a wavelength attribute. """ if wavelength is None: try: wavelength = self.wavelength except: wavelength = 1*u.micron center = int(size / 2) Airy = models.AiryDisk2D(amplitude=1e6, x_0=center, y_0=center, radius=first_zero_radius) xdata, ydata = np.meshgrid(np.arange(0, size), np.arange(0, size)) self.psf = self._normalize(Airy(xdata, ydata)) self.psf_resolution = 1.2196698912665045 * np.arctan(wavelength / self.diameter).to(u.mas) / first_zero_radius
def log_likelihoodJoint(theta, x, y, data, var, size=21):
"""
Logarithm of the likelihood function for joint fitting. Not really sure if this is right...
"""
#unpack the parameters
#[xpos, ypos]*images) +[amplitude, radius, focus])
images = len(theta[:-5]) / 2
amplitude, radius, focus, width_x, width_y = theta[-5:]
data[data < 1.] = 0.
lnL = 0.
for tmp in xrange(images):
#X and Y are always in pairs
center_x = theta[2*tmp]
center_y = theta[2*tmp+1]
#1)Generate a model Airy disc
airy = models.AiryDisk2D(amplitude, center_x, center_y, radius)
adata = airy.eval(x, y, amplitude, center_x, center_y, radius).reshape((size, size))
#2)Apply Focus, no normalisation as smoothing
f = models.Gaussian2D(1., center_x, center_y, focus, focus, 0.)
focusdata = f.eval(x, y, 1., center_x, center_y, focus, focus, 0.).reshape((size, size))
model = signal.convolve2d(adata, focusdata, mode='same')
#3)Apply CCD diffusion, approximated with a Gaussian -- max = 1 as centred
CCD = models.Gaussian2D(1., size/2.-0.5, size/2.-0.5, width_x, width_y, 0.)
CCDdata = CCD.eval(x, y, 1., size/2.-0.5, size/2.-0.5, width_x, width_y, 0.).reshape((size, size))
model = signal.convolve2d(model, CCDdata, mode='same').flatten()
lnL += - 0.5 * np.sum((data[tmp].flatten() - model)**2 / var[tmp].flatten())
# model[model < 1.] = 1.
# lnL1 = - np.sum(model - data*np.log(model))
# lnL2 = - 0.5 * np.sum((data - model)**2 / var)
# #lnL += np.logaddexp(lnL1, lnL2)
# lnL += lnL1 + lnL2
return lnL
def log_likelihood(theta, x, y, data, var, size):
"""
Logarithm of the likelihood function.
"""
#unpack the parameters
peak, center_x, center_y, radius, focus, width_x, width_y = theta
#1)Generate a model Airy disc
amplitude = _amplitudeFromPeak(peak,
center_x,
center_y,
radius,
x_0=int(size[0] / 2. - 0.5),
y_0=int(size[1] / 2. - 0.5))
airy = models.AiryDisk2D(amplitude, center_x, center_y, radius)
adata = airy.eval(x, y, amplitude, center_x, center_y,
radius).reshape(size)
#2)Apply Focus
f = models.Gaussian2D(1., center_x, center_y, focus, focus, 0.)
focusdata = f.eval(x, y, 1., center_x, center_y, focus, focus,
0.).reshape(size)
model = signal.convolve2d(adata, focusdata, mode='same')
#3)Apply CCD diffusion, approximated with a Gaussian
CCDdata = np.array(
[[0.0, width_y, 0.0],
[width_x, (1. - width_y - width_y - width_x - width_x), width_x],
[0.0, width_y, 0.0]])
model = signal.convolve2d(model, CCDdata, mode='same').flatten()
#true for Gaussian errors
#lnL = - 0.5 * np.sum((data - model)**2 / var)
#Gary B. said that this should be from the model not data so recompute var (now contains rn**2)
var += model.copy()
lnL = -(np.size(var) * np.sum(np.log(var))) - (0.5 * np.sum(
(data - model)**2 / var))
return lnL
def log_likelihood(theta, x, y, data, var, size=21):
"""
Logarithm of the likelihood function.
"""
#unpack the parameters
amplitude, center_x, center_y, radius, focus, width_x, width_y = theta
#1)Generate a model Airy disc
airy = models.AiryDisk2D(amplitude, center_x, center_y, radius)
adata = airy.eval(x, y, amplitude, center_x, center_y, radius).reshape((size, size))
#2)Apply Focus
f = models.Gaussian2D(1., center_x, center_y, focus, focus, 0.)
focusdata = f.eval(x, y, 1., center_x, center_y, focus, focus, 0.).reshape((size, size))
model = signal.convolve2d(adata, focusdata, mode='same')
#3)Apply CCD diffusion, approximated with a Gaussian
CCD = models.Gaussian2D(1., size/2.-0.5, size/2.-0.5, width_x, width_y, 0.)
CCDdata = CCD.eval(x, y, 1., size/2.-0.5, size/2.-0.5, width_x, width_y, 0.).reshape((size, size))
model = signal.convolve2d(model, CCDdata, mode='same').flatten()
#true for Gaussian errors, but not really true here because of mixture of Poisson and Gaussian noise
#lnL = - 0.5 * np.sum((data - model)**2 / var)
#others...
lnL = - 2. * np.sum((((data - model)**2) + np.abs(data - model))/var) #does not get the amplitude easily right
#using L1 norm would be true for exponential distribution
#lnL = - np.sum(np.abs(data - model) / var)
# data[data < 1.] = 0.
# model[model < 1.] = 1.
# lnL1 = - np.sum(model - data*np.log(model))
# lnL2 = - 0.5 * np.sum((data - model)**2 / var)
# #lnL = np.logaddexp(lnL1, lnL2)
# lnL = lnL1 + lnL2
return lnL
astmodels.Legendre2D(1, 1, c0_0=1, c0_1=2, c1_0=3),
astmodels.Hermite2D(1, 1, c0_0=1, c0_1=2, c1_0=3),
astmodels.Scale(3.4),
astmodels.RotateNative2Celestial(5.63, -72.5, 180),
astmodels.Multiply(3),
astmodels.Multiply(10 * u.m),
astmodels.RotateCelestial2Native(5.63, -72.5, 180),
astmodels.EulerAngleRotation(23, 14, 2.3, axes_order='xzx'),
astmodels.Mapping((0, 1), n_inputs=3),
astmodels.Shift(2. * u.deg),
astmodels.Scale(3.4 * u.deg),
astmodels.RotateNative2Celestial(5.63 * u.deg, -72.5 * u.deg, 180 * u.deg),
astmodels.RotateCelestial2Native(5.63 * u.deg, -72.5 * u.deg, 180 * u.deg),
astmodels.RotationSequence3D([1.2, 2.3, 3.4, .3], 'xyzx'),
astmodels.SphericalRotationSequence([1.2, 2.3, 3.4, .3], 'xyzy'),
astmodels.AiryDisk2D(amplitude=10., x_0=0.5, y_0=1.5),
astmodels.Box1D(amplitude=10., x_0=0.5, width=5.),
astmodels.Box2D(amplitude=10., x_0=0.5, x_width=5., y_0=1.5, y_width=7.),
astmodels.Const1D(amplitude=5.),
astmodels.Const2D(amplitude=5.),
astmodels.Disk2D(amplitude=10., x_0=0.5, y_0=1.5, R_0=5.),
astmodels.Ellipse2D(amplitude=10., x_0=0.5, y_0=1.5, a=2., b=4.,
theta=0.1),
astmodels.Exponential1D(amplitude=10., tau=3.5),
astmodels.Gaussian1D(amplitude=10., mean=5., stddev=3.),
astmodels.Gaussian2D(amplitude=10.,
x_mean=5.,
y_mean=5.,
x_stddev=3.,
y_stddev=3.),
astmodels.KingProjectedAnalytic1D(amplitude=10., r_core=5., r_tide=2.),
def forwardModelTest(file, CCDPSFmodel='Gaus', out='Data', gain=3.1, size=10, spotx=2888, spoty=3514,
burn=100, run=200, nwalkers=1000):
"""
A single file to quickly test if the method works
"""
#get data and convert to electrons
print '\n\n\n'
print '_'*120
print 'Processing:', file
o = pf.getdata(file)*gain
#roughly the correct location - to avoid identifying e.g. cosmic rays
data = o[spoty-(size*3):spoty+(size*3)+1, spotx-(size*3):spotx+(size*3)+1].copy()
#maximum position within the cutout
y, x = m.maximum_position(data)
#spot and the peak pixel within the spot, this is also the CCD kernel position
spot = data[y-size:y+size+1, x-size:x+size+1].copy()
CCDy, CCDx = m.maximum_position(spot)
bias = np.median(o[spoty-size: spoty+size, spotx-220:spotx-20]) #works for read o
rn = np.std(o[spoty-size: spoty+size, spotx-220:spotx-20])
print 'Readnoise (e):', rn
if rn < 2. or rn > 6.:
print 'NOTE: suspicious readout noise estimate...'
print 'ADC offset (e):', bias
#remove bias
spot -= bias
#save to file
fileIO.writeFITS(spot, out+'small.fits', int=False)
#make a copy ot generate error array
data = spot.copy().flatten()
data[data + rn**2 < 0.] = 0. #set highly negative values to zero
#assume errors scale as sqrt of the values + readnoise
sigma = np.sqrt(data + rn**2)
#variance is the true noise model
var = sigma**2
#maximum value
max = np.max(spot)
print 'Maximum Value:', max
#fit a simple model
print 'Least Squares Fitting...'
gaus = models.Gaussian2D(spot.max(), size, size, x_stddev=0.5, y_stddev=0.5)
gaus.theta.fixed = True #fix angle
p_init = gaus
fit_p = fitting.LevMarLSQFitter()
stopy, stopx = spot.shape
X, Y = np.meshgrid(np.arange(0, stopx, 1), np.arange(0, stopy, 1))
p = fit_p(p_init, X, Y, spot)
print p
model = p(X, Y)
fileIO.writeFITS(model, out+'BasicModelG.fits', int=False)
fileIO.writeFITS(model - spot, out+'BasicModelResidualG.fits', int=False)
airy = models.AiryDisk2D(spot.max(), size, size, 0.6)
p_init = airy
fit_p = fitting.LevMarLSQFitter()
a = fit_p(p_init, X, Y, spot)
print a
model = p(X, Y)
fileIO.writeFITS(model, out+'BasicModelA.fits', int=False)
fileIO.writeFITS(model - spot, out+'BasicModelResidualA.fits', int=False)
#goodness of fit
gof = (1./(len(data)-5.)) * np.sum((model.flatten() - data)**2 / var)
print 'GoF:', gof
print 'Done'
#MCMC based fitting
if 'Gaus' in CCDPSFmodel:
ndim = 7
print 'Model with a Gaussian CCD PSF, %i dimensions' % ndim
#Choose an initial set of positions for the walkers - fairly large area not to bias the results
#amplitude, center_x, center_y, radius, focus, width_x, width_y = theta
p0 = np.zeros((nwalkers, ndim))
p0[:, 0] = np.random.uniform(max, 2.*max, size=nwalkers) # amplitude
p0[:, 1] = np.random.uniform(7., 14., size=nwalkers) # x
p0[:, 2] = np.random.uniform(7., 14., size=nwalkers) # y
p0[:, 3] = np.random.uniform(.1, 1., size=nwalkers) # radius
p0[:, 4] = np.random.uniform(.1, 1., size=nwalkers) # focus
p0[:, 5] = np.random.uniform(.1, 0.5, size=nwalkers) # width_x
p0[:, 6] = np.random.uniform(.1, 0.5, size=nwalkers) # width_y
# Initialize the sampler with the chosen specs.
#Create the coordinates x and y
x = np.arange(0, spot.shape[1])
y = np.arange(0, spot.shape[0])
#Put the coordinates in a mesh
xx, yy = np.meshgrid(x, y)
#Flatten the arrays
xx = xx.flatten()
yy = yy.flatten()
#initiate sampler
pool = Pool(7) #A hack Dan gave me to not have ghost processes running as with threads keyword
sampler = emcee.EnsembleSampler(nwalkers, ndim, log_posteriorG, args=[xx, yy, data, var], pool=pool)
# Run a burn-in and set new starting position
print "Burning-in..."
pos, prob, state = sampler.run_mcmc(p0, burn)
best_pos = sampler.flatchain[sampler.flatlnprobability.argmax()]
pos = emcee.utils.sample_ball(best_pos, best_pos/100., size=nwalkers)
# Reset the chain to remove the burn-in samples.
sampler.reset()
# Starting from the final position in the burn-in chain
print "Running MCMC..."
pos, prob, state = sampler.run_mcmc(pos, burn)
sampler.reset()
pos, prob, state = sampler.run_mcmc(pos, run, rstate0=state)
# Print out the mean acceptance fraction
print "Mean acceptance fraction:", np.mean(sampler.acceptance_fraction)
#Get the index with the highest probability
maxprob_index = np.argmax(prob)
#Get the best parameters and their respective errors and print best fits
params_fit = pos[maxprob_index]
errors_fit = [sampler.flatchain[:,i].std() for i in xrange(ndim)]
_printResults2(params_fit, errors_fit, model=CCDPSFmodel)
#Best fit model
amplitude, center_x, center_y, radius, focus, width_x, width_y = params_fit
airy = models.AiryDisk2D(amplitude, center_x, center_y, radius)
adata = airy.eval(xx, yy, amplitude, center_x, center_y, radius).reshape(spot.shape)
f = models.Gaussian2D(1., center_x, center_y, focus, focus, 0.)
focusdata = f.eval(xx, yy, 1., center_x, center_y, focus, focus, 0.).reshape(spot.shape)
foc = signal.convolve2d(adata, focusdata, mode='same')
CCD = models.Gaussian2D(1., CCDx, CCDy, width_x, width_y, 0.)
CCDdata = CCD.eval(xx, yy, 1., CCDx, CCDy, width_x, width_y, 0.).reshape(spot.shape)
model = signal.convolve2d(foc, CCDdata, mode='same')
#save model
fileIO.writeFITS(model, out+'model.fits', int=False)
#residuals
fileIO.writeFITS(model - spot, out+'residual.fits', int=False)
fileIO.writeFITS(((model-spot)**2 / var.reshape(spot.shape)), out+'residualSQ.fits', int=False)
#results
_printFWHM(width_x, width_y, errors_fit[5], errors_fit[6])
#plot
samples = sampler.chain[:, burn:, :].reshape((-1, ndim))
fig = triangle.corner(samples,
labels=['amplitude', 'center_x', 'center_y', 'radius', 'focus', 'width_x', 'width_y'])
fig.savefig(out+'Triangle.png')
elif 'Cross' in CCDPSFmodel:
ndim = 8
print 'Model with a Cross CCD PSF, %i dimensions' % ndim
#amplitude, center_x, center_y, radius, focus, width_x, width_y, width_d = theta
# Choose an initial set of positions for the walkers using the Gaussian fit
p0 = [np.asarray([1.3*max,#p.amplitude.value,
p.x_mean.value,
p.y_mean.value,
np.max([p.x_stddev.value, p.y_stddev.value]),
0.5,
0.08,
0.1,
0.01]) + 1e-3*np.random.randn(ndim) for i in xrange(nwalkers)]
# Initialize the sampler with the chosen specs.
#Create the coordinates x and y
x = np.arange(0, spot.shape[1])
y = np.arange(0, spot.shape[0])
#Put the coordinates in a mesh
xx, yy = np.meshgrid(x, y)
#Flatten the arrays
xx = xx.flatten()
yy = yy.flatten()
#initiate sampler
pool = Pool(7) #A hack Dan gave me to not have ghost processes running as with threads keyword
sampler = emcee.EnsembleSampler(nwalkers, ndim, log_posteriorC, args=[xx, yy, data, var], pool=pool)
# Run a burn-in and set new starting position
print "Burning-in..."
pos, prob, state = sampler.run_mcmc(p0, burn)
best_pos = sampler.flatchain[sampler.flatlnprobability.argmax()]
pos = emcee.utils.sample_ball(best_pos, best_pos/100., size=nwalkers)
# Reset the chain to remove the burn-in samples.
sampler.reset()
# Starting from the final position in the burn-in chain
print "Running MCMC..."
pos, prob, state = sampler.run_mcmc(pos, burn)
sampler.reset()
pos, prob, state = sampler.run_mcmc(pos, run, rstate0=state)
# Print out the mean acceptance fraction
print "Mean acceptance fraction:", np.mean(sampler.acceptance_fraction)
#Get the index with the highest probability
maxprob_index = np.argmax(prob)
#Get the best parameters and their respective errors and print best fits
params_fit = pos[maxprob_index]
errors_fit = [sampler.flatchain[:,i].std() for i in xrange(ndim)]
_printResults2(params_fit, errors_fit, model=CCDPSFmodel)
#Best fit model
amplitude, center_x, center_y, radius, focus, width_x, width_y, width_d = params_fit
airy = models.AiryDisk2D(amplitude, center_x, center_y, radius)
adata = airy.eval(xx, yy, amplitude, center_x, center_y, radius).reshape(spot.shape)
f = models.Gaussian2D(1., center_x, center_y, focus, focus, 0.)
focusdata = f.eval(xx, yy, 1., center_x, center_y, focus, focus, 0.).reshape(spot.shape)
foc = signal.convolve2d(adata, focusdata, mode='same')
#3)Apply CCD diffusion kernel
kernel = np.array([[width_d, width_y, width_d],
[width_x, 1., width_x],
[width_d, width_y, width_d]])
kernel /= kernel.sum()
model = signal.convolve2d(foc, kernel, mode='same')
#save model
fileIO.writeFITS(model, out+'model.fits', int=False)
#residuals
fileIO.writeFITS(model - spot, out+'residual.fits', int=False)
fileIO.writeFITS(((model-spot)**2 / var.reshape(spot.shape)), out+'residualSQ.fits', int=False)
#results
print kernel
gaus = models.Gaussian2D(kernel.max(), 1.5, 1.5, x_stddev=0.3, y_stddev=0.3)
gaus.theta.fixed = True
p_init = gaus
fit_p = fitting.LevMarLSQFitter()
stopy, stopx = kernel.shape
X, Y = np.meshgrid(np.arange(0, stopx, 1), np.arange(0, stopy, 1))
p = fit_p(p_init, X, Y, kernel)
#print p
_printFWHM(p.x_stddev.value, p.y_stddev.value, errors_fit[5], errors_fit[6])
#plot
samples = sampler.chain[:, burn:, :].reshape((-1, ndim))
fig = triangle.corner(samples,
labels=['amplitude', 'center_x', 'center_y', 'radius', 'focus', 'width_x', 'width_y', 'width_d'])
fig.savefig(out+'Triangle.png')
# a simple goodness of fit
gof = (1./(len(data)-ndim)) * np.sum((model.flatten() - data)**2 / var)
print 'GoF:', gof, ' Maximum difference:', np.max(np.abs(model - spot))
def forwardModel(file,
out='Data',
wavelength=None,
gain=3.1,
size=10,
burn=500,
spotx=2888,
spoty=3514,
run=700,
simulation=False,
truths=None):
"""
Forward models the spot data found from the input file. Can be used with simulated and real data.
Notes:
- emcee is run three times as it is important to have a good starting point for the final run.
"""
print '\n\n\n'
print '_' * 120
print 'Processing:', file
#get data and convert to electrons
o = pf.getdata(file) * gain
if simulation:
data = o
else:
#roughly the correct location - to avoid identifying e.g. cosmic rays
data = o[spoty - (size * 3):spoty + (size * 3) + 1,
spotx - (size * 3):spotx + (size * 3) + 1].copy()
#maximum position within the cutout
y, x = m.maximum_position(data)
#spot and the peak pixel within the spot, this is also the CCD kernel position
spot = data[y - size:y + size + 1, x - size:x + size + 1].copy()
CCDy, CCDx = m.maximum_position(spot)
print 'CCD Kernel Position (within the postage stamp):', CCDx, CCDy
#bias estimate
if simulation:
bias = 9000.
rn = 4.5
else:
bias = np.median(o[spoty - size:spoty + size,
spotx - 220:spotx - 20]) #works for read o
rn = np.std(o[spoty - size:spoty + size, spotx - 220:spotx - 20])
print 'Readnoise (e):', rn
if rn < 2. or rn > 6.:
print 'NOTE: suspicious readout noise estimate...'
print 'ADC offset (e):', bias
#remove bias
spot -= bias
#save to file
fileIO.writeFITS(spot, out + 'small.fits', int=False)
#make a copy ot generate error array
data = spot.copy().flatten()
#assume that uncertanties scale as sqrt of the values + readnoise
#sigma = np.sqrt(data/gain + rn**2)
tmp = data.copy()
tmp[tmp + rn**2 < 0.] = 0. #set highly negative values to zero
var = tmp.copy() + rn**2
#Gary B. said that actually this should be from the model or is biased,
#so I only pass the readout noise part now
#fit a simple model
print 'Least Squares Fitting...'
gaus = models.Gaussian2D(spot.max(),
size,
size,
x_stddev=0.5,
y_stddev=0.5)
gaus.theta.fixed = True #fix angle
p_init = gaus
fit_p = fitting.LevMarLSQFitter()
stopy, stopx = spot.shape
X, Y = np.meshgrid(np.arange(0, stopx, 1), np.arange(0, stopy, 1))
p = fit_p(p_init, X, Y, spot)
print p
model = p(X, Y)
fileIO.writeFITS(model, out + 'BasicModel.fits', int=False)
fileIO.writeFITS(model - spot, out + 'BasicModelResidual.fits', int=False)
#goodness of fit
gof = (1. / (np.size(data) - 5.)) * np.sum(
(model.flatten() - data)**2 / var)
print 'GoF:', gof
print 'Done\n\n'
#maximum value
max = np.max(spot)
peakrange = (0.9 * max, 1.7 * max)
sum = np.sum(spot)
print 'Maximum Value:', max
print 'Sum of the values:', sum
print 'Peak Range:', peakrange
#MCMC based fitting
print 'Bayesian Model Fitting...'
nwalkers = 1000
# Initialize the sampler with the chosen specs.
#Create the coordinates x and y
x = np.arange(0, spot.shape[1])
y = np.arange(0, spot.shape[0])
#Put the coordinates in a mesh
xx, yy = np.meshgrid(x, y)
#Flatten the arrays
xx = xx.flatten()
yy = yy.flatten()
print 'Fitting full model...'
ndim = 7
#Choose an initial set of positions for the walkers - fairly large area not to bias the results
p0 = np.zeros((nwalkers, ndim))
#peak, center_x, center_y, radius, focus, width_x, width_y = theta
p0[:, 0] = np.random.normal(max, max / 100., size=nwalkers) # peak value
p0[:, 1] = np.random.normal(p.x_mean.value, 0.1, size=nwalkers) # x
p0[:, 2] = np.random.normal(p.y_mean.value, 0.1, size=nwalkers) # y
print 'Using initial guess [radius, focus, width_x, width_y]:', [
1.5, 0.6, 0.02, 0.03
]
p0[:, 3] = np.random.normal(1.5, 0.01, size=nwalkers) # radius
p0[:, 4] = np.random.normal(0.6, 0.01, size=nwalkers) # focus
p0[:, 5] = np.random.normal(0.02, 0.0001, size=nwalkers) # width_x
p0[:, 6] = np.random.normal(0.03, 0.0001, size=nwalkers) # width_y
#initiate sampler
pool = Pool(
cores
) #A hack Dan gave me to not have ghost processes running as with threads keyword
#sampler = emcee.EnsembleSampler(nwalkers, ndim, log_posterior, args=[xx, yy, data, var, peakrange, spot.shape],
sampler = emcee.EnsembleSampler(
nwalkers,
ndim,
log_posterior,
args=[xx, yy, data, rn**2, peakrange, spot.shape],
pool=pool)
# Run a burn-in and set new starting position
print "Burning-in..."
pos, prob, state = sampler.run_mcmc(p0, burn)
maxprob_index = np.argmax(prob)
params_fit = pos[maxprob_index]
print "Mean acceptance fraction:", np.mean(sampler.acceptance_fraction)
print 'Estimate:', params_fit
sampler.reset()
print "Running MCMC..."
pos, prob, state = sampler.run_mcmc(pos, run, rstate0=state)
print "Mean acceptance fraction:", np.mean(sampler.acceptance_fraction)
#Get the index with the highest probability
maxprob_index = np.argmax(prob)
#Get the best parameters and their respective errors and print best fits
params_fit = pos[maxprob_index]
errors_fit = [sampler.flatchain[:, i].std() for i in xrange(ndim)]
_printResults(params_fit, errors_fit)
#Best fit model
peak, center_x, center_y, radius, focus, width_x, width_y = params_fit
amplitude = _amplitudeFromPeak(peak,
center_x,
center_y,
radius,
x_0=CCDx,
y_0=CCDy)
airy = models.AiryDisk2D(amplitude, center_x, center_y, radius)
adata = airy.eval(xx, yy, amplitude, center_x, center_y,
radius).reshape(spot.shape)
f = models.Gaussian2D(1., center_x, center_y, focus, focus, 0.)
focusdata = f.eval(xx, yy, 1., center_x, center_y, focus, focus,
0.).reshape(spot.shape)
foc = signal.convolve2d(adata, focusdata, mode='same')
CCDdata = np.array(
[[0.0, width_y, 0.0],
[width_x, (1. - width_y - width_y - width_x - width_x), width_x],
[0.0, width_y, 0.0]])
fileIO.writeFITS(CCDdata, 'kernel.fits', int=False)
model = signal.convolve2d(foc, CCDdata, mode='same')
#save model
fileIO.writeFITS(model, out + 'model.fits', int=False)
#residuals
fileIO.writeFITS(model - spot, out + 'residual.fits', int=False)
fileIO.writeFITS(((model - spot)**2 / var.reshape(spot.shape)),
out + 'residualSQ.fits',
int=False)
# a simple goodness of fit
gof = (1. / (np.size(data) - ndim)) * np.sum(
(model.flatten() - data)**2 / var)
maxdiff = np.max(np.abs(model - spot))
print 'GoF:', gof, ' Maximum difference:', maxdiff
if maxdiff > 2e3 or gof > 4.:
print '\nFIT UNLIKELY TO BE GOOD...\n'
print 'Amplitude estimate:', amplitude
#plot
samples = sampler.chain.reshape((-1, ndim))
extents = None
if simulation:
extents = [(0.91 * truth, 1.09 * truth) for truth in truths]
extents[1] = (truths[1] * 0.995, truths[1] * 1.005)
extents[2] = (truths[2] * 0.995, truths[2] * 1.005)
extents[3] = (0.395, 0.425)
extents[4] = (0.503, 0.517)
truths[0] = _peakFromTruth(truths)
print truths
fig = triangle.corner(
samples,
labels=['peak', 'x', 'y', 'radius', 'focus', 'width_x', 'width_y'],
truths=truths) #, extents=extents)
fig.savefig(out + 'Triangle.png')
plt.close()
pool.close()
data = hdu[0].data.squeeze()
w = WCS(hdu[0].header, naxis=2)
y, x = np.mgrid[:data.shape[0], :data.shape[1]]
# In[17]:
# Fit the data using a Gaussian
g_init = models.Gaussian2D(amplitude=1.,
x_mean=data.shape[0] // 2,
y_mean=data.shape[1] // 2,
x_stddev=1.,
y_stddev=1.)
g_init.amplitude.fixed = True
fit_g = fitting.LevMarLSQFitter()
g_air = models.AiryDisk2D(amplitude=1.,
x_0=data.shape[0] // 2,
y_0=data.shape[1] // 2,
radius=1)
g_air.amplitude.fixed = True
g = fit_g(g_init, x, y, data, weights=(data / data.max())**2)
g_air = fit_g(g_air, x, y, data, weights=(data / data.max())**2)
# In[18]:
fig = plt.figure(figsize=(27, 10))
gs = GridSpec(nrows=1, ncols=4, wspace=0.05)
ax = fig.add_subplot(gs[0], projection=w)
ax.imshow(data,
origin='lower',
interpolation='nearest',
vmin=0,
vmax=1,
def forwardModel(file, out='Data', gain=3.1, size=10, burn=20, spotx=2888, spoty=3514, run=50,
simulation=False, truths=None):
"""
Forward models the spot data found from the input file. Can be used with simulated and real data.
Notes:
- The emcee is run three times as it is important to have a good starting point for the final run.
- It is very important to have the amplitude well estimated, otherwise it is difficult to get good parameter estimates.
"""
print '\n\n\n'
print '_'*120
print 'Processing:', file
#get data and convert to electrons
o = pf.getdata(file)*gain
if simulation:
data = o
else:
#roughly the correct location - to avoid identifying e.g. cosmic rays
data = o[spoty-(size*3):spoty+(size*3)+1, spotx-(size*3):spotx+(size*3)+1].copy()
#maximum position within the cutout
y, x = m.maximum_position(data)
#spot and the peak pixel within the spot, this is also the CCD kernel position
spot = data[y-size:y+size+1, x-size:x+size+1].copy()
CCDy, CCDx = m.maximum_position(spot)
print 'CCD Kernel Position (within the postage stamp):', CCDx, CCDy
#bias estimate
if simulation:
bias = 9000.
rn = 4.5
else:
bias = np.median(o[spoty-size: spoty+size, spotx-220:spotx-20]) #works for read o
rn = np.std(o[spoty-size: spoty+size, spotx-220:spotx-20])
print 'Readnoise (e):', rn
if rn < 2. or rn > 6.:
print 'NOTE: suspicious readout noise estimate...'
print 'ADC offset (e):', bias
#remove bias
spot -= bias
#save to file
fileIO.writeFITS(spot, out+'small.fits', int=False)
#make a copy ot generate error array
data = spot.copy().flatten()
data[data + rn**2 < 0.] = 0. #set highly negative values to zero
#assume errors scale as sqrt of the values + readnoise
#sigma = np.sqrt(data/gain + rn**2)
var = data.copy() + rn**2
#maximum value
max = np.max(spot)
print 'Maximum Value:', max
#MCMC based fitting
print 'Bayesian Fitting...'
ndim = 7
nwalkers = 1000
#Choose an initial set of positions for the walkers - fairly large area not to bias the results
#amplitude, center_x, center_y, radius, focus, width_x, width_y = theta
p0 = np.zeros((nwalkers, ndim))
p0[:, 0] = np.random.uniform(max, 2.*max, size=nwalkers) # amplitude
p0[:, 1] = np.random.uniform(7., 14., size=nwalkers) # x
p0[:, 2] = np.random.uniform(7., 14., size=nwalkers) # y
p0[:, 3] = np.random.uniform(.1, 1., size=nwalkers) # radius
p0[:, 4] = np.random.uniform(.1, 1., size=nwalkers) # focus
p0[:, 5] = np.random.uniform(.1, 0.5, size=nwalkers) # width_x
p0[:, 6] = np.random.uniform(.1, 0.5, size=nwalkers) # width_y
# Initialize the sampler with the chosen specs.
#Create the coordinates x and y
x = np.arange(0, spot.shape[1])
y = np.arange(0, spot.shape[0])
#Put the coordinates in a mesh
xx, yy = np.meshgrid(x, y)
#Flatten the arrays
xx = xx.flatten()
yy = yy.flatten()
#initiate sampler
pool = Pool(7) #A hack Dan gave me to not have ghost processes running as with threads keyword
sampler = emcee.EnsembleSampler(nwalkers, ndim, log_posterior, args=[xx, yy, data, var], pool=pool)
# Run a burn-in and set new starting position
print "Burning-in..."
pos, prob, state = sampler.run_mcmc(p0, burn)
best_pos = sampler.flatchain[sampler.flatlnprobability.argmax()]
pos = emcee.utils.sample_ball(best_pos, best_pos/100., size=nwalkers)
# Reset the chain to remove the burn-in samples.
sampler.reset()
# Starting from the final position in the burn-in chain
print "Running MCMC..."
pos, prob, state = sampler.run_mcmc(pos, burn)
sampler.reset()
pos, prob, state = sampler.run_mcmc(pos, run, rstate0=state)
# Print out the mean acceptance fraction
print "Mean acceptance fraction:", np.mean(sampler.acceptance_fraction)
#Get the index with the highest probability
maxprob_index = np.argmax(prob)
#Get the best parameters and their respective errors and print best fits
params_fit = pos[maxprob_index]
errors_fit = [sampler.flatchain[:,i].std() for i in xrange(ndim)]
amplitudeE, center_xE, center_yE, radiusE, focusE, width_xE, width_yE = errors_fit
_printResults(params_fit, errors_fit)
#Best fit model
amplitude, center_x, center_y, radius, focus, width_x, width_y = params_fit
airy = models.AiryDisk2D(amplitude, center_x, center_y, radius)
adata = airy.eval(xx, yy, amplitude, center_x, center_y, radius).reshape(spot.shape)
f = models.Gaussian2D(1., center_x, center_y, focus, focus, 0.)
focusdata = f.eval(xx, yy, 1., center_x, center_y, focus, focus, 0.).reshape(spot.shape)
foc = signal.convolve2d(adata, focusdata, mode='same')
CCD = models.Gaussian2D(1., CCDx, CCDy, width_x, width_y, 0.)
CCDdata = CCD.eval(xx, yy, 1., CCDx, CCDy, width_x, width_y, 0.).reshape(spot.shape)
model = signal.convolve2d(foc, CCDdata, mode='same')
#save model
fileIO.writeFITS(model, out+'model.fits', int=False)
#residuals
fileIO.writeFITS(model - spot, out+'residual.fits', int=False)
fileIO.writeFITS(((model - spot)**2 / var.reshape(spot.shape)), out+'residualSQ.fits', int=False)
# a simple goodness of fit
gof = (1./(np.size(data) - ndim)) * np.sum((model.flatten() - data)**2 / var)
print 'GoF:', gof, ' Maximum difference:', np.max(np.abs(model - spot))
#results and save results
_printFWHM(width_x, width_y, errors_fit[5], errors_fit[6])
res = dict(wx=width_x, wy=width_y, wxerr=width_xE, wyerr=width_yE, out=out,
peakvalue=max, CCDmodel=CCD, CCDmodeldata=CCDdata, GoF=gof)
fileIO.cPickleDumpDictionary(res, out+'.pkl')
#plot
samples = sampler.chain.reshape((-1, ndim))
extents = None
if simulation:
extents = [(0.91*truth, 1.09*truth) for truth in truths]
extents[1] = (truths[1]*0.995, truths[1]*1.005)
extents[2] = (truths[2]*0.995, truths[2]*1.005)
extents[3] = (0.395, 0.425)
extents[4] = (0.503, 0.517)
fig = triangle.corner(samples,
labels=['amplitude', 'x', 'y', 'radius', 'focus', 'width_x', 'width_y'],
truths=truths)#, extents=extents)
fig.savefig(out+'Triangle.png')
pool.close()
def create_synth_psf(model='gauss',
shape=(9, 9),
amplitude=1,
x_mean=None,
y_mean=None,
fwhm=4,
theta=0,
gamma=None,
alpha=1.5,
radius=None,
msdi=False):
""" Creates a synthetic 2d or 3d PSF with a 2d model: Airy disk, Gaussian or
Moffat, depending on ``model``.
Parameters
----------
model : {'gauss', 'moff', 'airy'}, str optional
Model to be used to create the synthetic PSF.
shape : tuple of ints, optional
Shape of the output 2d array.
amplitude : float, optional
Value of the amplitude of the 2d distribution.
x_mean : float or None, optional
Value of the centroid in X of the distributions: the mean of the
Gaussian or the location of the maximum of the Moffat or Airy disk
models. If None, the centroid is placed at the center of the array.
y_mean : float or None, optional
Value of the centroid in Y of the distributions: the mean of the
Gaussian or the location of the maximum of the Moffat or Airy disk
models. If None, the centroid is placed at the center of the array.
fwhm : float, tuple of floats, list or np.ndarray, optional
FWHM of the model in pixels. For the Gaussian case, it controls the
standard deviation of the Gaussian. If a tuple is given, then the
Gaussian will be elongated (fwhm in x, fwhm in y). For the Moffat, it is
related to the gamma and alpha parameters. For the Airy disk, it is
related to the radius (of the first zero) parameter. If ``msdi`` is True
then ``fwhm`` must be a list of 1d np.ndarray (for example for
SPHERE/IFS this sounds like a reasonable FWHM: np.linspace(4.5,6.7,39)).
theta : float, optional
Rotation angle in degrees of the Gaussian.
gamma : float or None, optional
Gamma parameter of core width of the Moffat model. If None, then it is
calculated to correspond to the given ``fwhm``.
alpha : float, optional
Power index of the Moffat model.
radius : float or None, optional
The radius of the Airy disk (radius of the first zero). If None, then it
is calculated to correspond to the given ``fwhm``.
msdi : bool, optional
Creates a 3d PSF, for emulating an IFS PSF.
Returns
-------
im : numpy ndarray
2d array with given ``shape`` and containing the synthetic PSF.
Notes
-----
http://docs.astropy.org/en/stable/api/astropy.modeling.functional_models.Gaussian2D.html
http://docs.astropy.org/en/stable/api/astropy.modeling.functional_models.Moffat2D.html
http://docs.astropy.org/en/stable/api/astropy.modeling.functional_models.AiryDisk2D.html
https://www.gnu.org/software/gnuastro/manual/html_node/PSF.html
web.ipac.caltech.edu/staff/fmasci/home/astro_refs/PSFtheory.pdf
web.ipac.caltech.edu/staff/fmasci/home/astro_refs/PSFsAndSampling.pdf
"""
# 2d case
if not msdi:
sizex, sizey = shape
if x_mean is None or y_mean is None:
y_mean, x_mean = frame_center(np.zeros((sizey, sizex)))
x = np.arange(sizex)
y = np.arange(sizey)
x, y = np.meshgrid(x, y)
if model == 'gauss':
if np.isscalar(fwhm):
fwhm_y = fwhm
fwhm_x = fwhm
else:
fwhm_x, fwhm_y = fwhm
gauss = models.Gaussian2D(amplitude=amplitude,
x_mean=x_mean,
y_mean=y_mean,
x_stddev=fwhm_x * gaussian_fwhm_to_sigma,
y_stddev=fwhm_y * gaussian_fwhm_to_sigma,
theta=np.deg2rad(theta))
im = gauss(x, y)
elif model == 'moff':
if gamma is None and fwhm is not None:
gamma = fwhm / (2. * np.sqrt(2**(1 / alpha) - 1))
moffat = models.Moffat2D(amplitude=amplitude,
x_0=x_mean,
y_0=y_mean,
gamma=gamma,
alpha=alpha)
im = moffat(x, y)
elif model == 'airy':
if radius is None and fwhm is not None:
diam_1st_zero = (fwhm * 2.44) / 1.028
radius = diam_1st_zero / 2.
airy = models.AiryDisk2D(amplitude=amplitude,
x_0=x_mean,
y_0=y_mean,
radius=radius)
im = airy(x, y)
return im
# 3d case
else:
if np.isscalar(fwhm):
raise ValueError('`Fwhm` must be a 1d vector')
cube = []
for fwhm_i in fwhm:
cube.append(
create_synth_psf(model, shape, amplitude, x_mean, y_mean,
fwhm_i, theta, gamma, alpha, radius))
cube = np.array(cube)
return cube
def fit_2D_Airy(box,
center=None,
fixed_center=False,
max_center_offset=None,
radius=None,
zoom_factor=1.0,
mask=None,
amplitude=None):
"""
This function ...
:param box:
:param center:
:param fixed_center:
:param deviation_center:
:param radius:
:param x_shift:
:param y_shift:
:param zoom_factor:
:param mask:
:return:
"""
# Get the dimensions of the box
box_ysize = box.shape[0]
box_xsize = box.shape[1]
# Set the initial guess for the center of the model (the one that is specified, otherwise the center of the box)
init_x0 = center.x if center is not None else 0.5 * (box_xsize - 1)
init_y0 = center.y if center is not None else 0.5 * (box_ysize - 1)
# Set the initial radius for the model (the one that is specified, otherwise one tenth of the width of the box)
init_radius = radius if radius is not None else 0.1 * box_xsize
# Initialize an empty dictionary to specify fixed parameters
fixed_parameters = {}
if fixed_center:
fixed_parameters['x_0'] = True
fixed_parameters['y_0'] = True
# Initialize an empty dictionary to specify bounds
bounds = {}
if max_center_offset is not None:
bounds['x_mean'] = [
init_x0 - max_center_offset, init_x0 + max_center_offset
]
bounds['y_mean'] = [
init_y0 - max_center_offset, init_y0 + max_center_offset
]
# Fit the data using astropy.modeling
airy_init = models.AiryDisk2D(amplitude=1.,
x_0=init_x0,
y_0=init_y0,
radius=init_radius,
fixed=fixed_parameters,
bounds=bounds)
fit_model = fitting.LevMarLSQFitter()
x_values = []
y_values = []
z_values = []
for x in range(box_xsize):
for y in range(box_ysize):
# If no mask is specified or the pixel is not masked, add the coordinates and value to the appropriate lists
if mask is None or not mask[y, x]:
x_values.append(x)
y_values.append(y)
z_values.append(box[y, x])
# Ignore model linearity warning from the fitter
with warnings.catch_warnings():
warnings.simplefilter('ignore')
airy = fit_model(
airy_init, x_values, y_values,
z_values) # What comes out is the model with the parameters set
# Adjust the position of the model to a different coordinate frame
if zoom_factor > 1.0:
airy.x_0.value = airy.x_0.value / zoom_factor
airy.y_0.value = airy.y_0.value / zoom_factor
airy.radius /= zoom_factor
# Return the fitted two-dimensional Airy Disk model
return airy
def autocorrelation_fit(im2, rough_sep = 44.93, rough_pa=0., cutout_sz=5, background_subtracted=False,
plot_cutout=False, plot_resids=False):
""" Fits to the distance of the second peak in the autocorrelation (i.e. the binary separation).
This will perform a Levenberg-Marquardt fit over a small, fixed region around the peak.
The model used for the fit will depend on the options set.
rough_sep, rough_pa: Defaults 44.93 pixels and 0 degrees
These define the position of the region used for the fit.
cutout_sz: Default 5 pixels
The radius of the box used for the fit.
background_subtracted: Default False
If True, the model used for the fit will be an Airy Disk + constant background.
If False, the model will be a Gaussian + planar background.
These seemed to work best.
"""
rough_pos = np.round([rough_sep*np.sin(rough_pa),rough_sep*np.cos(rough_pa)]).astype(int)
calc_pos = [rough_sep*np.sin(rough_pa),rough_sep*np.cos(rough_pa)]
cutout = np.copy(im2[im2.shape[0]//2+rough_pos[0]-cutout_sz:im2.shape[0]//2+rough_pos[0]+cutout_sz,
im2.shape[1]//2+rough_pos[1]-cutout_sz:im2.shape[1]//2+rough_pos[1]+cutout_sz])
cutout /= np.max(cutout)
if plot_cutout:
plt.imshow(cutout)
x,y = np.indices(cutout.shape)
x = x + rough_pos[0] - cutout_sz
y = y + rough_pos[1] - cutout_sz
# Fit a Gaussian
fit = fitting.LevMarLSQFitter()
if background_subtracted:
gauss = models.AiryDisk2D(amplitude=cutout.max(),x_0=calc_pos[0],y_0=calc_pos[1],radius=3.54)
bckgd = models.Const2D(amplitude=0.6)
else:
gauss = models.Gaussian2D(amplitude = cutout.max(),x_stddev=1.36,y_stddev=1.36,
x_mean=calc_pos[0],y_mean=calc_pos[1])
bckgd = models.Planar2D(slope_x = -0.00564816,slope_y=-0.02378304,intercept=1.01)
gauss.fixed['theta']=True
cutout_model = gauss + bckgd
# fit the data with the fitter
fitted_model = fit(cutout_model,x,y,cutout,maxiter=100000,acc=1e-7);
# Rename the parameters so the output looks the same
if background_subtracted:
fitted_model.x_mean_0 = fitted_model.x_0_0
fitted_model.y_mean_0 = fitted_model.y_0_0
if plot_resids:
test = fitted_model(x,y)
plt.figure(figsize=(12,4))
plt.clf()
plt.subplot(131)
plt.imshow(cutout,origin='lowerleft',vmin=0.7,vmax=1);plt.colorbar()
plt.subplot(132)
plt.imshow(test,origin='lowerleft',vmin=0.7,vmax=1);plt.colorbar()
plt.subplot(133)
plt.imshow(cutout-test,origin='lowerleft',vmin=-0.05,vmax=0.05);plt.colorbar()
return fitted_model
def larkin_transform_fit(params,transformed_im,plot=True,fit_airy=False,rough_sep_pix = 45):
""" Function to fit to the Larkin Transform of the image.
params = [x0, y0, flux0, width0, sep, pa, flux1, width1]
x0, y0 = position of primary relative to the central pixel
flux0, flux1 = flux of primary and secondary
width0,width1 = width of model for the primary and secondary
sep,pa = separation and position angle of the binary
transformed_im = larkin transformed image
rough_sep_pix = approximate separation of the binary. Used for the fixed windowing, not the fit.
plot: If set, will display a plot of the primary, model and residuals, and secondary, model and residuals
fit_airy: If False (default) with fit sqrt(AiryDisk) to the data. If True, will fit AiryDisk.
returns:
[primary_fit,secondary_fit] astropy models
"""
x0,y0,flux0,width0,sep,pa,flux1,width1 = params
rough_sep_pix = int(round(rough_sep_pix))
im_shape = transformed_im.shape
y,x = np.indices(im_shape)
y -= im_shape[0]//2
x -= im_shape[1]//2
x1 = x0 + sep*np.cos(pa*np.pi/180.)
y1 = y0 + sep*np.sin(pa*np.pi/180.)
fit = fitting.LevMarLSQFitter()
if fit_airy:
prim = models.AiryDisk2D(amplitude=flux0,x_0=x0,y_0=y0,radius=width0)
sec = models.AiryDisk2D(amplitude=flux1,x_0=x1,y_0=y1,radius=width1)
else:
# Sqrt(AiryDisk), i.e. J1(r)/r
prim = larkin_model(amplitude=flux0,x_0=x0,y_0=y0,radius=width0,background=0.)
sec = larkin_model(amplitude=flux1,x_0=x1,y_0=y1,radius=width1,background=0.)
# Fit the primary and secondary separately
# Cut out a region
cutsz = 6 # was 4
cut_prim_im = transformed_im[im_shape[0]//2-cutsz:im_shape[0]//2+cutsz,
im_shape[1]//2-cutsz:im_shape[1]//2+cutsz]
x_prim = x[im_shape[0]//2-cutsz:im_shape[0]//2+cutsz,
im_shape[1]//2-cutsz:im_shape[1]//2+cutsz]
y_prim = y[im_shape[0]//2-cutsz:im_shape[0]//2+cutsz,
im_shape[1]//2-cutsz:im_shape[1]//2+cutsz]
prim_fit = fit(prim,x_prim,y_prim,cut_prim_im,maxiter=100000,acc=1e-9)
cut_sec_im = transformed_im[im_shape[0]//2-cutsz:im_shape[0]//2+cutsz,
im_shape[1]//2-cutsz+rough_sep_pix:im_shape[1]//2+cutsz+rough_sep_pix]
x_sec = x[im_shape[0]//2-cutsz:im_shape[0]//2+cutsz,
im_shape[1]//2-cutsz+rough_sep_pix:im_shape[1]//2+cutsz+rough_sep_pix]
y_sec = y[im_shape[0]//2-cutsz:im_shape[0]//2+cutsz,
im_shape[1]//2-cutsz+rough_sep_pix:im_shape[1]//2+cutsz+rough_sep_pix]
sec_fit = fit(sec,x_sec,y_sec,cut_sec_im,maxiter=100000,acc=1e-9)
if plot:
# plt.imshow(model(x,y))
m1 = prim_fit(x_prim,y_prim)
m2 = sec_fit(x_sec,y_sec)
plt.subplot(231)
plt.imshow(cut_prim_im,origin='lower')
plt.subplot(232)
plt.imshow(m1,origin='lower')
plt.subplot(233)
plt.imshow(cut_prim_im-m1,origin='lower',vmin=-0.05,vmax=0.05)
plt.subplot(234)
plt.imshow(cut_sec_im,origin='lower')
plt.subplot(235)
plt.imshow(m2,origin='lower')
plt.subplot(236)
plt.imshow(cut_sec_im-m2,origin='lower',vmin=-0.05,vmax=0.05)
print(prim_fit.parameters)
print(sec_fit.parameters)
sep = np.sqrt((prim_fit.x_0-sec_fit.x_0)**2 + (prim_fit.y_0-sec_fit.y_0)**2)
# return sep
return prim_fit,sec_fit
def __init__(self, radius, **kwargs):
self._model = models.AiryDisk2D(1, 0, 0, radius)
self._default_size = _round_up_to_odd_integer(8 * radius)
super().__init__(**kwargs)
self.normalize()
def forwardModelJointFit(files, out, wavelength, gain=3.1, size=10, burn=50, run=100,
spotx=2888, spoty=3514, simulated=False, truths=None):
"""
Forward models the spot data found from the input files. Models all data simultaneously so that the Airy
disc centroid and shift from file to file. Assumes that the spot intensity, focus, and the CCD PSF kernel
are the same for each file. Can be used with simulated and real data.
"""
print '\n\n\n'
print '_'*120
images = len(files)
orig = []
image = []
noise = []
peakvalues = []
for file in files:
print file
#get data and convert to electrons
o = pf.getdata(file)*gain
if simulated:
data = o
else:
#roughly the correct location - to avoid identifying e.g. cosmic rays
data = o[spoty-(size*3):spoty+(size*3)+1, spotx-(size*3):spotx+(size*3)+1].copy()
#maximum position within the cutout
y, x = m.maximum_position(data)
#spot and the peak pixel within the spot, this is also the CCD kernel position
spot = data[y-size:y+size+1, x-size:x+size+1].copy()
orig.append(spot.copy())
#bias estimate
if simulated:
bias = 9000.
rn = 4.5
else:
bias = np.median(o[spoty-size: spoty+size, spotx-220:spotx-20])
rn = np.std(o[spoty-size: spoty+size, spotx-220:spotx-20])
print 'Readnoise (e):', rn
if rn < 2. or rn > 6.:
print 'NOTE: suspicious readout noise estimate...'
print 'ADC offset (e):', bias
#remove bias
spot -= bias
#set highly negative values to zero
spot[spot + rn**2 < 0.] = 0.
max = np.max(spot)
print 'Maximum Value:', max
peakvalues.append(max)
#noise model
variance = spot.copy() + rn**2
#save to a list
image.append(spot)
noise.append(variance)
#sensibility test, try to check if all the files in the fit are of the same dataset
if np.std(peakvalues) > 5*np.sqrt(np.median(peakvalues)):
#check for more than 5sigma outliers, however, this is very sensitive to the centroiding of the spot...
print 'POTENTIAL OUTLIER, please check the input files...'
print np.std(peakvalues), 5*np.sqrt(np.median(peakvalues))
#MCMC based fitting
ndim = 2*images + 5 #xpos, ypos for each image and single amplitude, radius, focus, and sigmaX and sigmaY
nwalkers = 1000
print 'Bayesian Fitting, model has %i dimensions' % ndim
# Choose an initial set of positions for the walkers using the Gaussian fit
p0 = np.zeros((nwalkers, ndim))
for x in xrange(images):
p0[:, 2*x] = np.random.uniform(7., 14., size=nwalkers) # x
p0[:, 2*x+1] = np.random.uniform(7., 14., size=nwalkers) # y
p0[:, -5] = np.random.uniform(max, 2.*max, size=nwalkers) # amplitude
p0[:, -4] = np.random.uniform(.1, 1., size=nwalkers) # radius
p0[:, -3] = np.random.uniform(.1, 1., size=nwalkers) # focus
p0[:, -2] = np.random.uniform(.1, 0.5, size=nwalkers) # width_x
p0[:, -1] = np.random.uniform(.1, 0.5, size=nwalkers) # width_y
# Initialize the sampler with the chosen specs.
#Create the coordinates x and y
x = np.arange(0, spot.shape[1])
y = np.arange(0, spot.shape[0])
#Put the coordinates in a mesh
xx, yy = np.meshgrid(x, y)
#Flatten the arrays
xx = xx.flatten()
yy = yy.flatten()
#initiate sampler
pool = Pool(7) #A hack Dan gave me to not have ghost processes running as with threads keyword
sampler = emcee.EnsembleSampler(nwalkers, ndim, log_posteriorJoint, args=[xx, yy, image, noise], pool=pool)
# Run a burn-in and set new starting position
print "Burning-in..."
pos, prob, state = sampler.run_mcmc(p0, burn)
best_pos = sampler.flatchain[sampler.flatlnprobability.argmax()]
pos = emcee.utils.sample_ball(best_pos, best_pos/100., size=nwalkers)
# Reset the chain to remove the burn-in samples.
sampler.reset()
# Starting from the final position in the burn-in chain
print "Running MCMC..."
pos, prob, state = sampler.run_mcmc(pos, burn)
sampler.reset()
pos, prob, state = sampler.run_mcmc(pos, run, rstate0=state)
# Print out the mean acceptance fraction
print "Mean acceptance fraction:", np.mean(sampler.acceptance_fraction)
#Get the index with the highest probability
maxprob_index = np.argmax(prob)
#Get the best parameters and their respective errors and print best fits
params_fit = pos[maxprob_index]
errors_fit = [sampler.flatchain[:,i].std() for i in xrange(ndim)]
print params_fit
#unpack the fixed parameters
amplitude, radius, focus, width_x, width_y = params_fit[-5:]
amplitudeE, radiusE, focusE, width_xE, width_yE = errors_fit[-5:]
#print results
_printFWHM(width_x, width_y, width_xE, width_yE)
#save the best models per file
size = size*2 + 1
gofs = []
for index, file in enumerate(files):
#path, file = os.path.split(file)
id = 'test/' + out + str(index)
#X and Y are always in pairs
center_x = params_fit[2*index]
center_y = params_fit[2*index+1]
#1)Generate a model Airy disc
airy = models.AiryDisk2D(amplitude, center_x, center_y, radius)
adata = airy.eval(xx, yy, amplitude, center_x, center_y, radius).reshape((size, size))
#2)Apply Focus
f = models.Gaussian2D(1., center_x, center_y, focus, focus, 0.)
focusdata = f.eval(xx, yy, 1., center_x, center_y, focus, focus, 0.).reshape((size, size))
model = signal.convolve2d(adata, focusdata, mode='same')
#3)Apply CCD diffusion, approximated with a Gaussian
CCD = models.Gaussian2D(1., size/2.-0.5, size/2.-0.5, width_x, width_y, 0.)
CCDdata = CCD.eval(xx, yy, 1., size/2.-0.5, size/2.-0.5, width_x, width_y, 0.).reshape((size, size))
model = signal.convolve2d(model, CCDdata, mode='same')
#save the data, model and residuals
fileIO.writeFITS(orig[index], id+'data.fits', int=False)
fileIO.writeFITS(image[index], id+'datafit.fits', int=False)
fileIO.writeFITS(model, id+'model.fits', int=False)
fileIO.writeFITS(model - image[index], id+'residual.fits', int=False)
fileIO.writeFITS(((model - image[index])**2 / noise[index]), id+'residualSQ.fits', int=False)
#a simple goodness of fit
gof = (1./(np.size(image[index])*images - ndim)) * np.sum((model - image[index])**2 / noise[index])
print 'GoF:', gof, ' Max difference', np.max(np.abs(model - image[index]))
gofs.append(gof)
#save results
res = dict(wx=width_x, wy=width_y, wxerr=width_xE, wyerr=width_yE, files=files, out=out,
wavelength=wavelength, peakvalues=np.asarray(peakvalues), CCDmodel=CCD, CCDmodeldata=CCDdata,
GoFs=gofs)
fileIO.cPickleDumpDictionary(res, 'test/' + out + '.pkl')
#plot
samples = sampler.chain.reshape((-1, ndim))
#extents = None
#if simulated:
# extents = [(0.9*truth, 1.1*truth) for truth in truths]
# print extents
fig = triangle.corner(samples, labels=['x', 'y']*images + ['amplitude', 'radius', 'focus', 'width_x', 'width_y'],
truths=truths)#, extents=extents)
fig.savefig('test/' + out + 'Triangle.png')
pool.close()
def fit_2dairydisk(array,
crop=False,
cent=None,
cropsize=15,
fwhm=4,
threshold=False,
sigfactor=6,
full_output=True,
debug=True):
""" Fitting a 2D Airy to the 2D distribution of the data.
Parameters
----------
array : numpy ndarray
Input frame with a single PSF.
crop : bool, optional
If True a square sub image will be cropped equal to cropsize.
cent : tuple of int, optional
X,Y integer position of source in the array for extracting the subimage.
If None the center of the frame is used for cropping the subframe (the
PSF is assumed to be ~ at the center of the frame).
cropsize : int, optional
Size of the subimage.
fwhm : float, optional
Initial values for the FWHM of the fitted 2d Airy disk, in px.
threshold : bool, optional
If True the background pixels (estimated using sigma clipped statistics)
will be replaced by small random Gaussian noise.
sigfactor : int, optional
The background pixels will be thresholded before fitting a 2d Moffat
to the data using sigma clipped statistics. All values smaller than
(MEDIAN + sigfactor*STDDEV) will be replaced by small random Gaussian
noise.
full_output : bool, optional
If False it returns just the centroid, if True also returns the
FWHM in X and Y (in pixels), the amplitude and the rotation angle.
debug : bool, optional
If True, the function prints out parameters of the fit and plots the
data, model and residuals.
Returns
-------
mean_y : float
Source centroid y position on input array from fitting.
mean_x : float
Source centroid x position on input array from fitting.
If ``full_output`` is True it returns a Pandas dataframe containing the
following columns:
'amplitude' : Float value. Moffat Amplitude.
'centroid_x' : Float value. X coordinate of the centroid.
'centroid_y' : Float value. Y coordinate of the centroid.
'fwhm' : Float value. FHWM [px].
"""
check_array(array, dim=2, msg='array')
if crop:
if cent is None:
ceny, cenx = frame_center(array)
else:
cenx, ceny = cent
imside = array.shape[0]
psf_subimage, suby, subx = get_square(array,
min(cropsize, imside),
ceny,
cenx,
position=True)
else:
psf_subimage = array.copy()
if threshold:
_, clipmed, clipstd = sigma_clipped_stats(psf_subimage, sigma=2)
indi = np.where(psf_subimage <= clipmed + sigfactor * clipstd)
subimnoise = np.random.randn(psf_subimage.shape[0],
psf_subimage.shape[1]) * clipstd
psf_subimage[indi] = subimnoise[indi]
# Creating the 2d Airy disk model
init_amplitude = np.ptp(psf_subimage)
xcom, ycom = cen_com(psf_subimage)
diam_1st_zero = (fwhm * 2.44) / 1.028
airy = models.AiryDisk2D(amplitude=init_amplitude,
x_0=xcom,
y_0=ycom,
radius=diam_1st_zero / 2.)
# Levenberg-Marquardt algorithm
fitter = fitting.LevMarLSQFitter()
y, x = np.indices(psf_subimage.shape)
fit = fitter(airy, x, y, psf_subimage)
if crop:
mean_y = fit.y_0.value + suby
mean_x = fit.x_0.value + subx
else:
mean_y = fit.y_0.value
mean_x = fit.x_0.value
amplitude = fit.amplitude.value
radius = fit.radius.value
fwhm = ((radius * 1.028) / 2.44) * 2
# compute uncertainties
if fitter.fit_info['param_cov'] is not None:
perr = np.sqrt(np.diag(fitter.fit_info['param_cov']))
amplitude_err, mean_x_err, mean_y_err, radius_err = perr
fwhm_err = ((radius_err * 1.028) / 2.44) * 2
else:
amplitude_err, mean_x_err, mean_y_err = None, None, None
radius_err, fwhm_err = None, None
if debug:
if threshold:
label = ('Subimage thresholded', 'Model', 'Residuals')
else:
label = ('Subimage', 'Model', 'Residuals')
plot_frames((psf_subimage, fit(x, y), psf_subimage - fit(x, y)),
grid=True,
grid_spacing=1,
label=label)
print('FWHM =', fwhm)
print('centroid y =', mean_y)
print('centroid x =', mean_x)
print('centroid y subim =', fit.y_0.value)
print('centroid x subim =', fit.x_0.value, '\n')
print('amplitude =', amplitude)
print('radius =', radius)
if full_output:
return pd.DataFrame(
{
'centroid_y': mean_y,
'centroid_x': mean_x,
'fwhm': fwhm,
'radius': radius,
'amplitude': amplitude,
'centroid_y_err': mean_y_err,
'centroid_x_err': mean_x_err,
'fwhm_err': fwhm_err,
'radius_err': radius_err,
'amplitude_err': amplitude_err
},
index=[0])
else:
return mean_y, mean_x
def find_stars_wfc3ir(img_file, threshold=4, N_passes=2):
print("Working on image: ", img_file)
img = fits.getdata(img_file)
# Calculate the bacgkround and noise (iteratively)
print("\t Calculating background")
bkg_threshold = 3
for nn in range(5):
if nn == 0:
bkg_mean = img.mean()
bkg_std = img.std()
else:
bkg_mean = img[good_pix].mean()
bkg_std = img[good_pix].std()
bad_hi = bkg_mean + (bkg_threshold * bkg_std)
bad_lo = 0.0
good_pix = np.where((img < bad_hi) & (img > bad_lo))
bkg_mean = img[good_pix].mean()
bkg_std = img[good_pix].std()
img_threshold = threshold * bkg_std
print('\t Bkg = {0:.2f} +/- {1:.2f}'.format(bkg_mean, bkg_std))
print('\t Bkg Threshold = {0:.2f}'.format(img_threshold))
# Detect stars
print('\t Detecting Stars')
radius_init_guess = 1.4
# Each pass will have an updated fwhm for the PSF.
for nn in range(N_passes):
print('\t Pass {0:d} assuming FWHM = {1:.1f}'.format(nn, fwhm))
daofind = DAOStarFinder(fwhm=fwhm,
threshold=img_threshold,
exclude_border=True)
sources = daofind(img - bkg_mean)
# Calculate FWHM for each detected star.
x_fwhm = np.zeros(len(sources), dtype=float)
y_fwhm = np.zeros(len(sources), dtype=float)
theta = np.zeros(len(sources), dtype=float)
cutout_half_size = int(round(fwhm * 2))
cutout_size = 2 * cutout_half_size
cutouts = np.zeros((len(sources), cutout_size, cutout_size),
dtype=float)
g2d_model = models.AiryDisk2D(1.0, cutout_half_size, cutout_half_size,
radius_init_guess)
g2d_fitter = fitting.LevMarLSQFitter()
cut_y, cut_x = np.mgrid[:cutout_size, :cutout_size]
for ss in range(len(sources)):
x_lo = int(round(sources[ss]['xcentroid'] - cutout_half_size))
x_hi = x_lo + cutout_size
y_lo = int(round(sources[ss]['ycentroid'] - cutout_half_size))
y_hi = y_lo + cutout_size
cutout_tmp = img[y_lo:y_hi, x_lo:x_hi].astype(float)
if ((cutout_tmp.shape[0] != cutout_size) |
(cutout_tmp.shape[1] != cutout_size)):
# Edge source... fitting is no good
continue
cutouts[ss] = cutout_tmp
cutouts[ss] /= cutouts[ss].sum()
# Fit an elliptical gaussian to the cutout image.
g2d_params = g2d_fitter(g2d_model, cut_x, cut_y, cutouts[ss])
x_fwhm[ss] = g2d_params.x_stddev.value / gaussian_fwhm_to_sigma
y_fwhm[ss] = g2d_params.y_stddev.value / gaussian_fwhm_to_sigma
theta[ss] = g2d_params.theta.value
sources['x_fwhm'] = x_fwhm
sources['y_fwhm'] = y_fwhm
sources['theta'] = theta
# Drop sources with flux (signifiance) that isn't good enough.
# Empirically this is <1.2
good = np.where(sources['flux'] > 1.2)[0]
sources = sources[good]
x_fwhm_med = np.median(sources['x_fwhm'])
y_fwhm_med = np.median(sources['y_fwhm'])
print('\t Number of sources = ', len(sources))
print('\t Median x_fwhm = {0:.1f} +/- {1:.1f}'.format(
x_fwhm_med, sources['x_fwhm'].std()))
print('\t Median y_fwhm = {0:.1f} +/- {1:.1f}'.format(
y_fwhm_med, sources['y_fwhm'].std()))
fwhm = np.mean([x_fwhm_med, y_fwhm_med])
formats = {
'xcentroid': '%8.3f',
'ycentroid': '%8.3f',
'sharpness': '%.2f',
'roundness1': '%.2f',
'roundness2': '%.2f',
'peak': '%10.1f',
'flux': '%10.6f',
'mag': '%6.2f',
'x_fwhm': '%5.2f',
'y_fwhm': '%5.2f',
'theta': '%6.3f'
}
sources.write(img_file.replace('.fits', '_stars.txt'),
format='ascii.fixed_width',
delimiter=None,
bookend=False,
formats=formats)
return