# Licensed under a 3-clause BSD style license - see LICENSE.rst
"""
This module provides window (or tapering) functions for matching PSFs
using Fourier methods.
"""
import numpy as np
__all__ = ['SplitCosineBellWindow', 'HanningWindow', 'TukeyWindow',
'CosineBellWindow', 'TopHatWindow']
def _radial_distance(shape):
"""
Return an array where each value is the Euclidean distance from the
array center.
Parameters
----------
shape : tuple of int
The size of the output array along each axis.
Returns
-------
result : 2D `~numpy.ndarray`
An array containing the Euclidean radial distances from the
array center.
"""
if len(shape) != 2:
raise ValueError('shape must have only 2 elements')
position = (np.asarray(shape) - 1) / 2.0
x = np.arange(shape[1]) - position[1]
y = np.arange(shape[0]) - position[0]
xx, yy = np.meshgrid(x, y)
return np.sqrt(xx**2 + yy**2)
[docs]
class SplitCosineBellWindow:
"""
Class to define a 2D split cosine bell taper function.
Parameters
----------
alpha : float, optional
The percentage of array values that are tapered.
beta : float, optional
The inner diameter as a fraction of the array size beyond which
the taper begins. ``beta`` must be less or equal to 1.0.
Examples
--------
.. plot::
:include-source:
import matplotlib.pyplot as plt
from photutils.psf import SplitCosineBellWindow
taper = SplitCosineBellWindow(alpha=0.4, beta=0.3)
data = taper((101, 101))
plt.imshow(data, cmap='viridis', origin='lower')
plt.colorbar()
A 1D cut across the image center:
.. plot::
:include-source:
import matplotlib.pyplot as plt
from photutils.psf import SplitCosineBellWindow
taper = SplitCosineBellWindow(alpha=0.4, beta=0.3)
data = taper((101, 101))
plt.plot(data[50, :])
"""
def __init__(self, alpha, beta):
self.alpha = alpha
self.beta = beta
[docs]
def __call__(self, shape):
"""
Call self as a function to return a 2D window function of the
given shape.
Parameters
----------
shape : tuple of int
The size of the output array along each axis.
Returns
-------
result : 2D `~numpy.ndarray`
The window function as a 2D array.
"""
radial_dist = _radial_distance(shape)
npts = (np.array(shape).min() - 1.0) / 2.0
r_inner = self.beta * npts
r = radial_dist - r_inner
r_taper = int(np.floor(self.alpha * npts))
if r_taper != 0:
f = 0.5 * (1.0 + np.cos(np.pi * r / r_taper))
else:
f = np.ones(shape)
f[radial_dist < r_inner] = 1.0
r_cut = r_inner + r_taper
f[radial_dist > r_cut] = 0.0
return f
[docs]
class HanningWindow(SplitCosineBellWindow):
"""
Class to define a 2D `Hanning (or Hann) window
<https://en.wikipedia.org/wiki/Hann_function>`_ function.
The Hann window is a taper formed by using a raised cosine with ends
that touch zero.
Examples
--------
.. plot::
:include-source:
import matplotlib.pyplot as plt
from photutils.psf import HanningWindow
taper = HanningWindow()
data = taper((101, 101))
plt.imshow(data, cmap='viridis', origin='lower')
plt.colorbar()
A 1D cut across the image center:
.. plot::
:include-source:
import matplotlib.pyplot as plt
from photutils.psf import HanningWindow
taper = HanningWindow()
data = taper((101, 101))
plt.plot(data[50, :])
"""
def __init__(self):
super().__init__(alpha=1.0, beta=0.0)
[docs]
class TukeyWindow(SplitCosineBellWindow):
"""
Class to define a 2D `Tukey window
<https://en.wikipedia.org/wiki/Window_function#Tukey_window>`_
function.
The Tukey window is a taper formed by using a split cosine bell
function with ends that touch zero.
Parameters
----------
alpha : float, optional
The percentage of array values that are tapered.
Examples
--------
.. plot::
:include-source:
import matplotlib.pyplot as plt
from photutils.psf import TukeyWindow
taper = TukeyWindow(alpha=0.4)
data = taper((101, 101))
plt.imshow(data, cmap='viridis', origin='lower')
plt.colorbar()
A 1D cut across the image center:
.. plot::
:include-source:
import matplotlib.pyplot as plt
from photutils.psf import TukeyWindow
taper = TukeyWindow(alpha=0.4)
data = taper((101, 101))
plt.plot(data[50, :])
"""
def __init__(self, alpha):
super().__init__(alpha=alpha, beta=1.0 - alpha)
[docs]
class CosineBellWindow(SplitCosineBellWindow):
"""
Class to define a 2D cosine bell window function.
Parameters
----------
alpha : float, optional
The percentage of array values that are tapered.
Examples
--------
.. plot::
:include-source:
import matplotlib.pyplot as plt
from photutils.psf import CosineBellWindow
taper = CosineBellWindow(alpha=0.3)
data = taper((101, 101))
plt.imshow(data, cmap='viridis', origin='lower')
plt.colorbar()
A 1D cut across the image center:
.. plot::
:include-source:
import matplotlib.pyplot as plt
from photutils.psf import CosineBellWindow
taper = CosineBellWindow(alpha=0.3)
data = taper((101, 101))
plt.plot(data[50, :])
"""
def __init__(self, alpha):
super().__init__(alpha=alpha, beta=0.0)
[docs]
class TopHatWindow(SplitCosineBellWindow):
"""
Class to define a 2D top hat window function.
Parameters
----------
beta : float, optional
The inner diameter as a fraction of the array size beyond which
the taper begins. ``beta`` must be less or equal to 1.0.
Examples
--------
.. plot::
:include-source:
import matplotlib.pyplot as plt
from photutils.psf import TopHatWindow
taper = TopHatWindow(beta=0.4)
data = taper((101, 101))
plt.imshow(data, cmap='viridis', origin='lower',
interpolation='nearest')
plt.colorbar()
A 1D cut across the image center:
.. plot::
:include-source:
import matplotlib.pyplot as plt
from photutils.psf import TopHatWindow
taper = TopHatWindow(beta=0.4)
data = taper((101, 101))
plt.plot(data[50, :])
"""
def __init__(self, beta):
super().__init__(alpha=0.0, beta=beta)