def analytic_ft(self, unit_x, unit_y):
''' Analytic fourier transform of a pixel aperture.
Args:
unit_x (`numpy.ndarray`): sample points in x axis.
unit_y (`numpy.ndarray`): sample points in y axis.
Returns:
`numpy.ndarray`: 2D numpy array containing the analytic fourier transform.
'''
xq, yq = np.meshgrid(unit_x, unit_y)
return (sinc(xq * self.size_x / 1e3) *
sinc(yq * self.size_y / 1e3)).astype(config.precision)
def generate_mtf(pixel_aperture=1, azimuth=0, num_samples=128):
"""Generate the 1D diffraction-limited MTF for a given pixel width and azimuth.
Parameters
----------
pixel_aperture : `float`
aperture of the pixel, microns. Pixel is assumed to be square
azimuth : `float`
azimuth to retrieve the MTF at, in degrees
num_samples : `int`
number of samples in the output array
Returns
-------
frequencies : `numpy.ndarray`
unit axis, cy/mm
mtf : `numpy.ndarray`
MTF values (rel. 1.0).
Notes
-----
Azimuth is not actually implemented yet.
"""
pitch_unit = pixel_aperture / 1e3
normalized_frequencies = m.linspace(0, 2, num_samples)
otf = m.sinc(normalized_frequencies)
mtf = abs(otf)
return normalized_frequencies / pitch_unit, mtf
def analytic_ft(self, unit_x, unit_y):
"""Analytic fourier transform of a pixel aperture.
Parameters
----------
unit_x : `numpy.ndarray`
sample points in x axis
unit_y : `numpy.ndarray`
sample points in y axis
Returns
-------
`numpy.ndarray`
2D numpy array containing the analytic fourier transform
"""
xq, yq = m.meshgrid(unit_x, unit_y)
return (m.sinc(xq * self.width_x) * m.sinc(yq * self.width_y)).astype(
config.precision)
def pixelaperture_analytic_otf(width_x, width_y, freq_x, freq_y):
"""Analytic MTF of a rectangular pixel aperture.
Parameters
----------
width_x : `float`
x diameter of the pixel, in microns
width_y : `float`
y diameter of the pixel, in microns
freq_x : `numpy.ndarray`
x spatial frequency, in cycles per micron
freq_y : `numpy.ndarray`
y spatial frequency, in cycles per micron
Returns
-------
`numpy.ndarray`
MTF of the pixel aperture
"""
return m.sinc(freq_x * width_x) * m.sinc(freq_y * width_y)
def analytic_ft(self, unit_x, unit_y):
"""Analytic fourier transform of a slit.
Parameters
----------
unit_x : `numpy.ndarray`
sample points in x frequency axis
unit_y : `numpy.ndarray`
sample points in y frequency axis
Returns
-------
`numpy.ndarray`
2D numpy array containing the analytic fourier transform
"""
xq, yq = m.meshgrid(unit_x, unit_y)
if self.width_x > 0 and self.width_y > 0:
return (m.sinc(xq * self.width_x) +
m.sinc(yq * self.width_y)).astype(config.precision)
elif self.width_x > 0 and self.width_y is 0:
return m.sinc(xq * self.width_x).astype(config.precision)
else:
return m.sinc(yq * self.width_y).astype(config.precision)