# -*- coding: utf-8 -*-
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from typing import Callable
import numpy as np
from .pfbase import PfBase
from .miepd import MiePd
from .distribution import Normal
[docs]class MieNormal(MiePd):
def __init__(self, center: float, sigma: float,
nsphere: float or complex,
nmedium: float or complex,
wavelength: float,
clip: float = 5, nd: int = 100):
'''
Scattering phase function of Normally distributed (number density)
spherical particles:
.. math::
p(d) = A e^{\\frac{-(d - center)^2}{2\\sigma^2}}
The value of parameter :math:`A` is computed so as to normalize the
integral of the density function on the clipped diameter interval
:math:`[center - \\sigma clip, center + \\sigma clip]` to 1:
Parameters
----------
center: float
Distribution/diameter mean (m).
sigma: float
Distribution/diameter standard deviation (m).
nsphere, nmedium, nd:
Parameters passed to the :py:meth:`xopto.pf.miepd.MiePd`
base class constructor.
See help of :py:class:`xopto.pf.miepd.MiePd` class for more details.
clip: float
Distribution/diameter range used to estimate the phase function
defined as :math:`[center - clip \\sigma, center + clip \\sigma]`.
Examples
--------
Scattering phase functions of Normally distributed microspherical
particles with a mean diameter of 1 um and a standard deviation of
100 nm, a mean diameter of 1 um and standard deviation of 50 nm, and
a mean diameter of 1 um and a standard deviation of 25 nm compared to
a monodisperse 1 um microspherical particles.
>>> from matplotlib import pyplot as pp
>>> import numpy as np
>>>
>>> cos_theta = np.linspace(-1.0, 1.0, 1000)
>>> nmie1 = MieNormal(1e-6, 0.1e-6, nsphere=1.6, nmedium=1.33, wavelength=550e-9, nd=1000)
>>> nmie2 = MieNormal(1e-6, 0.05e-6, nsphere=1.6, nmedium=1.33, wavelength=550e-9, nd=1000)
>>> nmie3 = MieNormal(1e-6, 0.025e-6, nsphere=1.6, nmedium=1.33, wavelength=550e-9, nd=1000)
>>> mmie = Mie(nsphere=1.6, nmedium=1.33, diameter=1e-6, wavelength=550e-9)
>>>
>>> pp.figure()
>>> pp.semilogy(costheta, nmie1(cos_theta), label='Normal(1 um, 100 nm)')
>>> pp.semilogy(costheta, nmie2(cos_theta), label='Normal(1 um, 50 nm)')
>>> pp.semilogy(costheta, nmie3(cos_theta), label='Normal(1 um, 25 nm)')
>>> pp.semilogy(costheta, mmie(cos_theta), label='Monodisperse(1 um)')
>>> pp.legend()
>>>
'''
self._center = float(center)
self._sigma = float(sigma)
self._clip = float(clip)
self._kwargs = {'nsphere':nsphere, 'nmedium':nmedium,
'wavelength':wavelength, 'nd':nd}
pd = Normal(center, sigma, clip)
super().__init__(pd=pd, drange=pd.range, **self._kwargs)
def __repr__(self):
return 'MieNormal(center={}, sigma={}, clip={}, **{})'.format(
self._center, self._sigma, self._clip, self._kwargs)