xopto.pf.miepd module¶

class MiePd(nsphere: float, nmedium: float, wavelength: float, pd: Callable[[float], float], drange: Tuple[float, float], nd: int = 1000)[source]¶

Bases: xopto.pf.pfbase.PfBase

Mie scattering phase function of an arbitrary size distribution of spherical particles over the specified diameter range.

Parameters

nsphere (float, complex) – Refractive index (complex) of the spherical particles.
nmedium (float, complex) – Refractive index (complex) of the surrounding medium.
wavelength (float) – Wavelength of light (m).
drange (list) – Diameter range of the spherical particles as [dmin, dmax], where dmin and dmax stand for the minimum and maximum diameters of the spherical particles, respectively.
pd (callable(float) -> float) – Particle distribution number probability density function. Integral of pd over drange should equal 1.0.
nd (int) – Number of equally spaced control points between dmin and dmax that are used to estimate the scattering phase function. A fixed-step Simpson numerical integration is used to estimate the scattering phase function at the given scattering angle cosines. If nd is None, an adaptive-step numerical integration is used (note that the computational time might increase dramatically!!!).

Examples

Mie scattering phase function for a normal distribution of spherical particles with a mean diameter of 1 um, standard deviation of 100 nm, and refractive index of 1.6, for 550 nm monochromatic light in water surrounding (refractive index 1.33). A 7-sigma diameter range is used for numerical computations.

>>> import numpy as np
>>> from matplotlib import pyplot as pp
>>>
>>> dmean = 1e-6    # normal particle distrbution mean
>>> dsigma = 0.1e-6 # normal particle distribution standard deviation
>>> pd = lambda d: 1.0/(dsigma*np.sqrt(2*np.pi))*np.exp(-(d - dmean)**2/(2*dsigma**2))
>>> cos_theta = np.linspace(-1.0, 1.0, 1000)
>>>
>>> miepd = MiePd(1.6, 1.33, 550e-9, pd, [dmean - 7*dsigma, dmean + 7*dsigma])
>>> pf_values = miepd(cos_theta)
>>>
>>> pp.figure()
>>> pp.semilogy(cos_theta, pf_values)

acs() → float[source]¶: Returns the absorption cross section.

distribution() → Callable[[float], float][source]¶

Returns the underlying distribution object.

Returns: pd
Return type: callable(float) -> float

ecs() → float[source]¶: Returns the extinction cross section.

fastg(n: int, *args, **kwargs) → float[source]¶: Overloads the PfBase.fastg() method of the base class. .. note:: If n is 1, a precalculated g1 is returned.

g(n: int, **kwargs) → float[source]¶: Overloads the PfBase.g() method of the base class. Computes the n-th Legendre moment of the scattering phase function.

Note

If n is 1, a precalculated g1 is returned.

pd(diameter: float) → float[source]¶

Evaluates the number density function at the specified particle diameter.

Parameters: diameter (float) – Particle diameter (m).
Returns: pd – The value of number density function at the specified particle diameter.
Return type: float

scs() → float[source]¶: Returns the scattering cross section.