add SFT electromagnetic model

smrt/emmodel/sft_rayleigh.py

@@ -0,0 +1,50 @@
+# coding: utf-8
+
+""" Compute Strong Fluctuation Theory scattering. This theory requires the scatterers to be smaller than the wavelength
+
+This model is only compatible with the Exponential autocorrelation function only
+
+"""
+
+import numpy as np
+
+from ..core.error import SMRTError
+from ..core.globalconstants import C_SPEED
+from .effective_permittivity import polder_van_santen
+from .rayleigh import Rayleigh
+
+class SFT_Rayleigh(Rayleigh):
+    """
+    """
+    def __init__(self, sensor, layer):
+
+        # check here the limit of the Rayleigh model
+
+        f = layer.frac_volume
+
+        eb = layer.permittivity(0, sensor.frequency)  # background permittivity
+        es = layer.permittivity(1, sensor.frequency)  # scatterer permittivity
+        e0 = 1  # always
+
+        lmda = C_SPEED / sensor.frequency
+        k0 = 2 * np.pi / lmda * np.sqrt(e0)
+
+        corr_length = layer.microstructure.corr_length
+
+        eg = polder_van_santen(f, eb, es)
+        kg = k0 * np.sqrt(eg/e0)
+
+        delta = 9 * eg**2/e0**2 * (f * ((es-eg)/(es+2*eg))**2 + (1-f) * ((eb-eg)/(eb+2*eg))**2 )
+
+        beta = 1/corr_length - 1j * kg
+
+        I1 = 1/(beta**2 + kg**2)
+        I2 = -3.0/2*beta/kg**2 + 1.0/(2*kg)*(3*beta**2 / kg**2+1) * np.arctan(kg/beta)
+        I3 = 3/kg**2 - 1/(beta**2+kg**2) - 3*beta / kg**3 * np.arctan(kg/beta)
+        I4 = 1.0/3 + beta**2/(2*kg**2) - beta/(2*kg) * (beta**2/kg**2 + 1) * np.arctan(kg/beta)
+
+        Eeff = eg + k0**2 * delta * (2*I1/3 - 1j*I2/kg - I3/3 + I4/(k0**2 * eg))
+
+        self.ka = 2 * k0 * np.sqrt(eg).imag
+        self.ks = 2 * k0 * np.sqrt(Eeff).imag - self.ka
+