minor

more examples

PyMieScatt/Mie.py

@@ -255,27 +255,6 @@ def ScatteringFunction(m, wavelength, diameter, minAngle=0, maxAngle=180, angula
     measure = (4*np.pi/wavelength)*np.sin(measure/2)*(diameter/2)
   return measure,SL,SR,SU
 
-def qSpaceScatteringFunction(m,wavelength,diameter,minAngle=0,maxAngle=180,angularResolution=0.5,normed=False):
-#  http://pymiescatt.readthedocs.io/en/latest/forward.html#qSpaceScatteringFunction
-  x = np.pi*diameter/wavelength
-  _steps = int(1+(maxAngle-minAngle)/angularResolution)
-  theta = np.logspace(np.log10(minAngle),np.log10(maxAngle),_steps)*np.pi/180
-  qR = (4*np.pi/wavelength)*np.sin(theta/2)*(diameter/2)
-  SL = np.zeros(_steps)
-  SR = np.zeros(_steps)
-  SU = np.zeros(_steps)
-  for j in range(_steps):
-    u = np.cos(theta[j])
-    S1, S2 = MieS1S2(m,x,u)
-    SL[j] = (np.sum(np.conjugate(S1)*S1)).real
-    SR[j] = (np.sum(np.conjugate(S2)*S2)).real
-    SU[j] = (SR[j]+SL[j])/2
-  if normed:
-    SL /= np.max(SL)
-    SR /= np.max(SR)
-    SU /= np.max(SU)
-  return qR,SL,SR,SU
-
 def SF_withSizeDistribution(m, wavelength, ndp, dp, minAngle=0, maxAngle=180, angularResolution=0.5, space='theta', normed=False):
 #  http://pymiescatt.readthedocs.io/en/latest/forward.html#SF_withSizeDistribution
   _steps = int(1+maxAngle/angularResolution)

PyMieScatt/__init__.py

@@ -1,6 +1,6 @@
 # A collection of forward and inverse Mie routines, q-Space analysis tools, and structure factor tools
 
-from PyMieScatt.Mie import MieQ, RayleighMieQ, LowFrequencyMieQ, Mie_withSizeDistribution, ScatteringFunction, SF_withSizeDistribution, qSpaceScatteringFunction, MatrixElements, MieQ_withDiameterRange, MieQ_withWavelengthRange, MieQ_withSizeParameterRange, Mie_Lognormal
+from PyMieScatt.Mie import MieQ, RayleighMieQ, LowFrequencyMieQ, Mie_withSizeDistribution, ScatteringFunction, SF_withSizeDistribution, MatrixElements, MieQ_withDiameterRange, MieQ_withWavelengthRange, MieQ_withSizeParameterRange, Mie_Lognormal
 from PyMieScatt.CoreShell import MieQCoreShell, CoreShellScatteringFunction, CoreShellMatrixElements
 from PyMieScatt.Inverse import GraphicalInversion, GraphicalInversion_SD, IterativeInversion, IterativeInversion_SD, Inversion, Inversion_SD
 from PyMieScatt._version import __version__

docs/examples.rst

@@ -174,4 +174,76 @@ This produces a nice video, which I'll embed here just as soon as ReadTheDocs su
 	<video width="320" height="240" controls>
 	  <source src="mir_ripples.mp4" type="video/mp4">
 	Your browser does not support the video tag.
-	</video>
+	</video>
+
+
+Angular Scattering Function of Salt Aerosol
+-------------------------------------------
+
+Recently, a colleague needed to know how much light a distribution of salt aerosol would scatter into two detectors, one at 60° and one at 90°. We modeled a lognormal distribution of NaCl particles based on laboratory measurements and then tried to figure out how much light we'd see at various angles.
+
+.. code-block:: python
+
+   import PyMieScatt as ps # import PyMieScatt and abbreviate as ps
+   import matplotlib.pyplot as plt # import standard plotting library and abbreviate as plt
+   import numpy as np # import numpy and abbreviate as np
+   from scipy.integrate import trapz # import a single function for integration using trapezoidal rule
+   
+   m = 1.536 # refractive index of NaCl
+   wavelength = 405 # replace with the laser wavelength (nm)
+   
+   dp_g = 85 # geometric mean diameter - replace with your own (nm)
+   sigma_g = 1.5 # geometric standard deviation - replace with your own (unitless)
+   N = 1e5 # total number of particles - replace with your own (cm^-3)
+   
+   B = ps.Mie_Lognormal(m,wavelength,sigma_g,dp_g,N,returnDistribution=True) # Calculate optical properties
+   
+   S = ps.SF_withSizeDistribution(m,wavelength,B[7],B[8])
+   
+   #%% Make graphs - lots of this is really unnecessary decoration for a pretty graph.
+   plt.close('all')
+   
+   fig1 = plt.figure(figsize=(10.08,6.08))
+   ax1 = fig1.add_subplot(1,1,1)
+   
+   ax1.plot(S[0],S[1],'b',ls='dashdot',lw=1,label="Parallel Polarization")
+   ax1.plot(S[0],S[2],'r',ls='dashed',lw=1,label="Perpendicular Polarization")
+   ax1.plot(S[0],S[3],'k',lw=1,label="Unpolarized")
+   
+   x_label = ["0", r"$\mathregular{\frac{\pi}{4}}$", r"$\mathregular{\frac{\pi}{2}}$",r"$\mathregular{\frac{3\pi}{4}}$",r"$\mathregular{\pi}$"]
+   x_tick = [0,np.pi/4,np.pi/2,3*np.pi/4,np.pi]
+   ax1.set_xticks(x_tick)
+   ax1.set_xticklabels(x_label,fontsize=14)
+   ax1.tick_params(which='both',direction='in')
+   ax1.set_xlabel("Scattering Angle ϴ",fontsize=16)
+   ax1.set_ylabel(r"Intensity ($\mathregular{|S|^2}$)",fontsize=16,labelpad=10)
+   handles, labels = ax1.get_legend_handles_labels()
+   fig1.legend(handles,labels,fontsize=14,ncol=3,loc=8)
+   
+   fig1.suptitle("Scattering Intensity Functions",fontsize=18)
+   fig1.show()
+   plt.tight_layout(rect=[0.01,0.05,0.915,0.95])
+   
+   # Highlight certain angles and compute integral
+   sixty = [0.96<x<1.13 for x in S[0]]
+   ninety = [1.48<x<1.67 for x in S[0]]
+   ax1.fill_between(S[0],0,S[3],where=sixty,color='g',alpha=0.15)
+   ax1.fill_between(S[0],0,S[3],where=ninety,color='g',alpha=0.15)
+   ax1.set_yscale('log')
+   
+   int_sixty = trapz(S[3][110:130],S[0][110:130])
+   int_ninety = trapz(S[3][169:191],S[0][169:191])
+   
+   # Annotate plot with integral results
+   ax1.annotate("Integrated value = {i:1.3f}".format(i=int_sixty),
+               xy=(np.pi/3, S[3][120]), xycoords='data',
+               xytext=(np.pi/6, 0.8), textcoords='data',
+               arrowprops=dict(arrowstyle="->",
+                               connectionstyle="arc3"),
+               )
+   ax1.annotate("Integrated value = {i:1.3f}".format(i=int_ninety),
+               xy=(np.pi/2, S[3][180]), xycoords='data',
+               xytext=(2*np.pi/5, 2), textcoords='data',
+               arrowprops=dict(arrowstyle="->",
+                               connectionstyle="arc3"),
+               )