Initial Commit

Examples/P_q_vs_a_p.py

@@ -0,0 +1,46 @@
+"""
+Plots Mie and Rayleigh form factors at varying particle radii.
+"""
+
+from scattering import *
+import numpy as np
+import matplotlib.pyplot as plt
+
+# Default Scattering Parameters
+n_p = 2.0  # particle refractive index
+n_s = 1.332  # medium refractive index (water)
+lambda_vac = 685e-9  # wavelength of light in vacuum [meters]
+phi = 0.03  # particle volume fraction
+n_ang = 100  # number of sampled angles
+
+a_p_range = [50e-9, 100e-9, 250e-9, 500e-9, 1000e-9]  # particle radii [meters]
+p_q = np.empty(shape=(n_ang, np.size(a_p_range), 2))  # initialize result array
+
+# Collect Scattering Data
+for i in range(np.size(a_p_range)):
+    _, _, _, _, [q, p_q[:, i, 0], _, _, _, _, _, _] = \
+        mie_scattering(n_p, n_s, a_p_range[i], lambda_vac, phi, n_ang=n_ang, struct='PY')
+    _, _, _, _, [_, p_q[:, i, 1], _, _] = \
+        rayleigh_scattering(n_p, n_s, a_p_range[i], lambda_vac, phi, n_ang=n_ang)
+
+# Generate Colors
+colormap = plt.get_cmap('plasma')
+c = np.empty(shape=(np.size(a_p_range), 3))
+for i in range(np.size(a_p_range)):
+    c[i, :] = colormap.colors[round(256 * i / np.size(a_p_range))]
+
+# Plot
+fig, ax1 = plt.subplots()
+for i in range(np.size(a_p_range)):
+    if i == 0:
+        ax1.plot(q, p_q[:, i, 0] / p_q[0, i, 0], label=r'Mie, $a_p$ = %i nm' % (a_p_range[i] * 1e9), c=c[i])
+        ax1.plot(q, p_q[:, i, 1] / p_q[0, i, 1], linestyle='--',
+                 label=r'Rayleigh, $a_p$ = %i nm' % (a_p_range[i] * 1e9), c=c[i])
+    else:
+        ax1.plot(q, p_q[:, i, 0] / p_q[0, i, 0], label=r'$a_p$ = %i nm' % (a_p_range[i] * 1e9), c=c[i])
+        ax1.plot(q, p_q[:, i, 1] / p_q[0, i, 1], linestyle='--', c=c[i])
+ax1.set(xlabel='q', ylabel='Normalized P(q)', title=r'$n_p$ = %.3f, $n_s$ = %.3f, $\lambda$ = %i nm, $\phi$ = %.2f' % (n_p, n_s, lambda_vac*1e9, phi))
+ax1.legend(loc='upper right')
+ax1.set(ylim=[-0.05, 1.1])
+plt.show()
+

Examples/S_q_models.py

@@ -0,0 +1,38 @@
+"""
+Plots various structure factor models.
+"""
+
+from scattering import *
+import numpy as np
+import matplotlib.pyplot as plt
+
+# Default Scattering Parameters
+a_p = 200e-9  # meters
+n_p = 1.5  # particle refractive index
+n_s = 1.332  # medium refractive index (water)
+lambda_vac = 685e-9  # wavelength of light in vacuum [meters]
+phi = 0.03  # particle volume fraction
+n_ang = 100  # number of sampled angles
+
+s_q = np.empty(shape=(n_ang, 3))  # initialize result array
+
+# Collect Scattering Data
+_, _, _, _, [q, _, s_q[:, 0], _, _, _, _, _] = mie_scattering(n_p, n_s, a_p, lambda_vac, phi, n_ang=n_ang,
+                                                              struct='PY')
+_, _, _, _, [_, _, s_q[:, 1], _, _, _, _, _] = mie_scattering(n_p, n_s, a_p, lambda_vac, phi, n_ang=n_ang,
+                                                              struct='PYAnnulus', optional_params=[1.2*a_p])
+_, _, _, _, [_, _, s_q[:, 2], _, _, _, _, _] = mie_scattering(n_p, n_s, a_p, lambda_vac, phi, n_ang=n_ang,
+                                                              struct='SHS', optional_params=[0.2, 0.05])
+
+# Plot
+fig, ax1 = plt.subplots()
+ax1.plot(q, np.ones_like(s_q[:, 0]), 'k', label='No Interaction', linewidth=2)
+ax1.plot(q, s_q[:, 0], 'k-.', label='Hard Sphere', linewidth=2)
+ax1.plot(q, s_q[:, 1], 'k:', label='1.2$a_p$ Excluded Annulus', linewidth=2)
+ax1.plot(q, s_q[:, 2], 'k--', label='Sticky Hard Sphere', linewidth=2)
+ax1.set(xlabel=r'$q$', ylabel='S(q)',
+        title=r'$n_p$ = %.3f, $n_s$ = %.3f, $a_p$ = %i nm, $\lambda$ = %i nm, $\phi$ = %.2f'
+              % (n_p, n_s, a_p*1e9, lambda_vac*1e9, phi))
+ax1.legend()
+
+plt.show()

Examples/intensity_plot.py

@@ -0,0 +1,56 @@
+"""
+Plots Mie intensities and form factor versus scattering angle.
+"""
+
+from scattering import *
+import matplotlib.pyplot as plt
+
+# Default Scattering Parameters
+a_p = 500e-9  # # particle radius [meters]
+n_p = 1.5  # particle refractive index
+n_s = 1.0  # medium refractive index
+lambda_vac = 685e-9  # wavelength of light in vacuum [meters]
+phi = 0.03  # particle volume fraction
+n_ang = 100  # number of sampled angles
+
+# Collect Data
+theta, i1, i2, _, _ \
+    = mie_scattering(n_p, n_s, a_p, lambda_vac, phi)
+_, i1r, i2r, _, _ \
+    = rayleigh_scattering(n_p, n_s, a_p, lambda_vac, phi)
+theta = np.append(theta, np.pi + theta)
+i1 = np.append(i1, i1[::-1])
+i2 = np.append(i2, i2[::-1])
+i1r = np.append(i1r, i1r[::-1])
+i2r = np.append(i2r, i2r[::-1])
+
+# Generate Colors
+n_colors = 3
+colormap = plt.get_cmap('plasma')
+c = np.empty(shape=(n_colors, 3))
+for i in range(n_colors):
+    c[i, :] = colormap.colors[round(256 * i / n_colors)]
+
+# Plot
+fig, (ax1, ax2) = plt.subplots(1, 2, subplot_kw=dict(projection='polar'))
+ax1.plot(theta, i1, label='Perpendicular Mie', c=c[0])
+ax1.plot(theta, i2, label='Parallel Mie', c=c[2])
+ax1.plot(theta, 0.5*(i1+i2), label='Mie P(q)', c=c[1])
+# ax1.plot(theta, i1r, label='Perpendicular Rayleigh', c=c[0], linestyle='--')
+# ax1.plot(theta, i2r, label='Parallel Rayleigh', c=c[2], linestyle='--')
+# ax1.plot(theta, 0.5*(i1r+i2r), label='Rayleigh P(q)', c=c[1], linestyle='--')
+ax1.set_title("Intensity")
+ax1.legend()
+
+ax2.plot(theta, np.log10(i1 + 1), label='Perpendicular Mie', c=c[0])
+ax2.plot(theta, np.log10(i2 + 1), label='Parallel Mie', c=c[2])
+ax2.plot(theta, np.log10(0.5*(i1+i2) + 1), label='Mie P(q)', c=c[1])
+# ax2.plot(theta, np.log10(i1r + 1), label='Perpendicular Rayleigh', c=c[0], linestyle='--')
+# ax2.plot(theta, np.log10(i2r + 1), label='Parallel Rayleigh', c=c[2], linestyle='--')
+# ax2.plot(theta, np.log10(0.5*(i1r+i2r) + 1), label='Rayleigh P(q)', c=c[1], linestyle='--')
+ax2.set_title("Log Intensity")
+ax2.legend()
+
+plt.suptitle(r'$n_p$ = %.3f, $n_s$ = %.3f, $a_p$ = %i nm, $\lambda$ = %i nm, $\phi$ = %.2f'
+             % (n_p, n_s, a_p*1e9, lambda_vac*1e9, phi))
+plt.show()

Examples/mie_vs_rayleigh.py

@@ -0,0 +1,58 @@
+"""
+Plots l* for varying input parameters for both Mie and Rayleigh scattering.
+"""
+
+from scattering import *
+import numpy as np
+import matplotlib.pyplot as plt
+
+# Default Scattering Parameters
+n_p = 1.8  # particle refractive index
+n_s = 1.332  # medium refractive index (water)
+a_p = 250e-9  # particle radii [meters]
+lambda_vac = 685e-9  # wavelength of light in vacuum [meters]
+phi = 0.03  # particle volume fraction
+
+# Generate Parameter Ranges
+n_range = 100  # number of data points between values
+phi_range = np.linspace(0.01, 0.15, n_range)
+a_p_range = np.linspace(150e-9/2, 1000e-9/2, n_range)
+n_p_range = np.linspace(1.6, 2, n_range)
+
+# Initialize Result Array
+l_star = np.empty(shape=(n_range, 3, 2))
+
+# Collect Scattering Data
+for i in range(n_range):
+    _, _, _, l_star[i, 0, 0], _ \
+        = mie_scattering(n_p, n_s, a_p, lambda_vac, phi_range[i])
+    _, _, _, l_star[i, 1, 0], _ \
+        = mie_scattering(n_p, n_s, a_p_range[i], lambda_vac, phi)
+    _, _, _, l_star[i, 2, 0], _ \
+        = mie_scattering(n_p_range[i], n_s, a_p, lambda_vac, phi)
+
+    _, _, _, l_star[i, 0, 1], _ \
+        = rayleigh_scattering(n_p, n_s, a_p, lambda_vac, phi_range[i])
+    _, _, _, l_star[i, 1, 1], _ \
+        = rayleigh_scattering(n_p, n_s, a_p_range[i], lambda_vac, phi)
+    _, _, _, l_star[i, 2, 1], _ \
+        = rayleigh_scattering(n_p_range[i], n_s, a_p, lambda_vac, phi)
+
+# Plot Data
+fig, (ax1, ax2, ax3) = plt.subplots(1, 3)
+ax1.plot(phi_range, l_star[:, 0, 0]*1e6, 'k', label='Mie', linewidth=2)
+ax1.plot(phi_range, l_star[:, 0, 1]*1e6, 'k--', label='Rayleigh', linewidth=2)
+ax1.legend()
+ax1.set(xlabel=r'$\phi$', ylabel='l* [µm]')
+
+ax2.plot(a_p_range*1e9, l_star[:, 1, 0]*1e6, 'k', label='Mie', linewidth=2)
+ax2.plot(a_p_range*1e9, l_star[:, 1, 1]*1e6, 'k--', label='Rayleigh', linewidth=2)
+ax2.set(xlabel=r'$a_p$ [nm]')
+
+ax3.plot(n_p_range, l_star[:, 2, 0]*1e6, 'k', label='Mie', linewidth=2)
+ax3.plot(n_p_range, l_star[:, 2, 1]*1e6, 'k--', label='Rayleigh', linewidth=2)
+ax3.set(xlabel=r'$n_p$')
+
+# title with default parameters listed
+plt.suptitle(r'$n_p$ = %.3f, $n_s$ = %.3f, $a_p$ = %i nm, $\lambda$ = %i nm, $\phi$ = %.2f' % (n_p, n_s, a_p*1e9, lambda_vac*1e9, phi))
+plt.show()

Examples/silica_data_fit.py

@@ -0,0 +1,55 @@
+"""
+Generates l* values versus particle volume concentration for silica particles with varying form factor models.
+Plots model versus experimental data (courtesy of Qi Li).
+"""
+
+from scattering import *
+import numpy as np
+import matplotlib.pyplot as plt
+
+# Scattering Parameters
+n_p = 1.446  # particle refractive index (silica)
+n_s = 1.332  # medium refractive index (water)
+a_p = 345e-9/2  # particle radii [meters]
+lambda_vac = 685e-9  # wavelength of light in vacuum [meters]
+
+# Generate Parameter Range
+n_range = 100  # number of data points between values
+phi_range = np.linspace(0.03, 0.15, n_range)
+
+# Initialize Result Array
+l_star_phi = np.empty(shape=(n_range, 4))
+
+# Silica Data (courtesy of Qi Li)
+silica_data = np.array([[0.065, 0.067, 0.069, 0.072, 0.075, 0.135],
+                        [0.000230, 0.000225, 0.000216, 0.000215, 0.000205, 0.000130]])
+
+# Collect Scattering Data
+for i in range(n_range):
+    _, _, _,  l_star_phi[i, 0], _ \
+        = mie_scattering(n_p, n_s, a_p, lambda_vac, phi_range[i])
+    _, _, _, l_star_phi[i, 1], _ \
+        = mie_scattering(n_p, n_s, a_p, lambda_vac, phi_range[i], struct='PY')
+    _, _, _, l_star_phi[i, 2], _ \
+        = mie_scattering(n_p, n_s, a_p, lambda_vac, phi_range[i], struct='SHS', optional_params=[0.2, 0.05])
+    _, _, _, l_star_phi[i, 3], _ \
+        = mie_scattering(n_p, n_s, a_p, lambda_vac, phi_range[i], struct='PYAnnulus', optional_params=[1.2*a_p])
+
+# Generate Colors
+n_colors = 4
+colormap = plt.get_cmap('plasma')
+c = np.empty(shape=(n_colors, 3))
+for i in range(n_colors):
+    c[i, :] = colormap.colors[round(256 * i / n_colors)]
+
+# Plot Data
+fig, ax1 = plt.subplots()
+ax1.plot(phi_range, l_star_phi[:, 0]*1e6, label='No Interactions', linewidth=2, c=c[0])
+ax1.plot(phi_range, l_star_phi[:, 1]*1e6, linestyle='--', label='Hard Sphere', linewidth=2, c=c[1])
+ax1.plot(phi_range, l_star_phi[:, 2]*1e6, linestyle=':', label='Sticky Hard Sphere', linewidth=2, c=c[2])
+ax1.plot(phi_range, l_star_phi[:, 3]*1e6, linestyle='-.', label='1.2$a_p$ Excluded Annulus', linewidth=2, c=c[3])
+ax1.plot(silica_data[0, :], silica_data[1, :]*1e6, 'k.', label='Silica Data', markersize=10)
+ax1.legend()
+ax1.set(xlabel=r'$\phi$', ylabel='l* [µm]')
+
+plt.show()