This example uses tmm and colorpy package to calculate the surface of stacked layers.
Note that tmm and colorpy packages are slightly altered from their original version. To successfully run this script, you have to download them from the following github repo:
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from __future__ import division, print_function, absolute_import
In [2]:
%load_ext autoreload
%autoreload 2
from pypvcell.tmm_core import (coh_tmm, unpolarized_RT, ellips, absorp_in_each_layer,
position_resolved, find_in_structure_with_inf)
from numpy import pi, linspace, inf, array
import numpy as np
from scipy.interpolate import interp1d
import matplotlib.pyplot as plt
from pypvcell.transfer_matrix_optics import get_ntotal_fn
%matplotlib inline
In [3]:
try:
import colorpy.illuminants
import colorpy.colormodels
import colorpy.plots
from pypvcell import color
colors_were_imported = True
except ImportError:
# without colorpy, you can't run sample5(), but everything else is fine.
colors_were_imported = False
# "5 * degree" is 5 degrees expressed in radians
# "1.2 / degree" is 1.2 radians expressed in degrees
degree = pi/180
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import colorpy.illuminants
import colorpy.colormodels
import colorpy.plots
In [5]:
if not colors_were_imported:
print('Colorpy was not detected (or perhaps an error occurred when',
'loading it). You cannot do color calculations, sorry!',
'http://pypi.python.org/pypi/colorpy')
else:
print("Colorpy is successfully installed.")
In [6]:
from pypvcell import color
In [7]:
def hsvc_from_rgb(rgb):
r=rgb[0]
g=rgb[1]
b=rgb[2]
arg_M=np.argmax(rgb)
arg_m=np.argmin(rgb)
M=rgb[arg_M]
m=rgb[arg_m]
C=M-m
if C==0:
H=np.nan
elif arg_M==0:
H=np.mod(float(g-b)/float(C),6.0)
elif arg_M==1:
H=float(b-r)/float(C)+2
elif arg_M==2:
H=float(r-g)/float(C)+4
H*=60
V=M
if V==0:
S=0
else:
S=C/V
return np.array([H,S,V,C])
def chroma_from_irgb(irgb):
rgb=colorpy.colormodels.rgb_from_irgb(irgb)
arg_M=np.argmax(rgb)
arg_m=np.argmin(rgb)
M=rgb[arg_M]
m=rgb[arg_m]
C=M-m
return C
def hue_from_irgb(irgb):
return hsvc_from_rgb(irgb)[0]
Color calculations: What color is a air / thin SiO2 / Si wafer?
In [8]:
%%time
# Crystalline silicon refractive index. Data from Palik via
# http://refractiveindex.info, I haven't checked it, but this is just for
# demonstration purposes anyway.
Si_n_fn = get_ntotal_fn('Si')
# SiO2 refractive index (approximate): 1.46 regardless of wavelength
SiO2_n_fn = get_ntotal_fn('SiO2_2')
TiO2_n_fn=get_ntotal_fn("TiO2_2")
aSi_n_fn=get_ntotal_fn("Si")
# air refractive index
air_n_fn = get_ntotal_fn("Air")
n_fn_list = [air_n_fn, SiO2_n_fn, TiO2_n_fn, Si_n_fn]
d_list = [inf, 200, 50, inf]
th_0 = 0
# Print the colors, and show plots, for the special case of 300nm-thick SiO2
reflectances = color.calc_reflectances(n_fn_list, d_list, th_0)
illuminant = colorpy.illuminants.get_illuminant_D65()
spectrum = color.calc_spectrum(reflectances, illuminant)
color_dict = color.calc_color(spectrum)
print('air / 300nm SiO2 / Si --- rgb =', color_dict['rgb'], ', xyY =', color_dict['xyY'])
plt.figure()
color.plot_reflectances(reflectances,
title='air / 300nm SiO2 / Si -- '
'Fraction reflected at each wavelength')
plt.figure()
color.plot_spectrum(spectrum,
title='air / 300nm SiO2 / Si -- '
'Reflected spectrum under D65 illumination')
In [9]:
Si_n_fn(500)
Out[9]:
In [10]:
plt.plot(reflectances[:,0],reflectances[:,1])
Out[10]:
In [11]:
lam_vac_arr=np.linspace(500,800,5)
for lam_vac in lam_vac_arr:
n_list = [np.asscalar(n_fn_list[i](lam_vac)) for i in range(len(n_fn_list))]
coh_data=coh_tmm('s',n_list,d_list,th_0,lam_vac)
zx=np.linspace(-50,1000,100)
z_response=np.ones_like(zx)
for i in range(zx.shape[0]):
d_layer,d=find_in_structure_with_inf(d_list,zx[i])
za=position_resolved(d_layer,d,coh_data)['absor']
z_response[i]=za
plt.plot(zx,z_response,label="wl=%s"%lam_vac)
plt.legend()
plt.xlabel("depth from sample surface (nm)")
plt.ylabel("absorption")
plt.show()
In [12]:
lam_vac_arr=np.linspace(500,1000,30)
abs_si=[]
index_of_si_layer=3
for lam_vac in lam_vac_arr:
n_list = [np.asscalar(n_fn_list[i](lam_vac)) for i in range(len(n_fn_list))]
coh_data=coh_tmm('s',n_list,d_list,th_0,lam_vac)
result=absorp_in_each_layer(coh_data)
abs_si.append(result[index_of_si_layer])
plt.plot(lam_vac_arr,abs_si)
plt.xlabel("wavelength (nm)")
plt.ylabel("total absorption in Si layer")
plt.title("absorption in silicon layer")
plt.show()
In [20]:
%%time
# Calculate irgb color (i.e. gamma-corrected sRGB display color rounded to
# integers 0-255) versus thickness of SiO2
max_SiO2_thickness = 300
SiO2_thickness_list = linspace(0,max_SiO2_thickness,num=80)
irgb_list = []
n_fn_list_2 = [air_n_fn, SiO2_n_fn, Si_n_fn]
for SiO2_d in SiO2_thickness_list:
d_list = [inf, SiO2_d ,inf]
reflectances_p = color.calc_reflectances(n_fn_list_2, d_list, th_0,pol='p')
reflectances_s = color.calc_reflectances(n_fn_list_2, d_list, th_0,pol='s')
reflectances_unp=(reflectances_p+reflectances_s)/2
reflectances_unp[:,0]=reflectances_p[:,0]
illuminant = colorpy.illuminants.get_illuminant_D65()
spectrum = color.calc_spectrum(reflectances_unp, illuminant)
color_dict = color.calc_color(spectrum)
irgb_list.append(colorpy.colormodels.irgb_string_from_irgb(color_dict['irgb']))
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# Plot those colors
print('Making color vs SiO2 thickness graph. Compare to (for example)')
print('http://www.htelabs.com/appnotes/sio2_color_chart_thermal_silicon_dioxide.htm')
colorpy.plots.color_tile_vs_1param_plot(SiO2_thickness_list,irgb_list,
xlabel_name="SiO2 thickness (nm)",
title_name="Air/SiO2/Si (nm)")
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%%time
# Calculate irgb color (i.e. gamma-corrected sRGB display color rounded to
# integers 0-255) versus thickness of SiO2
max_inc_angle = 80
max_d=150
inc_angle = linspace(0,max_inc_angle,num=10)
SiO2_d_list=linspace(0,max_d,num=10)
irgb_list =[]
for i,ang in enumerate(inc_angle):
for j,SiO2_d in enumerate(SiO2_d_list):
d_list = [inf, SiO2_d, 50, inf]
reflectances = color.calc_reflectances(n_fn_list, d_list, ang/180*pi)
illuminant = colorpy.illuminants.get_illuminant_D65()
spectrum = color.calc_spectrum(reflectances, illuminant)
color_dict = color.calc_color(spectrum)
color_string = colorpy.colormodels.irgb_string_from_irgb(color_dict['irgb'])
irgb_list.append(color_string)
colorpy.plots.color_tile_vs_2param_plot(inc_angle,SiO2_d_list,irgb_list,
xlabel_name="incident angle (pol-s)",
ylabel_name="SiO2 thickness (nm)",
title_name="Air/SiO2/Si color")
plt.tight_layout()
plt.savefig("color_tiles_demo.pdf")
plt.show()
In [15]:
%%time
# Calculate irgb color (i.e. gamma-corrected sRGB display color rounded to
# integers 0-255) versus thickness of SiO2
max_inc_angle = 80
max_d=150
inc_angle = linspace(0,max_inc_angle,num=10)
SiO2_d_list=linspace(0,max_d,num=15)
TiO2_d_list=linspace(0,max_d,num=15)
irgb_list =[]
for i,TiO2_d in enumerate(TiO2_d_list):
for j,SiO2_d in enumerate(SiO2_d_list):
d_list = [inf, SiO2_d, TiO2_d,inf]
reflectances = color.calc_reflectances(n_fn_list, d_list, 0/180*pi)
illuminant = colorpy.illuminants.get_illuminant_D65()
spectrum = color.calc_spectrum(reflectances, illuminant)
color_dict = color.calc_color(spectrum)
color_string = colorpy.colormodels.irgb_string_from_irgb(color_dict['irgb'])
irgb_list.append(color_string)
colorpy.plots.color_tile_vs_2param_plot(TiO2_d_list,SiO2_d_list,irgb_list,
xlabel_name="TiO2 thickness (nm)",
ylabel_name="SiO2 thickness (nm)",
title_name="Air/SiO2/TiO2/Si color")
plt.savefig("color_tiles_demo.png")
In [16]:
# convert the color string to hsv values
rgb_list=list(map(colorpy.colormodels.irgb_from_irgb_string,irgb_list))
chroma_list=list(map(chroma_from_irgb,rgb_list))
chroma_list=np.reshape(chroma_list,(TiO2_d_list.shape[0],SiO2_d_list.shape[0]))
plt.pcolormesh(TiO2_d_list,SiO2_d_list,chroma_list.T)
plt.colorbar()
plt.title("Air/SiO2/TiO2/Si Chroma")
plt.xlabel("TiO2 thicknesses (nm)")
plt.ylabel("SiO2 thicknesses (nm)")
plt.tight_layout()
plt.savefig("chroma.pdf")
plt.show()
In [17]:
# convert the color string to hsv values
rgb_list=list(map(colorpy.colormodels.irgb_from_irgb_string,irgb_list))
hue_list=list(map(hue_from_irgb,rgb_list))
hue_list=np.reshape(hue_list,(TiO2_d_list.shape[0],SiO2_d_list.shape[0]))
plt.pcolormesh(TiO2_d_list,SiO2_d_list,hue_list.T,cmap='hsv',vmin=0,vmax=360)
plt.colorbar()
plt.title("Air/SiO2/TiO2/Si Hue")
plt.xlabel("TiO2 thicknesses (nm)")
plt.ylabel("SiO2 thicknesses (nm)")
plt.tight_layout()
plt.savefig("hue.pdf")
plt.show()
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