#!/usr/bin/env python
# coding: utf-8

# # Blackbody

# A [blackbody](http://en.wikipedia.org/wiki/Black_body) or *planckian radiator* is an ideal thermal radiator that absorbs completely all incident radiation, whatever the wavelength, the direction of incidence or the polarization. <a name="back_reference_1"></a><a href="#reference_1">[1]</a>
# 
# A *blackbody* in [thermal equilibrium](http://en.wikipedia.org/wiki/Thermal_equilibrium) emits electromagnetic radiation called [blackbody radiation](http://en.wikipedia.org/wiki/Black-body_radiation).

# ## Planck's Law

# The spectral radiance of a blackbody at thermodynamic temperature $T [K]$ in a medium having index of refraction $n$ is given by the [Planck's law](http://en.wikipedia.org/wiki/Planck%27s_law) equation: <a name="back_reference_2"></a><a href="#reference_2">[2]</a>
# 
# $$
# \begin{equation}
# L_{e\lambda}(\lambda,T)=\cfrac{C_1n^{-2}\lambda^{-5}}{\pi}{\Biggl[\exp\biggl(\cfrac{C_2}{n\lambda T}\biggr)-1\Biggr]^{-1}}
# \end{equation}
# $$
# where
# $$
# \begin{equation}
# \begin{aligned}
# C_1&=2\pi hc^2\\
# C_2&=\cfrac{hc}{k}
# \end{aligned}
# \end{equation}
# $$
# 
# $h$ is Planck's constant, $c$ is the speed of light in vacuum, $k$ is the Boltzmann constant and $\lambda$ is the wavelength.
# 
# As per *CIE 015:2004 Colorimetry, 3rd Edition* recommendation $C_2$ value when used in colorimetry should be $C_2= 1,4388x10^{-2}mK$ as defined by the International Temperature Scale (ITS-90).
# 
# $C_1$ value is given by the Committee on Data for Science and Technology (CODATA) and should be $C_1=3,741771x10^{16}Wm^2$.
# 
# In the current *CIE 015:2004 Colorimetry, 3rd Edition* recommendation, colour temperature and correlated colour temperature are calculated with $n=1$.
# 
# [Colour](https://github.com/colour-science/colour/) implements various *blackbody* computation related objects in the `colour.colorimetry` sub-package:

# In[1]:


import colour.colorimetry


# > Note: `colour.colorimetry` package public API is also available from the `colour` namespace.

# The *Planck's law* is called using either the `colour.planck_law` or `colour.blackbody_spectral_radiance` definitions, they are expecting the wavelength $\lambda$ to be given in nanometers and the temperature $T$ to be given in degree kelvin:

# In[2]:


import colour

colour.colorimetry.planck_law(500 * 1e-9, 5500)


# Generating the spectral distribution of a *blackbody* is done using the `colour.sd_blackbody` definition:

# In[3]:


with colour.utilities.suppress_warnings(python_warnings=True):
    colour.sd_blackbody(6500, colour.SpectralShape(0, 10000, 10))


# With its temperature lowering, the blackbody peak shifts to longer wavelengths while its intensity decreases:

# In[4]:


from colour.plotting import *


# In[5]:


colour_style();


# In[6]:


# Plotting various *blackbodies* spectral distributions.
blackbodies_sds = [colour.sd_blackbody(i, colour.SpectralShape(0, 10000, 10)) 
                   for i in range(1000, 15000, 1000)]
with colour.utilities.suppress_warnings(python_warnings=True):
    plot_multi_sds(blackbodies_sds,
                   y_label='W / (sr m$^2$) / m',
                   use_sds_colours=True,
                   normalise_sds_colours=True,
                   legend_location='upper right',
                   bounding_box=[0, 1000, 0, 2.25e15]);


# Let's plot the blackbody colours from temperature in domain [150, 12500, 50]:

# In[7]:


plot_blackbody_colours(colour.SpectralShape(500, 12500, 50));


# ## Stars Colour

# Let's compare the extraterrestrial solar spectral irradiance to the blackbody spectral radiance of a thermal radiator with a temperature of 5778 K:

# In[8]:


# Comparing theoretical and measured *Sun* spectral distributions.
# Arbitrary ASTMG173_ETR scaling factor calculated with
# :def:`colour.sd_to_XYZ` definition.
ASTMG173_sd = ASTMG173_ETR.copy() * 1.37905559e+13

blackbody_sd = colour.sd_blackbody(
    5778,
    ASTMG173_sd.shape)
blackbody_sd.name = 'The Sun - 5778K'

plot_multi_sds([ASTMG173_sd, blackbody_sd],
               y_label='W / (sr m$^2$) / m',
               legend_location='upper right');


# As you can see the *Sun* spectral distribution is very close to the one from a blackbody at similar temperature $T$.
# 
# Calculating theoritical colour of any star is possible, for example the [VY Canis Majoris](http://en.wikipedia.org/wiki/VY_Canis_Majoris) red hypergiant in the constellation *Canis Major*.

# In[9]:


plot_blackbody_spectral_radiance(temperature=3500, blackbody='VY Canis Majoris');


# Or [Rigel](http://en.wikipedia.org/wiki/Rigel) the brightest star in the constellation *Orion* and the seventh brightest star in the night sky.

# In[10]:


plot_blackbody_spectral_radiance(temperature=12130, blackbody='Rigel');


# And finally the [Sun](http://en.wikipedia.org/wiki/Sun), our star:

# In[11]:


plot_blackbody_spectral_radiance(temperature=5778, blackbody='The Sun');


# ## Bibliography

# 1. <a href="#back_reference_1">^<a> <a name="reference_1"></a>CIE. (n.d.). 17-960 Planckian radiator. Retrieved June 26, 2014, from http://eilv.cie.co.at/term/960
# 2. <a href="#back_reference_2">^<a> <a name="reference_2"></a>CIE TC 1-48. (2004). APPENDIX E. INFORMATION ON THE USE OF PLANCK’S EQUATION FOR STANDARD AIR. In *CIE 015:2004 Colorimetry, 3rd Edition* (pp. 77–82). ISBN:978-3-901-90633-6