Source code for colour.colorimetry.blackbody

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

"""
Blackbody - Planckian Radiator
==============================

Defines objects to compute the spectral radiance of a planckian radiator and
its spectral power distribution.

See Also
--------
`Blackbody IPython Notebook
<http://nbviewer.ipython.org/github/colour-science/colour-ipython/blob/master/notebooks/colorimetry/blackbody.ipynb>`_  # noqa
colour.colorimetry.spectrum.SpectralPowerDistribution
"""

from __future__ import division, unicode_literals

try:
    from functools import lru_cache
except ImportError:
    from backports.functools_lru_cache import lru_cache
import math
import warnings

from colour.colorimetry import (
    DEFAULT_SPECTRAL_SHAPE,
    SpectralPowerDistribution)

__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013 - 2014 - Colour Developers'
__license__ = 'New BSD License - http://opensource.org/licenses/BSD-3-Clause'
__maintainer__ = 'Colour Developers'
__email__ = 'colour-science@googlegroups.com'
__status__ = 'Production'

__all__ = ['C1',
           'C2',
           'N',
           'planck_law',
           'blackbody_spectral_radiance',
           'blackbody_spd']

C1 = 3.741771e-16  # 2 * math.pi * PLANCK_CONSTANT * LIGHT_SPEED ** 2
C2 = 1.4388e-2  # PLANCK_CONSTANT * LIGHT_SPEED / BOLTZMANN_CONSTANT
N = 1


@lru_cache(maxsize=8192)
[docs]def planck_law(wavelength, temperature, c1=C1, c2=C2, n=N): """ Returns the spectral radiance of a blackbody at thermodynamic temperature :math:`T[K]` in a medium having index of refraction :math:`n`. Notes ----- The following form implementation is expressed in term of wavelength. The SI unit of radiance is *watts per steradian per square metre*. References ---------- .. [1] `CIE 015:2004 Colorimetry, 3rd edition: Appendix E. Information on the Use of Planck"s Equation for Standard Air. <https://law.resource.org/pub/us/cfr/ibr/003/cie.15.2004.pdf>`_ Parameters ---------- wavelength : numeric Wavelength in meters. temperature : numeric Temperature :math:`T[K]` in kelvin degrees. c1 : numeric, optional The official value of :math:`c1` is provided by the Committee on Data for Science and Technology (CODATA), and is :math:`c1=3,741771x10.16\ W/m_2` (Mohr and Taylor, 2000). c2 : numeric, optional Since :math:`T` is measured on the International Temperature Scale, the value of :math:`c2` used in colorimetry should follow that adopted in the current International Temperature Scale (ITS-90) (Preston-Thomas, 1990; Mielenz et aI., 1991), namely :math:`c2=1,4388x10.2\ m/K`. n : numeric, optional Medium index of refraction. For dry air at 15°C and 101 325 Pa, containing 0,03 percent by volume of carbon dioxide, it is approximately 1,00028 throughout the visible region although CIE 15:2004 recommends using :math:`n=1`. Returns ------- numeric Radiance in *watts per steradian per square metre*. Examples -------- >>> # Doctests ellipsis for Python 2.x compatibility. >>> planck_law(500 * 1e-9, 5500) # doctest: +ELLIPSIS 20472701909806.5... """ t = temperature l = wavelength try: with warnings.catch_warnings(): warnings.simplefilter('error') return (((c1 * n ** -2 * l ** -5) / math.pi) * (math.exp(c2 / (n * l * t)) - 1) ** -1) except (OverflowError, RuntimeWarning): return 0.0
blackbody_spectral_radiance = planck_law
[docs]def blackbody_spd(temperature, shape=DEFAULT_SPECTRAL_SHAPE, c1=C1, c2=C2, n=N): """ Returns the spectral power distribution of the planckian radiator for given temperature :math:`T[K]`. Parameters ---------- temperature : numeric Temperature :math:`T[K]` in kelvin degrees. shape : SpectralShape, optional Spectral shape used to create the spectral power distribution of the planckian radiator. c1 : numeric, optional The official value of :math:`c1` is provided by the Committee on Data for Science and Technology (CODATA), and is :math:`c1=3,741771x10.16\ W/m_2` (Mohr and Taylor, 2000). c2 : numeric, optional Since :math:`T` is measured on the International Temperature Scale, the value of :math:`c2` used in colorimetry should follow that adopted in the current International Temperature Scale (ITS-90) (Preston-Thomas, 1990; Mielenz et aI., 1991), namely :math:`c2=1,4388x10.2\ m/K`. n : numeric, optional Medium index of refraction. For dry air at 15°C and 101 325 Pa, containing 0,03 percent by volume of carbon dioxide, it is approximately 1,00028 throughout the visible region although CIE 15:2004 recommends using :math:`n=1`. Returns ------- SpectralPowerDistribution Blackbody spectral power distribution. Examples -------- >>> from colour import STANDARD_OBSERVERS_CMFS >>> cmfs = STANDARD_OBSERVERS_CMFS.get('CIE 1931 2 Degree Standard Observer') # noqa >>> blackbody_spd(5000, cmfs.shape) # doctest: +ELLIPSIS <colour.colorimetry.spectrum.SpectralPowerDistribution object at 0x...> """ return SpectralPowerDistribution( name='{0}K Blackbody'.format(temperature), data=dict( (wavelength, blackbody_spectral_radiance( wavelength * 1e-9, temperature, c1, c2, n)) for wavelength in shape))