# -*- coding: utf-8 -*-
"""
ITU-R BT.1886
=============
Defines *Recommendation ITU-R BT.1886* electro-optical transfer function
(EOTF / EOCF) and its reverse:
- :func:`colour.models.eotf_reverse_BT1886`
- :func:`colour.models.eotf_BT1886`
See Also
--------
`RGB Colourspaces Jupyter Notebook
<http://nbviewer.jupyter.org/github/colour-science/colour-notebooks/\
blob/master/notebooks/models/rgb.ipynb>`_
References
----------
- :cite:`InternationalTelecommunicationUnion2011h` : International
Telecommunication Union. (2011). Recommendation ITU-R BT.1886 - Reference
electro-optical transfer function for flat panel displays used in HDTV
studio production BT Series Broadcasting service. Retrieved from
https://www.itu.int/dms_pubrec/itu-r/rec/bt/\
R-REC-BT.1886-0-201103-I!!PDF-E.pdf
"""
from __future__ import division, unicode_literals
import numpy as np
__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013-2018 - Colour Developers'
__license__ = 'New BSD License - http://opensource.org/licenses/BSD-3-Clause'
__maintainer__ = 'Colour Developers'
__email__ = 'colour-science@googlegroups.com'
__status__ = 'Production'
__all__ = ['eotf_reverse_BT1886', 'eotf_BT1886']
[docs]def eotf_reverse_BT1886(L, L_B=0, L_W=1):
"""
Defines *Recommendation ITU-R BT.1886* reverse electro-optical transfer
function (EOTF / EOCF).
Parameters
----------
L : numeric or array_like
Screen luminance in :math:`cd/m^2`.
L_B : numeric, optional
Screen luminance for black.
L_W : numeric, optional
Screen luminance for white.
Returns
-------
numeric or ndarray
Input video signal level (normalized, black at :math:`V = 0`, to white
at :math:`V = 1`.
References
----------
- :cite:`InternationalTelecommunicationUnion2011h`
Examples
--------
>>> eotf_reverse_BT1886(0.11699185725296059) # doctest: +ELLIPSIS
0.4090077...
"""
L = np.asarray(L)
gamma = 2.40
gamma_d = 1 / gamma
n = L_W ** gamma_d - L_B ** gamma_d
a = n ** gamma
b = L_B ** gamma_d / n
V = (L / a) ** gamma_d - b
return V
[docs]def eotf_BT1886(V, L_B=0, L_W=1):
"""
Defines *Recommendation ITU-R BT.1886* electro-optical transfer function
(EOTF / EOCF).
Parameters
----------
V : numeric or array_like
Input video signal level (normalized, black at :math:`V = 0`, to white
at :math:`V = 1`. For content mastered per
*Recommendation ITU-R BT.709*, 10-bit digital code values :math:`D` map
into values of :math:`V` per the following equation:
:math:`V = (D-64)/876`
L_B : numeric, optional
Screen luminance for black.
L_W : numeric, optional
Screen luminance for white.
Returns
-------
numeric or ndarray
Screen luminance in :math:`cd/m^2`.
References
----------
- :cite:`InternationalTelecommunicationUnion2011h`
Examples
--------
>>> eotf_BT1886(0.409007728864150) # doctest: +ELLIPSIS
0.1169918...
"""
V = np.asarray(V)
gamma = 2.40
gamma_d = 1 / gamma
n = L_W ** gamma_d - L_B ** gamma_d
a = n ** gamma
b = L_B ** gamma_d / n
L = a * np.maximum(V + b, 0) ** gamma
return L