def eotf_BT2020(
E_p: FloatingOrArrayLike,
is_12_bits_system: Boolean = False,
constants: Structure = CONSTANTS_BT2020,
) -> FloatingOrNDArray:
"""
Define *Recommendation ITU-R BT.2020* electro-optical transfer function
(EOTF).
Parameters
----------
E_p
Non-linear signal :math:`E'`.
is_12_bits_system
*BT.709* *alpha* and *beta* constants are used if system is not 12-bit.
constants
*Recommendation ITU-R BT.2020* constants.
Returns
-------
:class:`numpy.floating` or :class:`numpy.ndarray`
Resulting voltage :math:`E`.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E_p`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`InternationalTelecommunicationUnion2015h`
Examples
--------
>>> eotf_BT2020(0.705515089922121) # doctest: +ELLIPSIS
0.4999999...
"""
E_p = to_domain_1(E_p)
a = constants.alpha(is_12_bits_system)
b = constants.beta(is_12_bits_system)
with domain_range_scale("ignore"):
E = np.where(
E_p < eotf_inverse_BT2020(b),
E_p / 4.5,
spow((E_p + (a - 1)) / a, 1 / 0.45),
)
return as_float(from_range_1(E))
def eotf_inverse_BT2020(
E: FloatingOrArrayLike,
is_12_bits_system: Boolean = False,
constants: Structure = CONSTANTS_BT2020,
) -> FloatingOrNDArray:
"""
Define *Recommendation ITU-R BT.2020* inverse electro-optical transfer
function (EOTF).
Parameters
----------
E
Voltage :math:`E` normalised by the reference white level and
proportional to the implicit light intensity that would be detected
with a reference camera colour channel R, G, B.
is_12_bits_system
*BT.709* *alpha* and *beta* constants are used if system is not 12-bit.
constants
*Recommendation ITU-R BT.2020* constants.
Returns
-------
:class:`numpy.floating` or :class:`numpy.ndarray`
Resulting non-linear signal :math:`E'`.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
+------------+-----------------------+---------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``E_p`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
References
----------
:cite:`InternationalTelecommunicationUnion2015h`
Examples
--------
>>> eotf_inverse_BT2020(0.18) # doctest: +ELLIPSIS
0.4090077...
"""
E = to_domain_1(E)
a = constants.alpha(is_12_bits_system)
b = constants.beta(is_12_bits_system)
E_p = np.where(E < b, E * 4.5, a * spow(E, 0.45) - (a - 1))
return as_float(from_range_1(E_p))