colour.contrast.sigma_Barten1999

colour.contrast.sigma_Barten1999(sigma_0=0.008333333333333333, C_ab=0.0013333333333333333, d=2.1)[source]

Returns the standard deviation \(\sigma\) of the line-spread function resulting from the convolution of the different elements of the convolution process using Barten (1999) method.

The \(\sigma\) quantity depends on the pupil diameter \(d\) of the eye lens. For very small pupil diameters, \(\sigma\) increases inversely proportionally with pupil size because of diffraction, and for large pupil diameters, \(\sigma\) increases about linearly with pupil size because of chromatic aberration and others aberrations.

Parameters:
  • sigma_0 (numeric or array_like, optional) – Constant \(\sigma_{0}\) in degrees.
  • C_ab (numeric or array_like, optional) – Spherical aberration of the eye \(C_{ab}\) in \(degrees\div mm\).
  • d (numeric or array_like, optional) – Pupil diameter \(d\) in millimeters.
Returns:

Standard deviation \(\sigma\) of the line-spread function resulting from the convolution of the different elements of the convolution process.

Return type:

ndarray

Warning

This definition expects \(\sigma_{0}\) and \(C_{ab}\) to be given in degrees and \(degrees\div mm\) respectively. However, in the literature, the values for \(\sigma_{0}\) and \(C_{ab}\) are usually given in \(arc min\) and \(arc min\div mm\) respectively, thus they need to be divided by 60.

References

[Barten1999], [Barten2003], [Cowan2004], [InternationalTelecommunicationUnion2015],

Examples

>>> sigma_Barten1999(0.5 / 60, 0.08 / 60, 2.1)  # doctest: +ELLIPSIS
0.0087911...