# 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

Examples

>>> sigma_Barten1999(0.5 / 60, 0.08 / 60, 2.1)
0.0087911...