content_image/326055.jpg
The last step towards a true colour image is a linear transformation ( M$_{3}$$_{×}$$_{3}$ ) from the CIE-XYZ to a displayable RGB colour space. In case of the sRGB space with D65 as reference white point this reads: 4 

<img src='content_image/326055.jpg'>

This gives an 1D-array containing one RGB-tuple for each angle, which has to be multiplied with the calculated integrated irradiance distribution (equation (9)). Note that with this, the ratio between the R,G, and B coordinates is unchanged which results in a sole change of the brightness, but not of the respective colour. Assuming again azimuthal symmetry this 1D-colour-brightness distribution can be expanded to a 2D-colour-image. 

## References 

[1] Sipe, J. E. New Green-function formalism for surface optics J. Opt. Soc. Am. B 4 , 481-489 (1987). 

[2] Heavens, O. S. Optical Properties of Thin Solid Films (Dover Publications, New York, 1991) 

[3] Commission Internationale de l’ ´ Eclairage, Fundamental chromaticity diagram with physiological axes–Part I (Tech- nical Report, CIE 170-1:2006, 2006). 

[4] Hunt, R. W. G. The reproduction of colour (Wiley, Chichester, 6th ed., 2004) 

