7.1.5 Attenuation

From [pov:6.6.6]:
Light attenuation is used to model the decrease in light intensity as the light travels through a transparent object. The keywords fade_power, fade_distance and fade_color are specified in the interior statement.

The fade_distance value determines the distance the light has to travel to reach half intensity while the fade_power value determines how fast the light will fall off. fade_color colorizes the attenuation. For realistic effects a fade power of 1 to 2 should be used. Default values for fade_power and fade_distance is 0.0 which turns this feature off. Default for fade_color is $\langle$0,0,0$\rangle$, if fade_color is $\langle$1,1,1$\rangle$ there is no attenuation. The actual colors give colored attenuation. $\langle$1,0,0$\rangle$ looks red, not cyan as in media.

The attenuation is calculated by a formula similar to that used for light source attenuation.

   attenuation$$=\frac1{1+(\frac{d}{\text{fade\_distance}})^{\text{fade\_power}}}$$

If you set fade_power in the interior of an object at 1000 or above, a realistic exponential attenuation function will be used:

   attenuation$$= \exp(-\operatorname{depth}/\operatorname{fade\_dist})$$