Atmospheric phenomena

Although nature contains a theoretically infinite amount of phenomena, we choose to only focus on those that occur due to the non-homogeneous (varying refraction indices) nature of the atmosphere. Diego et al.^[18] discusses seven of these: inferior mirages, superior mirages, the Viking’s end of the world, the green flash, the Fata Morgana and the Novaya-Zemlya effect. To render these effects properly, [18] considers three things. Firstly, Fermat’s principle is used to describe the path of light through the atmosphere. This is estimated by use of fast numerical methods. An accurate model of the atmosphere is used (USA 1976 temperature profile). And finally the APM, which is developed for [18] to recreate the conditions necessary for the effects to occur.

Simulation

[18] Describes three underlying parts of the simulation algorithm.

Light Trajectory

This is calculated by extensive use of Snell’s law:

n₁sinθ_i = n2sinθ_j,

where n_i is the index of refraction of medium i and θ is the incidence angle. The index of refraction, in turn, is calculated with:

n_i = v_i / c,

where v_i is the speed of light in medium i and c is the speed of light in a vacuum.

Accurate atmospheric model

The 1976 US Standard Atmosphere^[19] is used which defines average temperature and pressure for different latitudes. [18] Obtains the refraction indices by first calculating density:

p(h) = P(h)M / RT(h),

where P is pressure, M is the mean mass of molecules and R is the Gas constant. Then, they calculate refraction with the Gladstone-Dale^[20] formula:

n(h, λ) = p(h) . (n(λ) – 1) + 1

De-standardization

Finally, [18] obtains a de-standardized version of the atmosphere by using inversion layers, hot spots and noise grids.

Rendering

The combination of all these elements has allowed [18] to produce exceptionally good results with respect to realism and physical correctness.

Conclusion