Integration Angle Overview

Definition

Integration Angle has been introduced in case of a Direct Simulation to provide results in a system with specular contributions.

In a Direct Simulation, the rays come from the source and are propagated according to physic law (Monte-Carlo engine). The probability that a ray coming from a specular interaction has exactly the same direction as the integration direction (pixel on sensor plan to focal point), is almost null and the specular contribution is almost unsolvable.

To solve the issue, the sensors Radiance, Observer, Immersive use an internal algorithm (non-visible for users) called Gathering which basically forces/helps specular rays to find the sensors. The Integration Angle approximation will help the Gathering algorithm into avoiding the forced rays to be too deflected compared to its original direction (after last impact), allowing rays to be integrated into the solid angle (defined thanks to the Integration Angle). Thanks to this approximation, rays are integrated if the angular deflection between their propagation direction and the sensor integration direction is smaller than the integration angle.

The approximation makes possible that an infinitesimal small ray hits an infinitesimal small point, which is impossible without it because ray cannot hit a point, but a cone can. That’s why you need an integration angle to generate a cone.

Figure 1. Integration Angle Representation

• Virtual Ray: The integration direction (nominal direction) for one pixel to reach the focal point of the sensor (represented by the eye in the picture).
• Real Ray: The ray computed by the simulation.