Setting an Integration Angle

The following page gives you advices to help you find an integration angle that could fit your system.

We assume that if you are on this page, you have decided to use a Direct Simulation and so define an Integration Angle. However, if you have enough resources and you do not want to define an integration angle that will bring some approximation, use the inverse simulation. It will take longer than a direct simulation, but you will have a result without approximation.

There is no definite rule that will allow you to find the perfect integration angle each and every time. To find a good integration angle, only the empirical way is possible, because it highly depends on your system: the intensity distribution of the system, the scene size, the different materials and geometries.

Tips

These are no guidelines to absolutely follow but a non-exhaustive list of cases played and tips that could help you define your integration angle.

Important: Be aware that every project is unique and the result expectation can be different according to the project development phase. There is no standardized integration angle value that will work every time.

Most cases use an integration angle in [0,5° ; 5°].

Try launching one direct simulation for 5 minutes and one inverse simulation for 5 minutes of the same system. Compare both results. This could help you in deciding which simulation could be adequate.
When the last interaction is on lambertian surface, you can try to go slightly over 5° integration angle.
When the last interaction is specular, you can try to go under 1° integration angle.
When the result is a visualization, you can try under 5° integration angle.
When the result is an optimization, you may want to generate quick results for which you are only interested in measurements without deep details. In this case you can try to go over 5°.
In case of an headlamp visualization, if you want to better see the details of the prism structure of a Light Guide placed behind a cover lens, you can try an integration angle in [0.75 ; 2] to avoid blur.

Narrowing down the Integration Angle

The following tip can help you narrow down the integration angle.

In a pure specular system, you can backtrace the rays to the see integration angle approximation. By doing this, you can choose the approximation you want.

Create a system with a transparent object and a curved interactive source representing the size of the integration cone.

The Interactive Source is only defined to highlight the ray tracing of the extreme rays of an Integration Cone.
Simulate an Interactive Simulation.

The two extreme rays simulated out of the Interactive Source correspond to the maximum integration cone. Half of the integration cone corresponds to the Integration Angle. From this point, you can see how the rays are traced in the system.

The further the objects, the larger the region observed by the Integration Cone. That means, you will integrate rays that should not be integrated, resulting in a bigger approximation, therefore a bright spot.

You can use the trigonometry to help you find the maximum Integration Angle that you could use.

Be aware of the distance between objects in your system and the size of the integration angle.

Note: In case of a radiance sensor, the surface size of the radiance sensor plane is not considered by the simulation. The simulation considers the ray path to compute the radiance, then the simulation generate the image on the sensor plane with the right size.