Gaussian Intensity Distribution Influence

Integration and FWHM Angle

So far, only scenes with a lambertian intensity distribution have been studied. To study the effect of the angular distribution in the luminance simulation, let us consider a scene with a symmetrical gaussian intensity distribution and a FWHM variable angle. The visible surface of the scene is bigger than the pixel dimensions and the sensor is positioned in order to be close to the scene.

We need to consider at least two cases if we want to study the influence of the integration angle of the sensor and the FWHM angle of the scene on the luminance value:

Integration angle smaller than the FWHM angle of the scene	Integration angle bigger than the FWHM angle of the scene
When the integration angle is smaller than the FWHM angle of the scene, the luminance value is supposed to stay constant, as the photons are integrated under the same cone as the emission cone of the scene. There is a limitation when the integration angle is too small. Too few photons are integrated by the pixel, meaning that the luminance value is noisy and therefore not reliable.	When the integration angle is greater than the FWHM angle of the scene, the luminance value decreases as the integration angle increases, as the number of photons does not change, but is integrated under a bigger cone than the emission cone of the scene.

Luminance Variation

For a too small angle (1), the luminance is too noisy, therefore not reliable. Then the luminance starts to decrease as the integration angle increases (2).

As the value of the FWHM angle increases, the integration angle ranges for which the luminance stays constant raises.

On this example, the luminance starts to decrease even if the incident angle is lower than the FWHM angle as the luminance calculation is also influenced by other parameters such as the scene size, the distance between the scene and the sensor.