Planar Illuminance

This page describes how Planar Illuminance is calculated and integrated to the sensor (horizontally or vertically).

Planar Illuminance Overview

The illuminance on a point is calculated by the cosine on the angle of incidence ε. The formula is .

Figure 1. Planar mode with an integration direction normal to the sensor plan

Types of Integration Direction of Planar Illuminance

On the following examples, the source is simulated by a local point source.

Note: The source can also be an extended light source like luminaire, ambient, surface source, etc.

The pixel is only sensitive on one side. Its sensitivity is lambertian.

Horizontal plan

The horizontal illuminance is the most common way to calculate illuminance.

  • The integration direction is perpendicular to the horizontal plan and the surface sensor.
  • The normal illuminance follows the Bouguer law.
  • The formula is
Figure 2. Illuminance on horizontal sensor

Vertical plan

When the surface sensor is applied vertically, the lateral orientation becomes an important parameter to determinate the illuminance.

The integration direction is perpendicular to the vertical plan and parallel to the surface sensor (that is, a wall on the road).

The formula is

Figure 3. Illuminance on vertical sensor with lateral deviation (angle α)
Tip: In the specific case where α is equal to 0, the illuminance calculation is the same as for the horizontal type. It does not depend on the α factor. Only the mechanical plan is different, so the two coordinates systems have different orientations.

General case

In the general case, you must define the integration direction.

The same integration direction is applied on each pixel of the sensor.

On the figure below, the integration direction is perpendicular to the blue mechanical plans.

Figure 4. Planar illuminance in general case