Radiance and Irradiance
1. Radiance (L)
**Definition**:
Radiance describes the amount of light energy traveling in a specific direction from a given area.
**Key Characteristics**:
– **Units**: Watts per square meter per steradian (W·m⁻²·sr⁻¹).
– **Directional Nature**: Radiance includes both the spatial position (surface area) and the direction of light.
– **Measure**: It’s what a sensor measures when it ‘looks’ at a specific area.
**Example**:
The brightness of a particular point in the sky or a water body as seen from a sensor or an observer.
**Applications**:
Radiance is critical in remote sensing, where satellites measure the radiance coming from Earth or water to determine surface properties. It is used in calculating reflectance, water-leaving radiance, and atmospheric correction.
2. Irradiance (E)
**Definition**:
Irradiance is the total amount of light energy incident on (or passing through) a surface from all directions.
**Key Characteristics**:
– **Units**: Watts per square meter (W·m⁻²).
– **Non-Directional**: Unlike radiance, irradiance considers light from all angles.
– **Measure**:
– **Downwelling Irradiance (E_d)**: Light energy coming down toward a surface (e.g., sunlight reaching the water).
– **Upwelling Irradiance (E_u)**: Light energy leaving a surface upward (e.g., light reflected or scattered upward from the water).
**Example**:
The amount of sunlight striking the ocean surface or a sensor collecting light from the sky.
**Applications**:
Irradiance is used to calculate reflectance, albedo, and water optical properties. It is essential for characterizing light availability for photosynthesis in aquatic systems.
Comparison: Radiance vs. Irradiance
| Property | Radiance | Irradiance |
| Definition | Light energy traveling in a specific direction | Total light energy incident on a surface |
| Units | W·m⁻²·sr⁻¹ | W·m⁻² |
| Directional | Yes (directional) | No (all directions) |
| What It Describes | Brightness of a specific point or area | Total light energy hitting a surface |
| Applications | Remote sensing, atmospheric correction | Photosynthesis studies, energy budgets |
Relation Between Radiance and Irradiance
Irradiance can be calculated by integrating radiance over all directions (solid angles) of light striking the surface. Mathematically:
E = ∫₂π L · cos(θ) dΩ
where:
– L: Radiance
– cos(θ): Accounts for the angle of incidence relative to the surface
– dΩ: Solid angle of light beam