Question 2 of 5: Components of At-Sensor Radiance

Question 2: Components of At-Sensor Radiance (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

The total radiance $L_S$ measured by the sensor over a target pixel is the sum of three physically distinct photon paths. Only the first has interacted with the target along the actual Sun–target–sensor geometry, so only the first carries the target's bidirectional reflectance; the other two are, from the target's point of view, contamination that atmospheric correction seeks to remove. Writing them additively, $L_S = L_1 + L_2 + L_3$.

Component 1 — Direct solar radiance reflected by the target (the signal)

The direct solar beam is transmitted down through the atmosphere, strikes the target, is reflected toward the sensor, and is transmitted back up. Because the reflection happens at the target under a defined illumination direction and is viewed along a defined view direction, its magnitude is set by the target's bidirectional reflectance distribution function (BRDF) at that specific Sun–target–sensor geometry. This is the component that carries the surface bidirectional-reflectance information — it is the signal we actually want to recover.

Component 2 — Diffuse (sky) irradiance reflected by the target

A portion of the solar radiation is scattered by molecules and aerosols before it reaches the ground and arrives at the target as diffuse skylight from the whole sky hemisphere. The target reflects this hemispherically-incident irradiance toward the sensor. Because the illumination is no longer a single collimated beam, this component samples the target's hemispherical (albedo-like) reflectance rather than its directional BRDF; it adds to — and dilutes the directional information in — component 1.

Component 3 — Path radiance (atmospheric scattering into the sensor)

A fraction of the solar radiation is scattered by the atmosphere directly into the sensor's line of sight without ever touching the surface. This path radiance carries no target information at all; it is an additive haze term that raises the apparent brightness of every pixel (strongest in the blue, which is why dark-object subtraction estimates it from the shortest-wavelength band). It contains no bidirectional-reflectance information about the target.

Summary. Of the three at-sensor radiance components $L_S = L_1 + L_2 + L_3$, only $L_1$ — the direct, target-reflected solar term — encodes the surface bidirectional-reflectance (BRDF) information; $L_2$ (sky-reflected) samples only the hemispherical reflectance, and $L_3$ (path radiance) never touches the target. Atmospheric correction exists precisely to remove $L_2$ and $L_3$ and isolate $L_1$.