18-Geom-A5 Remote Sensing and Image Analysis · May 2014
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — May 2014 — 04-Geom-A5 Remote Sensing and Image Analysis. Closed-book; one approved Casio or Sharp calculator permitted. Format: five questions of equal value (20 marks each); most require essay-format answers, and all five are solved in full below. Radiometric and image-processing conventions follow standard North-American digital-image-processing practice (8-bit Landsat/ETM+ imagery).
Reference texts: J. R. Jensen, Introductory Digital Image Processing: A Remote Sensing Perspective (4th ed., Pearson, 2016); Lillesand, Kiefer & Chipman, Remote Sensing and Image Interpretation (7th ed., Wiley, 2015); J. A. Richards, Remote Sensing Digital Image Analysis (5th ed., Springer, 2013); J. R. Schott, Remote Sensing: The Image Chain Approach (2nd ed., Oxford, 2007).
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 $L_S$ reaching the sensor over the target pixel is the sum of four physically distinct photon paths. Only the first has interacted with the target under the specific Sun–target–sensor geometry, so only the first carries the target's bidirectional reflectance; the other three are, from the target's point of view, contamination that atmospheric correction seeks to remove.
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 a defined view direction, its magnitude is set by the target's bidirectional reflectance distribution function (BRDF) at that geometry. This is the component that carries the surface bidirectional-reflectance information — it is the signal we actually want.
Some solar radiation is scattered by molecules and aerosols before reaching 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 beam, this component samples the target's hemispherical (albedo-like) reflectance rather than its directional BRDF, and it adds to — and dilutes the directional information in — component 1.
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.
Because the target's background has a different reflectance (as the question stipulates), radiation reflected from the neighbouring background can be scattered sideways by the atmosphere into the sensor's line of sight to the target. This adjacency effect mixes some of the background's brightness into the target pixel; it is largest at high-contrast edges (for example a dark object in a bright field, exactly the Figure 1 geometry) and carries the background's reflectance, not the target's bidirectional reflectance.
In summary, writing the four contributions additively, $L_S = L_1 + L_2 + L_3 + L_4$, and only $L_1$ (the direct target-reflected term) contains the surface bidirectional-reflectance information; components 2–4 are the sky-reflected, path-radiance, and adjacency contaminants that atmospheric correction must strip away to recover surface reflectance.
