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Radiometric Concepts

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Radiometric Concepts

Remote Sensing

ERAU

Dr. Darrel Smith

September 30, 2008

- Radiometric Terms
- Blackbody radiation
- Inverse-Square Law for Irradiance
- Lambertian Surfaces

- Irradiance (E) --flux per unit area onto a surface
- Radiant Exitance (M)--flux per unit area away from the surface.

- Radiant Intensity (I) --describes the angular distribution of the flux from a point source.
- The “radiance” (L)--provides both angular and spatial information about the flux from a point source.

- Blackbody spectrum -- Planck (1901)Emissivity () -- ratio of the spectral exitance to the exitance from a blackbody at the same temperature.
- 0 < < 1

- = constant describes “gray bodies”
- = varies with describes “selective radiators”

- Transmission ReflectionAbsorptionConservation of Energy

Note: Kirchoff’s law =

- Calculate the “total exitance” from a blackbody radiator.where = 5.6710-8 W/(m2K4)
- Peak of the blackbody exitance (Wien’s Law)where A = 2898 mK

Note: 10 m window at T = 300K

- What fraction of the spectral radiant exitance M is in the visible spectrum (400 nm 700 nm) for the sun?Assume a temperature of 5800 K.

- How does stealth technology work?
- Reduce the RCS (Radar Cross Section)
- Choice of angles
- Materials that act like a blackbody

- How is the energy leaving a surface angularly distributed into the hemisphere above the surface?
- A lambertian surface has the following property:
- How is the radiance angularly distributed from a Lambertian surface? Note: the visual response is proportional to the radiance.

- The radiance along the normal from a Lambertian surface will be:The radiance into any direction from the normal is:Combining the previous 3 equations, we obtain:

- Note: Since perceived brightness is proportional to the radiance in the visible region, this means that a Lambertian surface would look the same from all direction.
- While we cannot assume that all surfaces are Lambertian, it is a good starting point for discussion of less well-behaved surfaces.