1. Radiometric Concepts Remote Sensing ERAU Dr. Darrel Smith September 30, 2008

2. Outline • Radiometric Terms • Blackbody radiation • Inverse-Square Law for Irradiance • Lambertian Surfaces

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

4. Radiometric Terms • 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.

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

6. Blackbody Radiation •  = constant describes “gray bodies” •  = varies with  describes “selective radiators”

7. Transmission, Reflection, Absorption • Transmission ReflectionAbsorptionConservation of Energy Note: Kirchoff’s law  = 

8. Properties of Blackbody Radiation • Calculate the “total exitance” from a blackbody radiator.where  = 5.6710-8 W/(m2K4) • Peak of the blackbody exitance (Wien’s Law)where A = 2898 mK Note: 10 m window at T = 300K

9. Homework Problem • 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.

10. Stealth Technologies • How does stealth technology work? • Reduce the RCS (Radar Cross Section) • Choice of angles • Materials that act like a blackbody

11. Lambertian Surfaces • 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.

12. Lambertian Surfaces • 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:

13. Lambertian Surface • 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.