Contents
Source: ResearchGate
Lambertian Emitters and Scatterers
Understanding Lambertian Scatterers
When light scatters on a surface, it can exhibit different angular distributions. One important case is that of a Lambertian scatterer, where the radiance of scattered light towards an observer remains constant regardless of the observation angle. This means that the scattering object appears equally bright from all directions within the hemisphere of the incident light.
The radiant intensity of a Lambertian scatterer follows Lambert’s cosine law, which states that the intensity is proportional to the cosine of the angle between the observation direction and the surface normal. This results in the intensity diminishing as the observation angle approaches 90°.
Consistency of Radiance and Lambert’s Cosine Law
While the constant radiance and Lambert’s cosine law may seem contradictory, they are actually complementary. The cosine law applies when measuring scattered light intensity with a photodiode at varying observation angles, leading to intensity reduction at higher angles. On the other hand, radiance is crucial when using imaging devices like cameras, where the image of the scatterer on the sensor decreases with increasing observation angles while maintaining constant brightness.
Real-world Applications
Materials like paper, wood, plastics, and ceramics often exhibit Lambertian scattering characteristics, making them suitable for various applications. Despite being a simplified model, Lambertian scattering is commonly assumed in calculations for its practicality, even though deviations can occur in real-world scenarios.
The Moon serves as a non-Lambertian scatterer example, deviating from Lambertian characteristics due to its surface properties causing preferential retroreflection.
Lambertian Emitters
In the context of light emitters, Lambertian characteristics indicate that the emitted radiance remains constant across all observation directions, while the radiant intensity follows Lambert’s cosine law for varying emission angles.
A blackbody source or a thermal emitter can exhibit Lambertian characteristics, resulting in uniform brightness from all viewing angles. The Sun, although not a Lambertian emitter, demonstrates limb darkening, showing reduced brightness towards its edges.
Conclusion
Understanding Lambertian scatterers and emitters is essential in various fields, from lighting design to remote sensing applications. While Lambertian models provide a simplified approach, real-world scenarios may deviate due to material properties and surface structures. By grasping the principles of Lambertian behavior, researchers and engineers can optimize their designs and calculations for better outcomes.
Source: LED professional
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