==== Lambertian Surface ====
**I.Definition**\\
A Lambertian surface (also referred to as a perfectly diffuse emitter or ideal diffuse reflector) is an idealized model in optics, radiometry, and photometry. It is defined as a surface whose radiance  is constant in all viewing directions.\\

In other words, the radiance of a Lambertian surface is independent of the direction of observation, although the observed intensity varies with angle due to geometric effects.\\

**II.Classification**\\
Based on the interaction between light and a surface, Lambertian behavior can be categorized into three idealized types:

**1. Lambertian Emitter**\\
A Lambertian emitter is an ideal surface that emits radiation with constant radiance.\\
  * The emission is isotropic in radiance. 
  * This model serves as a fundamental reference in thermal radiation theory. 
**Typical example:** a blackbody radiator.

{{ :yanding:成像基础知识:光学:辐射度学与光度学:erbe_黑体辐射_.gif?200|}}
Figure 1: blackbody radiator\\
Source: https://zh.wikipedia.org/wiki/File:Erbe.gif\\

**2. Lambertian Reflector**\\
A Lambertian reflector is an ideal diffuse reflecting surface that scatters incident radiation such that the reflected radiance is independent of viewing direction.
{{ :yanding:成像基础知识:光学:辐射度学与光度学:lambert6.gif?280|}}
Source: https://upload.wikimedia.org/wikipedia/commons/0/08/Lambert6.gif\\
**Typical examples:**standard whiteboards or gray cards, walls, and white paper.
{{ :yanding:成像基础知识:光学:辐射度学与光度学:灰卡.png?200|}}
Figure 2: standard whiteboards or gray cards\\



**3. Lambertian Transmitter**\\
A Lambertian transmitter is an ideal surface that transmits radiation diffusely, with transmitted radiance independent of viewing direction.\\
**Typical examples:** frosted glass and overcast clouds.\\
{{en:yanding:imaging_basics:optics:radiation_and_luminescence:朗博体.png?200|}}
Figure 2: Opal Glass\\
Source: https://www.ok-kk.com/uppic/upfile/image/guangxueyuanjian/lvguangpian/3547/DFO_p.jpg\\

**III.Lambert's Cosine Law**\\
Lambertian surfaces obey Lambert's cosine law. \\
The observed radiant intensity in a given direction is proportional to the cosine of the angle between that direction and the surface normal.\\
$$ I_\theta = I_n \cos\theta $$
where:
  * $I_\theta$ is the radiant intensity in direction  $\theta$ .
  * $I_n$ is the radiant intensity in the normal direction.
  * $\theta$ is the angle between the observation direction and the surface normal.