1. Definition
A Lambertian surface (also known as a cosine radiator or ideal diffuser) is an idealized model in optics, radiometry, and photometry. It refers to an object whose surface radiance (L) remains constant in all viewing directions, meaning the radiance L is independent of the viewing direction.

2. Classification
Based on the interaction between light and the surface, Lambertian surfaces are classified into three types:
1. Lambertian Radiator

• An ideal perfect radiator whose self-emitted radiation has uniform radiance in all directions; it serves as the benchmark model for thermal radiation theory.
• Typical example: Blackbody

(Image source: https://zh.wikipedia.org/wiki/File:Erbe.gif)

2. Lambertian Reflector

• Incident light reflected from the surface has uniform radiance in all reflection directions, making it an ideal diffuse reflector.

(Image source: https://upload.wikimedia.org/wikipedia/commons/0/08/Lambert6.gif)

• Typical examples: Standard white/gray cards, walls, white paper.

3. Lambertian Transmitter

• Incident light transmitted through the surface has uniform radiance in all transmission directions, making it an ideal diffuse transmitter.
• Typical examples: Frosted glass, overcast cloud layers.

3. Lambert's Cosine Law
A Lambertian surface strictly follows Lambert's cosine law: the radiant intensity of the surface in a given direction is directly proportional to the cosine of the angle between that direction and the surface normal.
Its mathematical expression is as follows:
$$ I_\theta = I_n \cos\theta $$

• $I_\theta$: Radiant intensity in the direction at an angle $\theta$ to the normal (unit: $\text{W}/(\text{sr})$)
• $I_n$: Radiant intensity in the normal direction ($\theta=0$)
• $\theta$: Angle between the viewing direction and the surface normal