Bidirectional Reflectance Distribution Function (BRDF)

The Bidirectional Reflectance Distribution Function (BRDF) describes how light is reflected from a surface in different directions. It indicates how much light is reflected depending on the angle of incidence and the angle of exit of the light .

BRDF is widely used in computer graphics, optics, materials science, and lighting technology to model realistic light reflections and material behavior .

1. Formal definition of BRDF

The BRDF is mathematically defined as:

whereby:

• $\theta_i, \phi_i$ → Angle of incidence and azimuthal angle of the incoming light.
• $\theta_r, \phi_r$ → Angle of incidence and azimuthal angle of the reflected light.
• $dL_r$ → Reflected luminance in the direction ( $\theta_r, \phi_r$ ).
• $dE_i$ → Incoming illuminance in the direction ( $\theta_i, \phi_i$ ).

The BRDF determines how light behaves when reflected from a surface and depends on the material, roughness and structure of the surface .

2. Applications of BRDF

🎨 Computer graphics & CGI → Realistic light reflections and material models in 3D rendering.
📷 Photography & Image Processing → Improved light simulations and HDR editing.
🔬 Materials science → Surface characterization in scientific and industrial applications.
🚗 Automotive & coatings → Simulation of paint reflections and light diffusion .
🌍 Satellite and climate research → Analyzing sunlight reflections on land and oceans .

3. Different types of reflection in BRDF

4. Difference between BRDF and BTDF

💡 In short:
The Bidirectional Reflectance Distribution Function (BRDF) describes how light reflects off a surface , depending on the angle of incidence and the material . It is essential for applications in computer graphics, optics, materials science, and lighting design .