Bidirectional transmittance distribution function (BTDF)

The Bidirectional Transmittance Distribution Function (BTDF) describes how light is transmitted through a semi-transparent or transparent material , depending on the angle of incidence and the direction of transmission . It is an extension of the Bidirectional Reflectance Distribution Function (BRDF) , but for transmission instead of reflection.

1. Formal definition of BTDF

The BTDF is defined as:

whereby:

• $\theta_i, \phi_i$ → Angle of incidence and azimuthal angle of the incoming light.
• $\theta_t, \phi_t$ → Angle of emission and azimuthal angle of the transmitted light.
• $dL_t$ → Transmitted luminance in the direction ( $\theta_t, \phi_t$ ).
• $dE_i$ → Incoming illuminance in the direction ( $\theta_i, \phi_i$ ).

The BTDF determines how light scatters after passing through a material , depending on the structure and properties of that material .

2. Applications of BTDF

🔹 Architecture & Daylight Simulations → How glass and coatings transmit and distribute light in buildings.
🔹 Optical Systems → How lenses and filters transmit and distribute light.
🔹 Display Technology → How LCD, OLED, and micro-LED displays transmit light and reach observers.
🔹 Photonics & Materials Science → Characterization of diffusive and structured materials .
🔹 Automotive Glass → Analysis of Light Scattering by Automotive Glass and HUD Systems .

3. Different types of transmission in BTDF

In materials such as prismatic glass, frosted glass and nanostructures, the BTDF plays a crucial role in light management and energy efficiency .

4. Difference between BTDF and BRDF

💡 In short:
The Bidirectional Transmittance Distribution Function (BTDF) describes how light passes through a transparent or semi-transparent material and how it is scattered . This is essential for applications in architecture, optics, display technology, and lighting .