## Definition

BSDF stands for  Bidirectional Scattering Distribution Function, which is a mathematical function that characterizes how light is scattered from a surface.

It is mathematically defined by the following formula:

Where:

• L is the luminance on the sample surface at the observer direction
• E is the illuminance on the sample surface from the source direction
• Λ is the wavelength

It is mathematically defined by the following formula:

In practice, this phenomenon is usually split into reflected and transmitted components, which are then treated separately as BRDF (Bidirectional Reflectance Distribution Function) and BTDF (Bidirectional Transmittance Distribution Function).

## Why is BSDF important to an optical design?

During an optical design process, accurate simulation results rely on accurate optical properties. Indeed, geometry alone does not determine light distribution; it’s the optical properties that determine how the energy and direction of the rays change. For this reason, it’s important to know as precisely as possible the optical characteristics of the materials that will be used. The best way to obtain precise characteristics is to measure the material directly and export the data to use in an optical software tool.

Requirements:

• Optical designers need accurate optical properties for ray tracing simulations
• R&D engineers need to design the right material with given optical properties
• The quality check in the manufacturing process must be perfectly controlled

Solutions:

• Angular optical scattering with BSDF
• Amount of light propagation TIS (Reflectance, Transmittance, Absorbance ratio)

## What solution does Synopsys offer for measuring BSDF?

There are two principal ways to measure BSDF: goniophotometer and camera-based system. Synopsys provides two solutions for both.

## Goniophotometer

You can measure BSDF with a classical goniophotometer, where a static light source illuminates a sample, and a mobile detector turns around the sample to collect the scattered light (or the opposite – with a mobile light source and a static detector).

Synopsys offers two goniophotometer solutions: the Synopsys REFLET 180S and the High Specular Bench.

For these high-resolution, high dynamic motorized scatterometer systems, we provide measurement services in our lab, but the Synopsys REFLET 180S is also available for purchase.

Synopsys REFLET 180S Synopsys High Specular
Type BRDF/BTDFBRDF/BTDF
Dynamic range 109 1013
Wavelength range 400nm to 1700nm 280nm to 10,6µm
Incident angles Tunable: +90° to -90° Tunable: 90° to 0°
Angular range Full sphere 1 Plan from -10° to +90°
Angular accuracy < 0.1° < 0.02°
Repeatability < 1% < 1%
Weight 80 kg 200 kg
• High dynamic range
• Very high dynamic range
• Measurement at 0,002° from the specular
• High precision
• High repeatability
• Customizable wavelength range

## Camera-Based System

You can also measure BSDF using a camera-based system, where a source illuminates the sample and a system of lenses sends all the scattered light to a camera.

Synopsys develops and assembles two camera-based systems: the Synopsys Mini-Diff V2 and the Synopsys Mini-Diff VPro, and both are available for purchase. The Synopsys Mini-Diff VPro (left) is delivered with its own “dark room” and temperature control. The Mini-Diff V2 (right) is a portable device that is fast and easy to use.

Synopsys Mini-Diff V2 Synopsys Mini-Diff VPro
Type BRDF/BTDFBRDF/BTDF
Dynamic range 105 BRDF 105
BTDF 106
Wavelength range 630nm, 525nm, 465nm, 940nm 630nm, 525nm, 465nm
Incident angles Fixed: 0°, 20°, 40°, 60° Tunable: 0° to 60°
Angular range Sphere [0° ; 75°] [0° ; 360°] Sphere [0° ; 75°] [0° ; 360°]
Angular accuracy 1° 0,5°
Repeatability <2% <2%
Weight 2 kg 42 kg
• Plug & play
• Easy to use & fast
• Portable & compact
• Attractive cost
• Dark Box included
• Tunable AOI
• High repeatability
• Attractive cost

All of these instruments enable you to export measurement data into simulation software to be used for design.

## Optical Scattering Measurements & Equipment

Precision Light Scatter Data for Faster, More Cost-Effective Optical Product Development

## Example of a vehicle dashboard measurement with the Synopsys REFLET 180S and design with LucidShape

The measurements of a surface for vehicle dashboard material can be used in R&D to evaluate the grain size to determine which one reflects the least and scatters the most. The goal is to have the most diffusing surface possible in order to decrease reflection in the windshield for driver safety.

To compare the scattering of two dashboard surfaces with different grain sizes, the measurement of the BRDF is performed for four angles of incidence (AOI=10°/30°/50°/70°) with a white light.

For both surfaces, there is a large Gaussian peak with scattering on each side and a Lambertian background.

The level of the background is similar, but Reference 1 is more specular and Reference 2 is more diffusive; this shows that Reference 2 is more suitable for use as a dashboard.

Thanks to the capability of exporting the measurement data to design software, you can use this data to perform a simulation in LucidShape.

Using the data in LucidShape, you can perform a simulation and draw the same conclusion: Reference 1 is more specular and Reference 2 is more diffusive, which means the driver will be experience less glare with Reference 2.

Directly measuring the BSDF enables designers to choose the right material or coating, achieve an accurate rendering, and reduce the cost of prototyping.