Total integrated scattering (TIS) describes how much light is deviated (or scattered) from the incident light direction by diffuse reflection and transmission from a surface or optical element. It is equal to the ratio of diffuse reflected and transmitted optical power to the incident optical power when light is incident upon a surface.

TIS = (diffuse reflectance radiant flux + diffuse transmittance radiant flux) / [(specular reflectance power + specular transmittance power) + (diffuse reflectance power + diffuse transmittance power)]

This implies that TIS is a unitless number with a value between 0 and 1.

Collect all scattered light in all directions without the specular beam

Why is TIS important to an optical design?

During an optical design process, accurate simulation results often rely upon accurate optical property definitions (surface and bulk properties). Geometry alone often cannot determine the light distribution. Optical material and surface properties determine how the energy and direction of a ray changes. It is often important to know with sufficient precision the optical characteristics of the materials that will be used. A useful way to obtain precise characteristics is to directly measure how light interacts with a material sample and export the results to optical design software.

Having accurate measurements is beneficial to:

  • Optical design engineers, who need accurate optical properties for optical design software simulations
  • R&D engineers, who need to design the right material that provide specific optical properties
  • QA/QC personnel, who check these properties as part of manufacturing quality assurance and control processes

Typical optical material performance metrics measured include:

  • Bidirectional Scattering Distribution Function (BSDF)
  • Total Integrated Scatter (TIS)
  • Reflectance, Transmittance, Absorbance ratio

How do you measure TIS?

TIS measurements are notoriously difficult to perform primarily because one must separate the specularly reflected and transmitted incident light from the scattered light. These radiation patterns normally overlap and cannot be easily separated by the geometry of the measurement equipment.

We have outlined a couple of methods for measuring TIS in the following paragraphs.

1. Measuring TIS using integrating spheres

You can measure the TIS of a material sample or a surface using specially designed integrating spheres. Ideally the measurement setup should measure all of the scattered light signal (without the specular) into a hemisphere: the scattered light from the sample is integrated by a Lambertian reflective hemisphere, then normalized by the total reflected and transmitted power of the incident beam (also measured into a reflective hemisphere).

In practice, the sample is placed on the exit and then entrance port of an integrated sphere and illuminated by a laser source to measure the (specular reflectance power + diffuse transmittance power ) and the (diffuse reflectance power + specular transmittance power), respectively. The same measurement is performed again after opening a port that permits the specular beam out of the integrating sphere so that it is not included in the measurements of the diffuse transmittance power and the diffuse reflectance power.

Measuring TIS using integrating spheres

2. Measuring TIS from BSDF

TIS can also be measured by using a goniometer with a detector that can be scanned in angular space to measure the BSDF of a sample or surface. TIS can be calculated directly from BSDF measurements as shown in the following formulas.

TIS can be calculated directly from BSDF measurements - Formula 1 | Synopsys
TIS can be calculated directly from BSDF measurements - Formula 2 | Synopsys

With θd and φd respectively the scattering angle and the azimuthal angle of the detector.
θi and φi respectively the scattering angle and the azimuthal angle of the source.

θd Specular max and θd Specular min are the limits of the specular part of the BSDF.

The TIS computation accuracy relies on the BSDF accuracy and BSDF sampling. The higher the resolution, the more accurate the TIS evaluation.

The TIS computation accuracy relies on the BSDF accuracy and BSDF sampling. The higher the resolution, the more accurate the TIS evaluation.

What solutions does Synopsys offer?

Synopsys offers measurement services in a light- and temperature-controlled laboratory. We can measure TIS using the integrating spheres method outlined above.

In addition, Synopsys offers high-end scattering measurement instruments for your lab to measure BSDF, which could be used for TIS computation. For example, the Synopsys REFLET 180S is able to measure BSDF in order to extract/calculate TIS from these measurements. The accuracy depends on the resolution of the measurements. The different angular resolutions of these instruments will allow you to extract the specular part from BSDF measurements with varying degrees of accuracy.

Synopsys TIS Pro | Synopsys

Optical Scattering Measurements and Equipment

Purchase solutions to measure optical samples and import custom data into Synopsys optical software tools.

See also this related term: light scattering

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