BRDF results and validation

As detailed in Andersen (2002), three types of graphical representations were developed to provide various visualization possibilities of the transmitted or reflected light distribution features, in addition to a recombined view of the six calibrated images, gathering the latter into a unique orthogonal projection:

• the projection of the BT(R)DF values on a virtual hemisphere, allowing a precise anal­ysis of the angular distribution;

• a photometric solid, representing the BT(R)DF data in spherical coordinates with grow­ing radii and lighter colors for higher values, illustrated in Figure 6;

• several section views of this solid, providing an accurate display of the numerical values distribution.

BRDF visualization*: photometric solid (hemispherical light reflectance* = 0,5)

BRDF visualization*: photometric solid (hemispherical light reflectance* = 0.01)


Figure 6: BRDF representation as a photometric solid.


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(a) Opalescentplexiglas, (вг, фг) = (40P, CP) (b) Holographic film (HOE), (вг, фг) = (OP, OP)

An in-depth validation of both BTDF and BRDF was conducted, based on different ap­proaches (Andersen, 2004): [13]

• bidirectional measurements of systems presenting a known symmetry and verification against standard luminance-meter data or analytical calculations;

• empirical validation based on bidirectional measurements comparisons between dif­ferent devices; in case of disagreement, however, no conclusion can be established;

• assessment of hemispherical optical properties by integrating BT(R)DF data over the whole hemisphere and comparison to Ulbricht sphere measurements (Commission Internationale de l’Eclairage, 1998);

• comparison of monitored data with ray-tracing simulations to achieve a higher level of details in the BT(R)DF behaviour assessment.

These studies led to a relative error on BT(R)DF data of only 10%, allowing to confirm the high accuracy and reliability of this novel device.


This paper presents the conception and construction of an innovative, time-efficient bidi­rectional goniophotometer based on digital imaging techniques and combining BTDF and BRDF assessments. To allow reflection measurements, a controlled passage of the incident beam into the measurement space was created, minimizing parasitic reflections around the sample. Openings in the detection screen for the situations where it obstructs the incom­ing light flux were also required, made as small as possible to restrict the produced blind zones; to remove these elliptic covers, a motorized extraction and repositioning system was developed and tested successfully

This design proved efficient and reliable, for both the light beam penetration into the mea­surement space and the passage through the obstructing screen. The high accuracy achieved for BTDF assessments was checked to be kept for BRDF measurements as well, placing re­liance on the assumptions made in the construction of the instrument.


This work was supported by the Swiss Federal Institute of Technology (EPFL) and the Com­mission for Technology and Innovation (CTI). The authors wish to thank Pierre Loesch and Serge Bringolf for their contribution in the photogoniometer’s mechanical development.

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