Open Access Te Herenga Waka-Victoria University of Wellington
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Metrology of Scattering Distributions

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posted on 2023-07-24, 04:25 authored by Ellen Molloy

We are continuously making judgements based on the appearance of objects around us. The appearance of an object depends on the way in which the object’s surface reflects, transmits, and absorbs the incident light. In recent years, there has been an increasing demand for traceable measurements of ‘appearance’ across various industries. While there has been extensive work carried out in national metrology institutes to develop traceable colour measurements, there are more and more requirements for multidimensional measurements, for example of the bidirectional reflectance and transmittance distribution functions (BRDF, BTDF). Measurements of these quantities require an instrument that allows changes to both the incident and detection angles, such as a goniospectrophotomer. Achieving traceability for measurements of the bidirectional scattering distribution function (BSDF, referring to either the BRDF or BTDF) and integrated BSDF requires an in-depth understanding of the instrument and all of the errors in the measurements.

This thesis describes the measurement model developed for measurements of BSDF and integrated BSDF using the Measurement Standards Laboratory of New Zealand’s (MSL) goniospectrophotometer. This model considers all of the errors in the alignment of the instrument and the angles set by the instrument and propagates these through to the measured BSDF. A correction factor for the non-uniformity in the response of the detector is calculated and a new design for the detector is proposed to remove the need for this correction factor. The effect of the instrument signature is also considered.

The measurement model is applied to various samples to demonstrate the insights that can be gained from a detailed model, which are then used to help lower the measurement uncertainty. The relative standard uncertainty in the BRDF of a white Spectralon sample at 550 nm is less than 0.1% for in-plane measurements, while the relative standard uncertainty in the diffuse reflectance (calculated from integrated BRDF measurements) of a white Spectralon sample at 560 nm is 0.25%.

Finally, the model is applied to measurements of BTDF, which is integrated to calculate transmittance haze. The haze values measured using the goniospectrophotometer are compared with measurements of haze made according to the documentary standards using an integrating sphere. It is demonstrated that these two methods of measuring transmittance haze do not agree due to a conflict in the definition of transmittance haze. The BTDF measurements are used to simulate the integrating sphere haze and to calculate the sensitivity of the sphere measurements to various alignment errors.


Copyright Date


Date of Award



Te Herenga Waka—Victoria University of Wellington

Rights License


Degree Discipline


Degree Grantor

Te Herenga Waka—Victoria University of Wellington

Degree Level


Degree Name

Doctor of Philosophy

ANZSRC Type Of Activity code

4 Experimental research

Victoria University of Wellington Item Type

Awarded Doctoral Thesis



Victoria University of Wellington School

School of Chemical and Physical Sciences


Koo, Annette; Auguie, Baptiste