Metrological issues related to BRDF measurements around the specular direction in the particular case of glossy surfaces

Abstract

Among the complete bidirectional reflectance distribution function (BRDF), visual gloss is principally related to physical reflection characteristics located around the specular reflection direction. This particular part of the BRDF is usually referred to as the specular peak. A good starting point for the physical description of gloss could be to measure the reflection properties around this specular peak. Unfortunately, such a characterization is not trivial, since for glossy surfaces the width of the specular peak can become very narrow (typically a full width at half maximum inferior to 0.5° is encountered). In result, new BRDF measurement devices with a very small solid angle of detection are being introduced. Yet, differences in the optical design of BRDF measurement instruments engender different measurement results for the same specimen, complicating direct comparison of the measurement results.This issue is addressed in this paper. By way of example, BRDF measurement results of two samples, one being matte and the other one glossy, obtained by use of two high level goniospectrophotometers with a different optical design, are described. Important discrepancies in the results of the glossy sample are discussed. Finally, luminance maps obtained from renderings with the acquired BRDF data are presented, exemplifying the large visual differences that might be obtained. This stresses the metrological aspects that must be known for using BRDF data. Indeed, the comprehension of parameters affecting the measurement results is an inevitable step towards progress in the metrology of surface gloss, and thus towards a better metrology of appearance in general.

Using a Robotic Arm for Measuring BRDFs

“…Several precise, robot-based gonioreflectometers exist today [5,1,16,4,15,8]. At Physikalisch-Technische Bundesanstalt (PTB), for example, they have developed a robot-based gonioreflectometer with a five-axis robot holding the sample and a homogeneous sphere radiator mounted on a ring-shaped rotation stage for illumination [5,4].…”

“…This system relies on calibrated incident radiance and is generally comprised of more purpose-built components than our setup. Baribeau et al [1] also use a five-axis robot for holding the sample and others [16,15] use a six-axis robot for the same task. These systems employ a ring-shaped rotation stage for holding either a light source [1,15] or a spectroradiometer [16].…”

Relating Optical and Geometric Surface Characteristics for Gloss Management in Printing Applications

“…This common form has been shown to represent a wide range of different surface reflection measurements. Research [10][11][12][13] has focused on the creation of error metric functions to quantify differences between two BRDFs. These functions vary both in the distance metric and in the weight applied to different components of the BRDF.…”

“…The cos(θ i ) term is introduced under the assumption that for illumination angles closer to the grazing angle, measured BRDFs and analytical models are less accurate and therefore less weight is applied to these angles. Several studies such as those of Lafortune et al 10 and Fores et al 12 have discussed the use of other error metrics and approaches for BRDF sampling as well; 13 however, it is mentioned that only a minor difference in the behavior is observed on low gloss anisotropic samples.…”

What Is the True Width and Height of the Specular Peak According the Level of Gloss?

“…Valid assessment of this peak request then a measurement setup that will have an illumination and collection solid angles small enough in front of these variations, so with a half aperture angle lower than 0,02°. If measured with a larger aperture, the result will not reflect the specular peak, but the convolution between the peak and the apparatus function of the goniospectrophotometer [Obein, 2015]. In consequence, if classical spectrophotometers can provide a trustable measurement of the BRDF for a satin surface, most of them will be incapable to resolve the specular peak of high gloss surfaces.…”