Abstract
The Bidirectional Reflectance Distribution Function (BRDF) of iridescent (or goniochromatic) surfaces may vary notably with both spectral and angular variables, and, therefore, finite spectral bandwidth and collection solid angles inherent to any measuring instrument introduce a deviation from the correct value. Experimental data of highly goniochromatic samples are used to analyse their impact on measurement uncertainty. The results indicate that it is advisable to standardize spectral and angular bandwidths because the systematic error is not negligible for typical measuring systems. The 95th percentile of the error distribution of the measurement of the BRDF due to these finite bandwidths, and also the 95th percentile of the calculated resulting color differences, are used as criteria to establish recommended values of spectral and angular bandwidths. The impact of the bandwidth is more critical in the measurement of the BRDF of diffraction-based than of interference-based coatings.
Highlights
The Bidirectional Reflectance Distribution Function (BRDF) is a quantity describing the variation of the reflectance for any combination of irradiation and reflection directions [1], and it allows the reflectance to be calculated for any irradiation and collection solid angle
Since the appearance of goniochromatic surfaces notably depends on both spectral and angular variables, the non-infinitesimal measurement spectral bandwidth and the non-infinitesimal size of the measurement collection solid angles introduce a deviation from the correct value, and it might be non-negligible in some measuring systems
The impact of using non-infinitesimal spectral and angular bandwidths has been assessed for spectral BRDF measurements of goniochromatic surfaces, considering a set of interferenceand difraction-based coatings
Summary
The Bidirectional Reflectance Distribution Function (BRDF) is a quantity describing the variation of the reflectance for any combination of irradiation and reflection directions [1], and it allows the reflectance to be calculated for any irradiation and collection solid angle. Most of the research work on the appearance of goniochromatic surfaces has dealt with the proper methodology to describe their color by selecting adequate geometries, and to use measurements for representing such surfaces [6,7,8,9,10,11,12,13,14,15,16,17]. Since the appearance of goniochromatic surfaces notably depends on both spectral and angular variables, the non-infinitesimal measurement spectral bandwidth and the non-infinitesimal size of the measurement collection solid angles introduce a deviation from the correct value, and it might be non-negligible in some measuring systems. The non-infinitesimal solid angles impact on the measured angular distribution but affect the measured spectral distribution. Vice-versa, the non-infinitesimal spectral bandwidth affects on the measured spectral distribution and on the measured angular distribution. The proper understanding of the Coatings 2020, 10, 1128; doi:10.3390/coatings10111128 www.mdpi.com/journal/coatings
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