Visibility of sparkle in metallic paints ERIC KIRCHNER, 1, *IVO VAN DER LANS, 1 ESTHER PERALES, 2 FRANCISCO MARTÍNEZ-VERDÚ, 2 JOAQUÍN CAMPOS, 3 AND ALEJANDRO FERRERO 3 1 Color RD&I, AkzoNobel Performance Coatings, Sassenheim, The Netherlands 2 Color & Vision Group, University of Alicante, Carretera de San Vicente del Raspeig s/n 03690 Alicante, Spain 3 Instituto de Óptica, Consejo Superior de Investigaciones Científicas (CSIC), Madrid 28006, Spain *Corresponding author: eric.kirchner@akzonobel.com Received 13 November 2014; revised 13 March 2015; accepted 15 March 2015; posted 17 March 2015 (Doc. ID 226828); published 27 April 2015 For suitable illumination and observation conditions, sparkles may be observed in metallic coatings. The visibility of these sparkles depends critically on their intensity, and on the paint medium surrounding the metallic flakes. Based on previous perception studies from other disciplines, we derive equations for the threshold for sparkles to be visible. The resulting equations show how the visibility of sparkles varies with the luminosity and distance of the light source, the diameter of the metallic flakes, and the reflection properties of the paint medium. The pre- dictions are confirmed by common observations on metallic sparkle. For example, under appropriate conditions even metallic flakes as small as 1 μm diameter may be visible as sparkle, whereas under intense spot light the finer grades of metallic coatings do not show sparkle. We show that in direct sunlight, dark coarse metallic coatings show sparkles that are brighter than the brightest stars and planets in the night sky. Finally, we give equations to predict the number of visually distinguishable flake intensities, depending on local conditions. These equations are confirmed by previous results. Several practical examples for applying the equations derived in this article are provided. © 2015 Optical Society of America OCIS codes: (330.1710) Color, measurement; (330.1070) Vision - acuity; (330.1720) Color vision; (330.1800) Vision - contrast sensitivity; (330.6180) Spectral discrimination; (350.1260) Astronomical optics. http://dx.doi.org/10.1364/JOSAA.32.000921 1. INTRODUCTION The visual appearance of metallic coatings is characterized not only by their color, but also by texture. Under intense direc- tional light, this texture shows up as a multitude of tiny but intense light spots that are brighter than surround, a phenome- non that is often referred to as sparkle [ 1]. There is a clear need to quantitatively describe how the perceived sparkle depends on parameters such as concentration and size of sparkling pigments and their contrast with the surrounding paint. Thus far, only qualitative relationships have been published [ 2, 3], as well as a few crude estimations suggesting that the sparkle effect is strong for metallic flakes with average diameter exceeding 15 [ 4], 18 [ 3], 20 [ 5], 25 [ 6], or 30 μm[ 7]. These estimations probably vary so widely because the vis- ibility of sparkle can be expected to depend strongly on illumi- nation and viewing conditions. Perception studies have shown that the perceived brightness of a stimulus depends critically on the luminance ratio between stimulus and its surround [ 8]. In this article, we will use existing literature from other disciplines to predict under which conditions light reflection from a met- allic flake will lead to a perceived sparkle effect. The derived equations take into account the influence from illumination and observation conditions, as well as the relevant physical properties of the metallic flakes and the paint medium sur- rounding them. The equations presented here may be useful for physical models that aim to convert photographic images of sparkle into sparkle measurements. For such models, it is necessary to math- ematically distinguish sparkle pixels from surround [ 9, 10]. Also, for rendering algorithms to generate realistic images of sparkle, it is necessary to account for sparkle as perceived by human observers [ 11, 12]. The visibility of objects in natural waters [ 13] and the visibility of solar glitter on a ruffled sea [ 14– 16] are other application areas of the present work. 2. VISUAL THRESHOLD FOR SPARKLE INTENSITY The term sparkle intensity is widely used in the paint industry, and refers to its perceived brightness. However, intensity is a problematic quantity, since it has different definitions in differ- ent but related fields of optics [ 17]. Before discussing visual thresholds, we first need to clearly define the term sparkle intensity. Research Article Vol. 32, No. 5 / May 2015 / Journal of the Optical Society of America A 921 1084-7529/15/050921-07$15/0$15.00 © 2015 Optical Society of America