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The Snell's Window Image for Remote Sensing of the Upper Sea Layer

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The Snell's Window Image for Remote Sensing of the Upper Sea Layer Journal of Marine Science and Engineering Article The Snell’s Window Image for Remote Sensing of the UpperArticle Sea Layer: Results of Practical Application The Snell’s Window Image for Remote Sensing of the AlexanderUpper A. Sea Molkov Layer * and Lev: Results S. Dolin of Practical Application Institute of Applied Physics of the Russian Academy of Sciences, 46 Uljanova St., 603950 Nizhny Novgorod, AlexanderRussia; [email protected] A. Molkov * and Lev S. Dolin *InstituteCorrespondence: of Applied [email protected]; Physics of the Russian Tel.: Academy +7-831-416-4859 of Sciences, 46 Uljanova St., 603950 Nizhny Novgorod, Russia; [email protected] Received:* Correspondence 28 February: a.molkov 2019; Accepted:@inbox.ru 15; Tel.: March +7-831 2019;-416 Published:-4859 19 March 2019 Received: 28 February 2019; Accepted: 15 March 2019; Published: 19 March 2019 Abstract: Estimation of water optical properties can be performed by photo or video registration of rough sea surface from underwater at an angle of total internal reflection in the away from the Abstract: Estimation of water optical properties can be performed by photo or video registration of sun direction at several depths. In this case, the key characteristic of the obtained image will be rough sea surface from underwater at an angle of total internal reflection in the away from the sun the border of the Snell’s window, which is a randomly distorted image of the sky. Its distortion direction at several depths. In this case, the key characteristic of the obtained image will be the changes simultaneously under the action of the sea roughness and light scattering; however, after border of the Snell’s window, which is a randomly distorted image of the sky. Its distortion correctchanges “decoding” simultaneously of this under image, the their action separate of the sea determination roughness and is possible. light scattering This paper; however, presents after the correspondingcorrect “decoding” algorithms of this image for achieving, their separate thesepossibilities determination by is the possible. Snell’s This window paper images. presents These the imagescorresponding were obtained algorithms in waters for achiev with differenting these optical possibilities properties by the and Snell wave’s conditionswindow images under. severalThese typesimages of were illumination. obtained Practical in waters guidelines with different for recording, optical properties processing and and wave analyzing conditions images under of the Snell’sseveral window types of are illumination also formulated.. Practical guidelines for recording, processing and analyzing images of the Snell’s window are also formulated. Keywords: underwater vision; Snell’s window image; inherent optical properties; slope variance; remoteKeywords: sensing underwater vision; Snell’s window image; inherent optical properties; slope variance; remote sensing 1.1. Introduction Introduction TheThe underwater underwater skysky image,image, oror thethe Snell’sSnell’s window, is a contrasting object object frequently frequently observed observed in in photosphotos of of professional professionaland and amateuramateur diversdivers alikealike (Figure1 1).). However,However, thethe useuse ofof such images to to solve solve scientificscientific problems problems has has not not beenbeen noticednoticed untiluntil recently.recently. (a) (b) (c) FigureFigure 1.1. TheThe Snell’sSnell’s windowwindow image obtained from oceanographic oceanographic platform platform in in the the Black Black Sea Sea (a ()a )for for a a flatflat seasea surfacesurface fromfrom depthdepth of 0.5 m and for a rough sea sea s surfaceurface from from depth depthss of of (b (b) )1.5 1.5 m m and and (c ()c )5 5m m (attenuation(attenuation coefficientcoefficient waswas aboutabout 0.60.6 mm−11).). ForFor aa flatflat seasea surface,surface, the Snell’sSnell’s window looks like like a a light light circle circle with with an an angular angular radius radius equal equal to to thethe angleangle ofof totaltotal internalinternal reflectionreflection of 48.7548.75°◦ (Figure 11a).a). An apparent radiance of of the the sea sea surface surface at at anglesangles moremore than than 48.75 48.75°◦ is is determined determined through through the the upwelling upwelling light light reflected reflected by by water water boundary boundary to to the lowerthe lower hemisphere. hemisphere. In fact, In the fact upwelling, the upwelling radianceis radiance too low inis comparison too low in with comparison the downwelling with the one; downwelling one; therefore, the apparent radiance of the surface beyond Snell’s window appears to be comparatively low. Surface waves randomly distort the border of the Snell’s window resulting in J. Mar. Sci. Eng. 2019, 7, 70; doi:10.3390/jmse7030070 www.mdpi.com/journal/jmse J. Mar. Sci. Eng. 2019, 7, 70; doi:10.3390/jmse7030070 www.mdpi.com/journal/jmse J. Mar. Sci. Eng. 2019, 7, 70 2 of 18 therefore, the apparent radiance of the surface beyond Snell’s window appears to be comparatively low. Surface waves randomly distort the border of the Snell’s window resulting in the appearance of lots of dark and light spots near it (Figure1b). Thus, contours of light and dark spots around the Snell’s window border outline the surface patches where the slope exceeds the certain value depending on spot location. This opens up possibilities for retrieval of the slope distribution function or its parameters like slope variance by distortions of the Snell’s window border. The effects of multiple scattering and absorption of light in water also affect the distortion of the Snell’s window border, getting stronger with depth increase (Figure1b,c). The first images of the Snell’s window for estimation of sea roughness parameters were obtained in the Black Sea in 2010 during the photo registration of the underwater solar path at the time of sunset. In this case, the sun solar path was near the border of the of Snell’s window. Its study allowed us to establish that the Snell’s window border is very sensitive to the sea surface roughness and can be used to determine its statistical properties [1]. The first algorithm for estimating the slope variance by value of its border distortion in case of slope less than 20◦ was proposed in [2]. Similar estimation for roughness with breaking waves based on the roughness representation as a sine curve with known characteristics was obtained in [3]. Subsequently, on the basis of a simplified model of the Snell’s window [4], a new algorithm for reconstructing the wind-waves frequency spectra was developed [5]. On the one hand, it was assumed that both algorithms were applicable at optical depths less than one, where the effects of light scattering and absorption can be neglected. On the other hand, it created the background for determining the optical properties of water at greater depths. As a result, in [6], the outcome of the theoretical study in estimating the absorption and scattering coefficient of water through the Snell’s window distortion was presented under the assumption that there was a known parameter, characterizing sea roughness like slope variance. Results of the first testing of the proposed algorithms for images from the Black Sea and empirical regressions between the inherent optical properties (IOP) at 532 nm [7] are presented in [8]. Subsequently, the possibility of determining the absorption coefficient for three spectral channels (420 nm, 530 nm and 650 nm) was demonstrated for fresh water of the Gorky Reservoir, characterized by high concentrations of chlorophyll a and dissolved organic matter [9]. The scope of the present investigation was aimed at estimating both the characteristics of the sea roughness and the optical properties of water for both its types (Case 1 and Case 2), for different illumination and sea roughness conditions and without applying empirical regressions between IOP. In addition, practical recommendations of the Snell’s window image registration, processing and analysis will be made in this work. Additionally, we would like to note that the emphasis on our own research in this article is connected with the fact that there have been no similar results from other research teams. The analysis of modern studies on using Snell’s window image for estimating characteristics of the upper water layer confirms the assertion made. At the present time, a great number of methods, approaches and techniques for studying the sea surface parameters and the optical properties of water have been developed; however, we were interested in the possibility of specifically using underwater images for this purpose. 2. Materials and Methods The work was based on the theoretical model of the accumulated Snell’s window image [8,10], the proposed algorithms for solving inverse problem and the data of field measurements from several expeditions of 2018. For a better understanding of the paper we will briefly consider the theoretical model of the instantaneous image of the Snell’s window, explain the physical principles of its formation and provide a table of abbreviations and symbols used in this paper (Table1). J. Mar. Sci. Eng. 2019, 7, 70 3 of 18 Table 1. Abbreviations and Symbols. Symbols Meaning Ji Angle of incident light J Angle of refracted light Angle of observation of the Snell’s window border for a flat sea surface J Sn (angle of total internal reflection) J− Random angle less than JSn J+ Random angle more than JSn J Mean angle of distortion of the Snell’s window border Z Depth 4Z Thickness of the water layer
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