Topic 2: Reflection 1

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1 Topic 2: Reflection 1 Topic 2b: Reflectance (Why the way you look affects what you see) The major points: The apparent color, contrast and texture of a target is a function of the illumination (angle, spectral composition, etc.) the viewing conditions (clouds, shadows, et.c.) surface morphology of the target (roughness, slope, orientation,etc.) internal absorption and scattering by the target The same object may look drastically different under different conditions. We can emphasize which characteristics are visible by adjusting the way that we view it. Specular reflection (Fresnel reflectance) Mirror-like reflection from an optically smooth surface separating two regions with different refractive indices. Specular reflection is surface reflection for which the angle of reflection is equal to the angle of incidence. In most cases there is little absorption associated with specular reflection, i.e., there is little change in color. Snell's Law: n 1 sin θ 1 = n 2 sin θ 2 θ 1 θ 1 n 1 n 2 θ 1 = angle of incidence = angle of reflection θ 2 = angle of refraction n 1 = index of refraction in medium 1 n 2 = index of refraction in medium 2 θ 2 Specular Reflectance With specular reflection from a flat water surface: reflection from a flat surface produces an image in the absence of absorption at the surface, there is no color difference between the original object and the image at large incidence/viewing angles, the specular reflection completely overwhelms any contribution of volume reflectance from within the water. in the vicinity of Brewster's angle specular reflection is strongly polarized.

2 Topic 2: Reflection 2 Diffuse Surface Reflectance Scattering (reflectance) from a rough surface (Two possible definitions) 1) Reflection from a surface that is rough compared to the optical wavelength. The definition of "rough" depends both on the wavelength and the incidence angle of the incoming light, i.e., a surface is smooth if Δh < (λ sec θ)/8 (Rayleigh criterion), where Δh is the characteristic height of the surface. 2) Non-directional reflectance (not image producing). Examples: Diffuse surface reflectance: 1) reflection from a wavy sea surface. 2) reflectance from a brushed metal surface. Volume Reflectance Reflectance originating within the interior of an object. Volume reflectance may be the result of internal reflections or scattering from the interior region. Absorption is often significant in volume reflectance. Examples: 1) reflection from within a water body. 2) reflection from the interior of a leaf. Surface vs. Volume reflectance Two views of optically deep water with a wavy surface: 1. At oblique angles, reflectance from the water surface dominates (note the apparent blue color of water). Brushed stainless steel 2. At vertical (nadir viewing), volume reflectance is more prominent (green color) although the surface reflectance is still apparent Virtually all the light is reflected diffusely at the surface. Scratched metal surface Surface (image) and volume (color) reflectance Surface (specular) reflection from smooth, glossy surface: image of the adjacent car little or no change in color of the reflected light. Volume reflectance from the pigmented underlayer: diffuse reflectance red due to broadband absorption of light by the paint pigment.

3 Topic 2: Reflection 3 Shadow information Find the parking space (lack of shadow is a clue) Find another parking space (a clue isn't proof) Reflectance The light source is in the direction (θ s, φ s ), and the detector is located at the viewing direction (θ v, φ v ). The specular direction is the direction that a level mirror surface would reflect light: (θs, 180º), with θs = θv. The retroreflection direction is the direction of exact backscatter. The phase angle, ξ, is the angle between the source and detector and is computed as: cos ξξ = cos θθ ss cos θθ vv + sin θθ ss sin θθ vv cos φφ vv Irradiance Reflectance is the ratio of the downwelling cosine irradiance, Eu, to the upwelling cosine irradiance, Ed: RR RRRR = EE uu EE dd This is also called the Albedo. It defines the ratio of total power reflected (scattered) by a surface to the total power incident on that surface. It ranges from [0,1]. There are two problems with this definition: 1) E is difficult to measure, 2) observations are generally looking in one direction. Remote Sensing Reflectance: RR RRRR = LL rr (θθ rr, φφ rr ) EE dd (ssrr 1 ) The ratio of upwelling radiance in the direction (θθ rr, φφ rr ) to the total downwelling irradiance. This is helpful it characterizes the viewing zenith angle but does not account for directional illumination or the direction of view relative to the source (sun).

4 Topic 2: Reflection 4 Directional Reflectance Schematic drawings of different types of scattering: BRDF - Bidirectional Reflectance Distribution Function The full reflectance distribution is described by the Bidirectional Reflectance Distribution Function (BRDF), which takes into account reflectance variations with both incidence and reflectance angles. BRDF = L R = E v d The ratio of the radiance reflected in the viewing direction (θθ vv, φφ vv ) from a surface, da, when the surface is illuminated by irradiance ccccccθ ss. EEdd = EE The BRDF includes both specular and diffuse components. zenith (incidence) angle, θ Note that the irradiance is assumed to be collimated radiation, EE, from direction θ ss. The sun is a highly collimated light source. We are ignoring sky irradiance for the moment. (Since sky radiance tends to be quite diffuse, reflectance due to sky radiance is also diffuse and generally non-directional.) For a mirror surface, the BRDF is essentially unidirectional in the specular reflectance direction. For most real surfaces reflection (BRDF) is a mixture of specular reflection diffuse surface reflection volume reflection. The BRDF varies with Solar angle (zenith & azimuth) Wavelength Target reflectance Target geometry

5 Topic 2: Reflection 5 Diffuse Reflectance SPECIAL CASE: Lambertian reflection Lambertian reflection is reflection from an ideally rough surface. For any uniform illumination of a surface, the reflected radiation is distributed isotropically (i.e., equal radiance in all directions). A Lambertian surface has the property that its reflectivity, ρ, equals its irradiance reflectance, R. BRDF lamb = L v /E d = ρ / π ρ = L v π / E d L v Ε θ s θ v L v A A' Ω Α LL vv = ΦΦ AA ΩΩ = ΦΦ = LL ccccccθθ AA ssssssθθ ΩΩ The Lambertian model works surprisingly well for near-nadir views and for mid-range sun angles (30-60 ). But what's really going on? Shadow: texture vs. color View of grass looking toward the sun: strong shadow component in reflectance texture differences are readily apparent View of grass looking away from the sun: minimal shadow component in reflectance color differences are much more noticeable.

6 Topic 2: Reflection 6 The issue of texture and brightness vs. color occurs even when shadowing is not obvious on the surface. Strong specular reflection loss of brightness and contrast when viewing away from the sun increase in brightness and contrast when viewing toward the sun. 16:30, 20 Oct 2005; Stennis Space Center, "Specular" component of diffuse surface reflection Strong forward scattering in the forward direction no image Forward scattering becomes more important at higher angles of incidence (i.e., as the zenith angle approaches 90 ) Color is primarily that of the illuminating radiation. Wolff, Nayar & Owen (1998) Int. J. of Computer Vision 30(1), 55 71

7 Topic 2: Reflection 7 Retroreflection: the opposition effect The opposition effect (or "dry heiligenschein" or the "hot spot") occurs as the result of the lack of shadows in the opposition direction. Apollo 17 astronaut Eugene Cernan photographs his own shadow cast on the coal black lunar surface December From the book Full Moon by Michael Light. Retroreflection / heiligenschein Heiligenschein on dewy grass presumably due to internal reflections and/or focusing by the water droplets. It only appears around the head of the observer. When Benvenuto Celline, the 16 th century Italian artist saw the halo about his head but not those of his companions he took it as a sign of his own genius. (Minnaert, 1974) Retroreflection / shadow hiding In the area just above the mountain shadows is the antisolar point, or opposition direction, there are no shadows and the reflectance is brighter on average than in adjacent areas where shadows are apparent. Spectroradiometer entrance slit diffraction i detector shutter View of Vie folding mirror lens Wavelength (µm)

8 Topic 2: Radiative Transfer 8 Remote Sensing reflectance: measurement Lv Remote Sensing Reflectance, Rrs, is defined as: Rrs = Ed Where Lv is the upwelling radiance from the target and Ed is the downwelling irradiance (skylight and sunlight). The actual measurements must be corrected by subtracting the dark current and gain at each wavelength. If it is not possible to measure E d directly, we measure the upwelling radiance from a diffusely reflecting target with a known reflectance, rs and use the Lambertian properties of the reflectance standard to determine the downwelling irradiance: Remote sensing reflectance using a single detector is then given by: R Example reflectance Spectra rs Lv Lv ρsg (Vt V dk) ρs(vt V dk) = = = = E πl πg (V V ) π(v V ) d s s dk s dk

9 Topic 2: Radiative Transfer 9 Polarization notation The direction of polarization is specified relative to the plane containing the incident, reflected and refracted rays. Plane containing the incident, reflected and refracted rays as well as the normal to the reflecting surface (dark plane). = perpendicular polarization (horizontal polarization) the electric field is perpendicular to the light colored plane. = parallel polarization (vertical polarization) the electric field is parallel to the light-colored plane Specular reflection (from non-absorbing media) is governed by Fresnel's Equations: rr = sin(θθ 1 θθ 2 ) sin(θθ 1 +θθ 2 ) rr = tan(θθ 1 θθ 2 ) tan(θθ 1 +θθ 2 ) θ 1 = angle of incidence = angle of reflection θ 2 = angle of refraction n = n 1 / n 2 (relative index of refraction of medium 1 to medium 2) Examples: 1) reflection from a calm water surface. 2) reflection from the surface of a waxy (glabrous) leaf. 3) reflection from a polished metal surface. Polarized reflectance & Brewster's Angle Brewster's Angle occurs when: rr = tan2 (θθ 1 θθ 2 ) tan 2 (θθ 1 + θθ 2 ) = 0 θθ 1 = tan 1 nn 2 /nn 1

10 Topic 2: Radiative Transfer 10 Thermal emission Viewing the water at Brewster's angle at 8-14 μ (thermal) Vicki Zanoni, Stennis Space Center μ-µwave reflectance and emissivity H Fr o For visible and IR radiation over water: r(0) = e(0) = For 3 cm microwaves r(0) = 0.61 e(0) = 0.39 V V n2/n1 =1.34 (water) H Br ew

11 Topic 2: Radiative Transfer 11 POLDER IMAGES POLarization and Directionality of the Earth's Reflectances Three consecutive images during a single orbit red =865 nm; green = 670 nm; blue = 443 nm. The polarized image is mainly blue because of polarization by molecular scattering in the 443 nm band. The ground surface has a very low contribution to the polarized signal. Sun glitter on the water surface generates a bright spot (A) on natural light images as well as a strong signal (B) on polarized images. The rougher the surface, the wider and less intense the glitter pattern. The backscatter area (C) is dark because polarization is close to zero when the scattering angle, γ = 180.