![]() Incident and reflected beams travel in same medium same l hence we arrive at the law of reflection: True for any boundary point and time, so let’s take or hence, the frequencies are equal and if we now consider which means all three propagation vectors lie in the same plane Using diagram from Pedrotti3 boundary pointġ1 At the boundary point: phases of the three waves must be equal: Oscillating electric field y y x x Any polarization state can be described as linear combination of these two: “complex amplitude” contains all polarization infoġ0 Derivation of laws of reflection and refraction Plane of incidence: formed by and k and the normal of the interface plane k normalĨ Polarization modes (= confusing nomenclature!)Īlways relative to plane of incidence TE: transverse electric s: senkrecht polarized (E-field sticks in and out of the plane) TM: transverse magnetic p: plane polarized (E-field in the plane) M E E M perpendicular ( ), horizontal parallel ( || ), vertical E ![]() Y light is a 3-D vector field z x linear polarization circular polarizationħ …and consider it relative to a plane interface 5 T qi R T 0° ° ° ° Incidence angle, qi and the change in the phase upon reflectionĦ Let’s start with polarization… light is a 3-D vector field transmitted external reflection, R 1.0. We’ll also determine the fraction of the light reflected vs. Where c is the velocity of the propagating wave,ĥ and the change in the phase upon reflection Normal Law of reflection: qi qr n1 n2 Law of refraction “Snell’s Law”: qt Incident, reflected, refracted, and normal in same plane Easy to derive on the basis of: Huygens’ principle: every point on a wavefront may be regarded as a secondary source of wavelets Fermat’s principle: the path a beam of light takes between two points is the one which is traversed in the least timeģ Today, we’ll show how they can be derived when we consider light to be an electromagnetic waveĤ E and B are harmonic Also, at any specified point in time and space, Int J Comput Vis 24(2): 105–124Īdato Y, Vasilyev Y, Ben-Shahar O, Zickler T (2007) Toward a theory of shape from specular flow.1 Chapter 23: Fresnel equations Chapter 23: Fresnel equations Oren M, Nayar SK (1997) A theory of specular surface geometry. In: 2nd IEEE international conference on computer vision (ICCV 1988), Tampa, pp 394–403 J Opt Soc Am A 21:2004īlake A, Brelstaff G (1988) Geometry from specularities. Tan RT, Nishino K, Ikeuchi K (2004) Color constancy through inverse-intensity chromaticity space. In: 8th IEEE international conference on computer vision (ICCV 2001), Vancouver, pp 599–606 Nishino K, Zhang Z, Ikeuchi K (2001) Determining reflectance parameters and illumination distribution from a sparse set of images for view-dependent image synthesis. Healey G (1989) Using color for geometry-insensitive segmentation. Shafer S (1985) Using color to separate reflection components. IEEE Trans Pattern Anal Mach Intell 12(4):402–409 Lee H, Breneman E, Schulte C (1990) Modeling light reflection for computer color vision. Lambert JH (1760) Photometria sive de mensura de gratibus luminis., colorum et umbrae. Wolff LB, Nayar S, Oren M (1998) Improved diffuse reflection models for computer vision. Nayar SK, Fang XS, Boult T (1996) Separation of reflection components using color and polarization. IEEE Trans Pattern Anal Mach Intell 12(11):1059–1071 Wolff LB (1990) Polarization-based material classification from specular reflection. In: 9th IEEE international conference on computer vision (ICCV 2003), Nice, pp 982–987 ![]() Miyazaki D, Tan RT, Hara K, Ikeuchi K (2003) Polarization-based inverse rendering from a single view. IEEE Trans Pattern Anal Mach Intell 27(2):178–193 ![]() Tan RT, Ikeuchi K (2005) Separating reflection components of textured surfaces using a single image. Comput Graph 15:307–316īeckmann P, Spizzochino A (1963) The scattering of electromagnetic waves from rough surfaces. IEEE Trans Pattern Anal Mach Intell 13(7):611–634Ĭook R, Torrance K (1981) A reflectance model for computer graphics. Nayar S, Ikeuchi K, Kanade T (1991) Surface reflection: physical and geometrical perspectives. Torrance K, Sparrow E (1966) Theory for off-specular reflection from roughened surfaces.
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