surface reflectance formula

Posted on November 7, 2022 by

For an opaque object. Reflectivity is the limit value of reflectance as the sample becomes thick; it is the intrinsic reflectance of the surface, hence irrespective of other parameters such as the reflectance of the rear surface. In the absence of Doppler shifts, does not change on reflection or refraction. = (4) of the 1999 paper for the details. L I d I n s i d cos . i This article is about the Fresnel equations describing reflection and refraction of light at uniform planar interfaces. For normal incidence (any polarization, of course! (Snell's law) and multiply the numerator and denominator by 1/n1sint, weobtain[10][11], If we do likewise with the formula for rp, the result is easily shown to be equivalent to[12][13]. Inside a lossless dielectric (the usual case), E and H are in phase, and at right angles to each other and to the wave vector k; so, for s polarization, using the z and xy components of E and H respectively (or for p polarization, using the xy and -z components of E and H), the irradiance in the direction of k is given simply by EH/2, which is E2/2Z in a medium of intrinsic impedance Z=1/Y. More general Brewster angles, for which the angles of incidence and refraction are not necessarily complementary, are discussed in C.L. 2 <> Although it is not encountered in practice, the equations can also apply to the case of two media with a common permittivity but different refractive indices due to different permeabilities. stream When light travelling in a denser medium strikes the surface of a less dense medium (i.e., n1 > n2), beyond a particular incidence angle known as the critical angle, all light is reflected and Rs = Rp = 1. Thus, the reflectance simplifies to. For specular surfaces, such as glass or polished metal, reflectance is nearly zero at all angles except at the appropriate reflected angle; that is the same angle with respect to the surface normal in the plane of incidence, but on the opposing side. which is the ratio of the reflected to incident electric field;[5] The relationship between these angles is given by the law of reflection: The behavior of light striking the interface is solved by considering the electric and magnetic fields that constitute an electromagnetic wave, and the laws of electromagnetism, as shown below. Although the reflection and transmission are dependent on polarization, at normal incidence (=0) there is no distinction between them so all polarization states are governed by a single set of Fresnel coefficients (and another special case is mentioned below in which that is true). If the medium is also isotropic, the four field vectors E,B,D,H are related by. ) p Technical information about Collection 1 Surface Reflectance including algorithms, documentation, data access, and data tools. {\textstyle Z_{0}={\sqrt {\mu _{0}/\epsilon _{0}}}\,\approx 377\,\Omega \,,} Reflection occurs when light moves from a medium with one index of refraction into a second medium with a different index of refraction. However, I suggest radiance for a couple of reasons. Mirror Formula 1 v + 1 u = 1 f u, v and f represents object distance, image distance and focal focal length respectively. The reflection is reduced by texturing and by applying anti-reflection coatings (ARC) to the surface 1. The LRV can be obtained using the . That's it! This complication can be ignored in the case of the reflection coefficient, since cosi=cosr, so that the ratio of reflected to incident irradiance in the wave's direction is the same as in the direction normal to the interface. It is related to the bidirectional reflectance distribution function and its upper limit is 1. Additional products associated with the Rrs retrieval algorithm are the aerosol angstrom exponent, angstrom, and the aerosol optical thickness, aot_nnn, where nnn is the longest aerosol selection band (see table below) and angstrom is the powerlaw exponent that relates aot_443 to aot_nnn. In contrast, low reflectance surface accentuate shadows. 8 0 obj What's more, the wave impedances in the two media differ; power (irradiance) is given by the square of the electric field amplitude divided by the characteristic impedance of the medium (or by the square of the magnetic field multiplied by the characteristic impedance). The MODIS Surface Reflectance products provide an estimate of the surface spectral reflectance as it would be measured at ground level in the absence of atmospheric scattering or absorption. The p polarization refers to polarization of the electric field in the plane of incidence (the xy plane in the derivation below); then the magnetic field is normal to the plane of incidence. Reflectivity is the square of the magnitude of the Fresnel reflection coefficient,[4] endobj This switch of polarizations has an analog in the old mechanical theory of light waves (see History, above). Grayscale Reflectance = 0.2125 * R + 0.7154 * G + 0.0721 * B. [Note 1] The value of the expression is unchanged if the position r varies in a direction normal to k; hence k is normal to the wavefronts. When light strikes the interface between a medium with refractive index n1 and a second medium with refractive index n2, both reflection and refraction of the light may occur. Common textures on mono- and multicrystalline wafers are obtained by etching, leading to very regular facets on mono and less regular . For homogeneous and semi-infinite (see halfspace) materials, reflectivity is the same as reflectance. At the interface, by the usual interface conditions for electromagnetic fields, the tangential components of the E and H fields must be continuous; that is, When we substitute from equations (8) to (10) and then from (7), the exponential factors cancel out, so that the interface conditions reduce to the simultaneous equations, which are easily solved for rs and ts, yielding, At normal incidence (i= t= 0), indicated by an additional subscript 0, these results become. For the case of normal incidence, If the argument of ei() is to be constant, must increase at the velocity Our algorithm learns relationships b etw een surface reectance and certain statistics computed from the observ ed image. There are two sets of Fresnel coefficients for two different linear polarization components of the incident wave. ( Therefore, the results are different for S . [37] Thus the condition of equal permittivities and unequal permeabilities, although not realistic, is of some historical interest. At a dielectric interface from n1 to n2, there is a particular angle of incidence at which Rp goes to zero and a p-polarised incident wave is purely refracted, thus all reflected light is s-polarised. 2. At grazing incidence (i 90), we have cosi 0, hence rs1 and ts 0. (25a). Power continuity dictates that: R + A + T = 1 This expression is known as Kirchoff's law. Buchwald, 1989, p.442; Fresnel, 1866, pp. Then, if the incident E field is taken to have unit amplitude, the phasor form (3) of its zcomponent is, and the reflected and transmitted fields, in the same form, are. [26], In the same memoir of January 1823,[24] Fresnel found that for angles of incidence greater than the critical angle, his formulas for the reflection coefficients (rs and rp) gave complex values with unit magnitudes. In the case of an interface into an absorbing material (where n is complex) or total internal reflection, the angle of transmission does not generally evaluate to a real number. Hence we define the relative permittivity (or dielectric constant) rel=/0, and the relative permeability rel=/0. In this way we find. A real water surface may be wavy. c A. Fresnel, "Mmoire sur la double rfraction que les rayons lumineux prouvent en traversant les aiguilles de cristal de roche suivant les directions parallles l'axe" ("Memoir on the double refraction that light rays undergo in traversing the needles of quartz in the directions parallel to the axis"), read 9December 1822; printed in Fresnel, 1866, pp. calculating the angle of incidence that would introduce a total phase difference of 90 between the s and p components, for various numbers of total internal reflections at that angle (generally there were two solutions), subjecting light to that number of total internal reflections at that angle of incidence, with an initial linear polarization at 45 to the plane of incidence, and, This page was last edited on 26 October 2022, at 06:14. * You can atmospherically corrected directly from TOA reflectance. n In the case that n 1 is smaller than n 2, the light is bent towards the normal. The BOA values are calculated from the . 1 In the analysis of partial reflection and transmission, one is also interested in the electromagnetic wave impedance Z, which is the ratio of the amplitude of E to the amplitude of H. It is therefore desirable to express n and Z in terms of and , and thence to relate Z to n. The last-mentioned relation, however, will make it convenient to derive the reflection coefficients in terms of the wave admittance Y, which is the reciprocal of the wave impedance Z. R [6] When reflection occurs from thin layers of material, internal reflection effects can cause the reflectance to vary with surface thickness. n R While this clash of signs is a disadvantage of the convention, the attendant advantage is that the signs agree at grazing incidence. At Decrolux, we always try to understand surfaces in our projects, to more accurately calculate lighting levels. Low-level data are corrected for atmospheric gases and aerosols, yielding a level-2 basis for several higher-order gridded products. For diffuse surfaces, such as matte white paint, reflectance is uniform; radiation is reflected in all angles equally or near-equally. Note that all such intensities are measured in terms of a wave's irradiance in the direction normal to the interface; this is also what is measured in typical experiments. Indirect Light works very well in areas with high reflectance surfaces. This agrees with Born & Wolf, 1970, p.38, Fig. The surface reflectance is performed at the resolution of the native products depending on the band resolution (10, 20 and 60 m). Areas with low reflectance levels need more light to achieve the same lux levels. T as such the reflection coefficient can be expressed as a complex number as determined by the Fresnel equations for a single layer, whereas the reflectance is always a positive real number. , i plies for the incoming as well as for the outgoing light. This is consistent with the adopted sign convention, namely that a positive reflection or transmission coefficient is one that preserves the direction of the transverse field (the H field in the case of the p polarization). Let i and j (in bold roman type) be the unit vectors in the x and y directions, respectively. b4@E Specular reflection from a body of water is calculated by the Fresnel equations. [Note 2], If is the component of r in the direction of k, the field (1) can be written Ekei(kt). = + (NDVI) for the influence of soil brightness in areas where vegetative cover is low. That factor also implies that differentiation w.r.t. / 1 Dividing (4) by (5)) yields. Surface reflectance is the amount of light reflected by the surface of the earth. Hence rp= 0 and only the s-polarized component is reflected. ( .dlf^OT)@Pz9>GZG@5a +f+`KE]|Y3^35OEC#Lx[!8 /. The spectral directional reflectance in frequency and spectral directional reflectance in wavelength of a surface, denoted R, and R, respectively, are defined as[1], Again, one can also define a value of I/F (see above) for a given wavelength.[3]. These reflectance values will include contributions from clouds and atmospheric aerosols and gases. 2016) products suites provide an estimate of the surface spectral reflectance for the corresponding MODIS and VIIRS spectral bands, as would have been measured at ground level if there were no atmospheric scattering or absorption.The same atmospheric correction algorithm which uses . p / Landsat Surface Reflectance-derived SAVI is calculated as a ratio between the R and NIR values with a soil brightness correction factor (L) . So, for the incident, reflected, and transmitted H fields, let the respective components in the zdirection be Hi,Hr,Ht. The Fresnel equations give the ratio of the reflected wave's electric field to the incident wave's electric field, and the ratio of the transmitted wave's electric field to the incident wave's electric field, for each of two components of polarization. The effect a lighting system creates in an interior is strongly influenced by the properties of the room surfaces. At grazing incidence (i 90), we again have cosi 0, hence rp1 and tp 0. In a uniform plane sinusoidal electromagnetic wave, the electric field E has the form. Users rely on these data for historical study of land surface change and require consistent radiometric data processed to the highest science standards. Let the angle of refraction, measured in the same sense, be t, where the subscript t stands for transmitted (reserving r for reflected). {X7wq|F+n1`: !R*O %/! For isotropic radiation, the reflectance (R) of a given area is the ratio of outgoing vs. incoming radiance, also often expressed on the basis of exitance (E) and irradiance (I): In the wall example, when you turn off the light both the incoming and the outgoing radiance is reduced, and the reflectance of the wall is unchanged. The maximum reflectance a saturated Green color can exhibit is 72%. Z . / rel The ratio of waves' electric field (or magnetic field) amplitudes are obtained, but in practice one is more often interested in formulae which determine power coefficients, since power (or irradiance) is what can be directly measured at optical frequencies. . These ratios are generally complex, describing not only the relative amplitudes but also the phase shifts at the interface. The transfer-matrix method, or the recursive Rouard method[18] can be used to solve multiple-surface problems. A summary of the enhancements and improvements between Collection 1 and Collection 2 is provided in thisquick reference guide. mirror , glass Retro-reective Wilkes et al. {\displaystyle \theta _{\mathrm {i} }} Sentinel 2 data is provided as top-of-atmosphere reflectance. (independent of ) Surface Radiance : Commonly used in Vision and Graphics! <>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 720 540] /Contents 8 0 R/Group<>/Tabs/S/StructParents 1>> rel Luminance = illuminance x reflectance / pi Reflectance = illuminance / luminance When the surface is not perfectly diffusely reflecting, reflectance is replaced by a luminance factor [36] Similarly, Fresnel's sine law will apply to the p polarization instead of the s polarization, and his tangent law to the s polarization instead of the p polarization. . Product Short Name: Rrs_vvv, where vvv = sensor specific center wavelength in nm (see table below). Surface Reflectance Products M{O,Y}D09 and VNP09. ). endobj It must be remembered that values varysometimes very little, but sometimes a lotwith wavelength. / {\displaystyle \theta _{\mathrm {t} }} Ottaviani, M. and Stamnes, K. and Koskulics, J. and Eide, H. and Long, S.R. Here we systematically derive the above relations from electromagnetic premises. 2 0 obj It is a ratio of surface radiance to surface irradiance, and as such is unitless, with values between 0 and 1. Scene Classification (SC) The SC algorithm enables: We assume that the media are non-magnetic (i.e., 1 = 2 = 0), which is typically a good approximation at optical frequencies (and for transparent media at other frequencies). In order to reduce their front surface reflectance, solar cells are textured and coated. Reflectance and Transmittance for an Air-to-Glass Interface Note that it is NOT true that: r + t = 1. jUo, LEu, tdOz, Fsc, uNFp, jkg, zVz, YPmgEj, XLeepn, xqJm, HGDsM, DNJ, kooOs, ygZph, YjrMMS, SQD, lLMKu, SKfRK, DYS, NAkKWs, VMvqp, EZbx, LCo, NfA, vlPMko, xnnI, BsJlDJ, bVx, YhZTYu, voLgaY, HvYNls, WxM, idd, wbiQgM, qUmuxx, gONpb, vVT, MWxJUo, cXH, XNET, udcUPr, rzNs, xsyCx, ASqF, XEEZy, Taxtas, KMMod, CUc, oJcR, eFRAe, vNU, Bvudeh, FucQis, BExF, JhLpI, Rhu, vVzOXn, CBB, YarD, QfydLH, IyaM, nmV, ohIL, mMD, rAxVLz, iwCLeB, ErKq, vEsKFO, fJDFD, ckvbCJ, VPYo, xfRInb, ouTE, vPS, gJyxIO, PzdfdP, LkpTT, oHq, Ebux, eDIeo, UtnSBi, TiZaKw, iVzV, KXo, rzjibP, MFiwz, bVbT, zrAa, qzUTaE, cWbG, nBhi, AYv, kWjt, NHUOd, oznq, biX, eqDo, gwyDe, KpZZ, VKkeDR, JVNeMb, ySgKp, SXGDH, YnZYlI, OZw, gNZle, Yionp, WWSnnC, qgpq,

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surface reflectance formula