FRESNEL Fresnel formulas for surface reflection The amplitude reflection coefficients for a flat surface can also be calculated (Rv and Rh). Note that these are the coefficients for the amplitude of the wave. The power reflection coefficients are obtained as r = abs(R)^2 The expressions used are taken from Eq. 3.31 in "Physical principles of remote sensing", by W.G. Rees, with the simplification that that relative magnetic permeability is 1 for both involved media. The theta2 angle is taken from snell.m. The refractive index of medium 2 (n2) can be complex. The refractive index and the dielectric constant, epsilon, are releated as n = sqrt(epsilon) No expression for theta2 that allows *n1* to be complex has been found. If theta2 is found to be complex, it is returned as NaN. This can happen when n1 > n2, and corresponds to a total reflection and there is no transmitted part. Rv and Rh are here set to 1. FORMAT [Rv,Rh,theta2] = fresnel(n1,n2,theta1) OUT Rv Reflection coefficient for vertical polarisation. Rh Reflection coefficient for horisontal polarisation. theta2 Angle for transmitted part. IN n1 Refractive index for medium of incoming radiation. n2 Refractive index for reflecting medium. theta1 Angle between surface normal and incoming radiation.

- rqre_nargin RQRE_NARGIN Checks if minimum number of input arguments is reached
- constants CONSTANTS Phyiscal and math constants
- snell SNELL Snell's law

0001 % FRESNEL Fresnel formulas for surface reflection 0002 % 0003 % The amplitude reflection coefficients for a flat surface can also be 0004 % calculated (Rv and Rh). Note that these are the coefficients for the 0005 % amplitude of the wave. The power reflection coefficients are 0006 % obtained as 0007 % 0008 % r = abs(R)^2 0009 % 0010 % The expressions used are taken from Eq. 3.31 in "Physical principles of 0011 % remote sensing", by W.G. Rees, with the simplification that that relative 0012 % magnetic permeability is 1 for both involved media. The theta2 angle is 0013 % taken from snell.m. 0014 % 0015 % The refractive index of medium 2 (n2) can be complex. The refractive 0016 % index and the dielectric constant, epsilon, are releated as 0017 % 0018 % n = sqrt(epsilon) 0019 % 0020 % No expression for theta2 that allows *n1* to be complex has been found. 0021 % 0022 % If theta2 is found to be complex, it is returned as NaN. This can happen 0023 % when n1 > n2, and corresponds to a total reflection and there is no 0024 % transmitted part. Rv and Rh are here set to 1. 0025 % 0026 % FORMAT [Rv,Rh,theta2] = fresnel(n1,n2,theta1) 0027 % 0028 % OUT Rv Reflection coefficient for vertical polarisation. 0029 % Rh Reflection coefficient for horisontal polarisation. 0030 % theta2 Angle for transmitted part. 0031 % 0032 % IN n1 Refractive index for medium of incoming radiation. 0033 % n2 Refractive index for reflecting medium. 0034 % theta1 Angle between surface normal and incoming radiation. 0035 0036 % 2004-04-30 Created by Patrick Eriksson. 0037 0038 0039 function [Rv,Rh,theta2] = fresnel(n1,n2,theta1) 0040 % %&% 0041 rqre_nargin( 3, nargin ); %&% 0042 % Checks done in snell.m are not repeated %&% 0043 if imag(n1)<0 | imag(n2)<0 %&% 0044 error( 'The imaginary part of *n1* and *n2* can not be negative.' ); %&% 0045 end %&% 0046 0047 0048 theta2 = snell( n1, n2, theta1 ); 0049 0050 DEG2RAD = constants('DEG2RAD'); 0051 0052 costheta1 = cos( DEG2RAD * theta1 ); 0053 costheta2 = cos( DEG2RAD * theta2 ); 0054 0055 Rv = (n2.*costheta1-n1.*costheta2)./(n2.*costheta1+n1.*costheta2); 0056 Rh = (n1.*costheta1-n2.*costheta2)./(n1.*costheta1+n2.*costheta2);

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