Walsh's Analytic Solution for R1
The integral of the first moment of the Fresnel reflection R1 has been
found analytically by Walsh, (see [53,54])
| R1Walsh |
= |
![$\displaystyle {1\over2}+{(m-1)(3m+1)\over 6(m+1)^2}
+\left[ {m^2(m^2-1)^2\over (m^2+1)^3} \right]
\ln{m-1\over m+1}$](img671.gif) |
|
| |
- |
![$\displaystyle {2m^3(m^2+2m-1)\over (m^2+1)(m^4-1)}
+ \left[{8m^4(m^4+1)\over (m^2+1)(m^4-1)^2}\right]\ln m$](img672.gif) |
(B41) |
where Walsh's parameter m is the reciprocal of the index of refraction
ratio in Equation (B.2) that is, m=1/n=nt/ni. Equation
(B.41) was used as a check on the numerical integration of
R1. Equation (B.41) is only valid when ni<nt then
Equation (B.14) should be used.
|
