absorbing_glass_RT

iadpython.fresnel.absorbing_glass_RT(n_i, n_g, n_t, nu_i, b)[source]

Reflection and transmission of an absorbing slide.

Calculates the total specular reflection and transmission (i.e., including multiple internal reflections) based on the indices of refraction of the incident medium ‘n_i’, the glass ‘n_g’, and medium into which the light is transmitted ‘n_t’ for light incident at an angle from the normal having cosine ‘nu_i’. The optical thickness of the glass b = nu_a d is measured normal to the glass.

This routine was generated to help solve a problem with the inverse adding-doubling program associated with samples with low absorbances. A particular situation (in the IR) arises when the slides have significant absorption relative to the sample absorption. Anyway, it is not hard to extend the result for non-absorbing slides to the absorbing case

\[r = r_1 + \frac{(1-r_1)^2 r_2 e^{-2b/\nu_g}}{1 - r_1 r_2e^{-2b/\nu_g}}\]

Here r_1 is the reflection at the sample-glass interface and r_2 is the reflection at the glass-air interface and nu_g is the cosine of the angle inside the glass. Note that if b≠0 then the reflection depends on the order of the indices of refraction, otherwise ‘n_i’ and ‘n_t’ can be switched and the result should be the same.

The corresponding result for transmission is

\[t = \frac{(1-r_1)(1-r_2)e^{-b/\nu_g}} {1 - r_1 r_2e^{-2b/\nu_g}}\]

There are two potential pitfalls in the calculation. The first is when the angle of incidence exceeds the critical angle then the formula causes division by zero. If this is the case, ‘Fresnel’ will return r_1 = 1 and this routine responds appropriately. The second case is when the optical thickness of the slide is too large.

I don’t worry too much about optimal coding, because this routine does not get called all that often and also because ‘Fresnel’ is pretty good at avoiding unnecessary computations. At worst this routine just has a couple of extra function calls and a few extra multiplications.

Parameters:

  • n_i – index of medium from which light is incident

  • n_g – index of glass

  • n_t – index of slab

  • nu_i – cosine of angle of incidence (in n_i)

  • b – optical thickness of glass

Returns

r, t: unscattered reflectance(s) and transmission(s)