fresnel

typhon.physics.fresnel(n1, n2, theta1)

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

$$r=|R{|}^2$$

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

$$n=\sqrt{ϵ}$$

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.

Parameters:

• n1 (float or ndarray) – Refractive index for medium of incoming radiation.

• n2 (float or ndarray) – Refractive index for reflecting medium.

• theta1 (float or ndarray) – Angle between surface normal and incoming radiation [degree].

Returns:

Reflection coefficient for vertical polarisation, reflection coefficient for horisontal polarisation.

Return type:

float or ndarray, float or ndarray