Total internal reflection microscopy

Total internal reflection of light occurs at the interface between materials of differing indices of refraction at incident angles greater than the critical angle, ${\displaystyle \theta _{c}}$, where

${\displaystyle \theta _{c}=\sin ^{-1}(n_{2}/n_{1})}$

and ${\displaystyle n_{1}}$ is the index of the incident medium and ${\displaystyle n_{2}}$ the index of the transmission medium and ${\displaystyle \theta _{c}}$ is measured from the normal to the interface.

Under conditions of total internal reflection, the electromagnetic field in the transmission medium takes on the form of an evanescent wave, whose intensity ${\displaystyle I(z)}$ decays exponentially with distance from the interface such that,

${\displaystyle I(z)=I_{0}e^{-\beta z}}$

with ${\displaystyle \beta ={\frac {4\pi }{\lambda }}{\sqrt {(n_{1}\sin(\theta ))^{2}-n_{2}^{2}}}}$. For practical purposes, the transmission medium is often chosen to be a fluid—usually water—in which a microscopic object can be immersed. The object, when brought close to the interface, is expected to scatter light proportional to the intensity of the field at its height, ${\displaystyle z}$.^[1] Since the penetration depth of the evanescent field is on the order of hundreds of nanometers, this technique is among the most sensitive for tracking displacements in the direction perpendicular to a surface.^[2]