Page 125 - Vibrational Spectroscopic Imaging for Biomedical Applications

Evanescent W ave Imaging 101

The depth over which this focus is maintained is given by z
40 . λ
z = (4.2)
n sin θ
2
2
1
Using values typical of an infrared microscope (e.g., sin θ = 0.6) in
air, d becomes ~ 2λ and z ~11λ. Neglecting "z" for the moment, if one
were to immerse the sample in germanium (n = 4.0), d could be
1
reduced to ~0.5λ, which is a significant improvement. Thus, for a
transmission measurement with the sample immersed between two
germanium hemispheres, one would expect a 4X improvement in
spatial resolution. However, when taking z into consideration, the
short wavelength limit (2.5 μm) dictates that the sample thickness be
less than 1.7 μm in order that the focused beam width is not degraded
when the radiation transmits through the sample. This thickness is
difficult to achieve via normal methods used to prepare thin tissue
sections. More problematic is that coupling of light through the hemi-
spheres becomes more difficult as the index increases. Carr and Lavalle
et al. demonstrated the benefits of transmission immersion infrared
3,4
microspectroscopy using two ZnSe hemispheres. However, in the
work of Lavalle, the method required Nujol oil to efficiently couple
light through the hemisphere/sample/ hemisphere interface.
A solution for many of these problems is to employ ATR reflection.
As depicted in Fig. 4.1, light from the objective is brought into the
−1
hemisphere beyond the critical angle [θ = sin (n /n )]. In
c sample hemisphere
doing so the light is internally reflected at the hemisphere/sample
interface. Although commonly referred to as “total internal reflection,”
a better term is frustrated internal reflection since some of the light
penetrates into the sample where it can undergo absorption. The
depth to which light penetrates into the sample is given by

λ
d = (4.3)
p π 2 θ − 21 /2
2 n (sin n ( / n ))
hemisphere sample hemisphere e
where n = refractive index of the sample
sample
n = refractive index of the internal reflection element
hemisphere
(IRE)
θ = incident angle of light coupled into the hemisphere
It should be noted that penetration depth is an arbitrary value,
which corresponds to the point where the electric field intensity drops
to 1/e of its value at the surface (interface). 5
Several major benefits arise from the use of the ATR configuration.
First, sample thickness is not an issue, since the penetration depth
over the range of wavelengths employed with the above parameters
is no greater than 2.2 μm. This limited path length through the sample
means that highly absorbing materials can be studied, as well as