150
A. Saha
with a terahertz beam which is focused at the plane of a sample. In the following
subsections, THz reflection, transmission and conductivity imaging are discussed.
3.2.1 Reflection Spectroscopy
Here, an explanation is given about how the complex sample refractive index can
be extracted by interpreting the complex reflection data. A collimated THz beam is
assumed. However, the same algorithm can also be used with minor modifications
for THz beams which are focused and used for imaging every point. A sample with
thickness l (media 3) and characterized by complex refractive index ˜
n 3 is considered
[34], which is located behind media 1 and 2, characterized by complex refractive
indices ˜
n 1 and ˜
n 2 , respectively. It is assumed that probing terahertz wave is incident
normally.
The equations for normalized reflection function (depending on polarization of
the collimated THz beam as well as incidence angle) can be derived using Eq. (1).
A schematic of reflection spectroscopy experimental set-up is illustrated in Fig. 4a.
A window having thickness l (media 2) is placed in air (media 1), and the sample
for which the study (media 3) is to be done is placed behind the window. Both THz
emitter and receiver are assumed to be on the same side and a THz beam is incident
normally on the sample. This set-up has been used to characterize liquids in plastic
bottles [35–39]. For sufficiently thick window, the traces reflected from air–window
interface, E aw (ω), and that reflected from window–sample interface, E ws (ω), can be
separated in time domain. In this case for the window neglecting the Fabry–Perot
effect, the normalized function for reflection can be written as
S r (ω) =
E ws (ω)
E aw (ω)
=
t 12 r 23 t 21
r 12
exp
−
i ˜
n 2 ωl
c
=
4 ˜
n 1 ˜
n 2
˜
n 2
1 ˜
n 2
2
exp
−
i ˜
n 2 ωl
c
˜
n 2 − ˜
n 3
˜
n 2 + ˜
n 3
(2)
Media 2 Media
Media 1 Media 2 Media 3
(air)
(window) (sample)
(air)
(sample)
(air)
l
l
(a)
(b)
Fig. 4 Schematic experimental set-ups for measurements of a reflection and b transmission
coefficients
A. Saha
with a terahertz beam which is focused at the plane of a sample. In the following
subsections, THz reflection, transmission and conductivity imaging are discussed.
3.2.1 Reflection Spectroscopy
Here, an explanation is given about how the complex sample refractive index can
be extracted by interpreting the complex reflection data. A collimated THz beam is
assumed. However, the same algorithm can also be used with minor modifications
for THz beams which are focused and used for imaging every point. A sample with
thickness l (media 3) and characterized by complex refractive index ˜
n 3 is considered
[34], which is located behind media 1 and 2, characterized by complex refractive
indices ˜
n 1 and ˜
n 2 , respectively. It is assumed that probing terahertz wave is incident
normally.
The equations for normalized reflection function (depending on polarization of
the collimated THz beam as well as incidence angle) can be derived using Eq. (1).
A schematic of reflection spectroscopy experimental set-up is illustrated in Fig. 4a.
A window having thickness l (media 2) is placed in air (media 1), and the sample
for which the study (media 3) is to be done is placed behind the window. Both THz
emitter and receiver are assumed to be on the same side and a THz beam is incident
normally on the sample. This set-up has been used to characterize liquids in plastic
bottles [35–39]. For sufficiently thick window, the traces reflected from air–window
interface, E aw (ω), and that reflected from window–sample interface, E ws (ω), can be
separated in time domain. In this case for the window neglecting the Fabry–Perot
effect, the normalized function for reflection can be written as
S r (ω) =
E ws (ω)
E aw (ω)
=
t 12 r 23 t 21
r 12
exp
−
i ˜
n 2 ωl
c
=
4 ˜
n 1 ˜
n 2
˜
n 2
1 ˜
n 2
2
exp
−
i ˜
n 2 ωl
c
˜
n 2 − ˜
n 3
˜
n 2 + ˜
n 3
(2)
Media 2 Media
Media 1 Media 2 Media 3
(air)
(window) (sample)
(air)
(sample)
(air)
l
l
(a)
(b)
Fig. 4 Schematic experimental set-ups for measurements of a reflection and b transmission
coefficients