Chemistry Reference
In-Depth Information
but different phases. They interfere at the power detector. The phase difference is
given by
z
2
2
k
p
(
)
dz
.
ϕ
=
2ϕ
1
(
ω
1
)
−
ϕ
2
(
2ω
1
)
=
ω
)
−
k
p
(
2ω
(6.15)
z
1
It does not contain any path length and is insensitive to length variations. Phase
fluctuations from length variations cancel at the detector and need not to be measured
as necessary in the two-color interferometer. While mainly applied at high probing
frequencies in the FIR and IR with laser interferometers [116], the basic two-color
interferometer method is also applied at mm wavelengths [118].
6.2.4.3 Steady State Operation
Under long plasma pulse and steady state conditions high stability of the interferom-
eter system is required. Phase changes are measured only during the plasma buildup
and can reach many multiples of 2π. Interruption of the signal path destroys the infor-
mation. Recovery is only possible at fixed probing frequency for plasma phase shift
within
−
≤
≤
2π. By varying the probing frequency, however, the line density
can be determined in plasma columns existing prior to the interferometer operation.
Referring to (6.10), the frequency variation with rate
2π
ϕ
∂
ω
/∂
t
introduces a phase
variation or beat frequency, respectively, given by
ω
dz
,
z
2
∂
ϕ
∂
t
=
∂
ω
∂
L
∂
k
∂
k
p
ω
+
(6.16)
t
∂
∂
z
1
where
L
is as before the net difference in waveguide length between the plasma and
the reference paths. The frequency is swept at constant rate giving rise to a constant
beat frequency. All information on plasma density is contained in the change of the
beat frequency, compared to the vacuum case, from which the line density can be
determined [121].
6.2.4.4 Components
To measure the phase shift ϕ of the probing wave the IF section of the interferometer
contains a phase measuring device. At probing frequencies in the 100 GHz range of
frequencies ϕ typically exceeds multiples of 2π which the phase meter must be able
to handle. Electronic circuits exist separating the ranges
2π and counting
multiples of 2π. It is especially important that during rapid changes the phase meter
is able to follow to avoid so-called fringe losses, errors in counting multiples of 2π
[122,123]. The temporal resolution τ of the interferometer is generally limited by the
IF frequency τ
−
2π
≤
ϕ
≤
>
2π
/
ω
IF
. For a given rate of phase change
ϕ
/
t
the IF bandwidth
around ω
IF
needs to have at least a bandwidth of [111]:
ω
IF
=
ϕ
/
t
. As signal
sources different types can be used
1. Sources including active semiconductor elements such as Gunn diodes
or IMPATT (impact ionization avalanche transit time diode) elements.
