Image Processing Reference
In-Depth Information
Performance
65
2
1
2
)
(
2
(
2
)
−
σ
S
=−
1
σ
≈
e
.
(6.5)
p
p
In the case of a long exposure, the core diameter is give by Eq. 6.6 and the peak in-
tensity is shown in Eq. 6.7:
1
2
2
λ
D
2
a
=
122
.
1 517
+
.
σ
α
(6.6)
D
λ
and
(
2
)
−σ
e
p
(6.7)
S
=
,
2
D
2
1517
+
.
σ
α
λ
σ
α
is the mean-square angular tilt and
D
is the aperture diameter. Note that in
Eq. 6.7, when the tilt value is set to zero, this returns to the form of the extended
Marechal approximation.
where
6.4 Performance Evaluation
An evaluation of the performance of the image-stabilization system relies on deter-
mining the uncorrelated individual error sources in the wavefront phase. This is
given as a summation of the individual errors:
2
2
σ
=∑
σ
i
.
(6.8)
phase
The sum of these errors can then be transformed into the Strehl ratio using the ex-
tended Marechal approximation.
In determining the phase error, the fitting error, temporal error, isoplanatic er-
ror, and the error due to sensor noise need to be considered in detail. That summa-
tion can be written explicitly as
2
2
2
2
2
σ
=
σ
+
σ
+
σ
+
σ
+
others .
(6.9)
system
fitting
temporal
isoplanatic
senso
rnoise
The fitting error of a tip-tilt mirror will be very poor if there is any corrugation in
the wavefront. As a result, it will only remove the global tilt from the image. The tilt
included and removed variances are given as
