Image Processing Reference
In-Depth Information
66
Chapter 6
5
3
5
3
D
r
D
r
2
2
σ
=
1 075
.
,
σ
=
0 141
.
.
(6.10)
TW
,
W
o
o
This shows that the variance is reduced by a factor of 93% through perfect tilt re-
moval.
The mirror may be able to perfectly compensate the global tilt in the system,
but there will be a lag in the time the sensor reads the wavefront, the angle is deter-
mined, and the corrective element is moved to complement the tilt. This introduces
a temporal error, known as the Greenwood frequency, based on the bandwidth of
the system and the speed of the atmosphere:
5
3
=
F
F
2
G
σ
temp
.
(6.11)
3
dB
Usually, the Greenwood frequency ranges up to a few hundred hertz. The band-
width or 3 dB point of the corrective element must also be able to respond at these
rates. The effect of the bandwidth of the mirror with the Greenwood frequency is
shown in Fig. 6.4.
If the tilt is measured using a quadrant-type wavefront sensor, the error associ-
ated with the centroiding is determined by
W
SNR D
3
πλ
gap
2
σ
=
,
(6.12)
C
16
(
)
effective
where
W
gap
is the spacing between the detector cells, SNR is the signal-to-noise ra-
tio, and
D
effective
is the sensing aperture when
r
0
> aperture and
r
0
when the aper-
ture is >
r
0
. The error associated with centroiding is shown in Fig. 6.5, which illus-
trates the effect of changing the cell gap for various apertures.
