Biomedical Engineering Reference
In-Depth Information
Light from
telescope
Adaptive
mirror
Distorted
wavefront
Beam splitter
Control
system
Corrected
wavefront
High-resolution
camera
Wavefront
sensor
FIGuRE 8.10
Astonomical.AO.system..Light.with.a.distorted.wavefront.enters.a.telescope.and.is.relected.of.of.
an.adaptive.mirror..Part.of.the.light.is.relected.from.a.beam.splitter.and.enters.a.wavefront.sensor.that.generates.
correction.signals.for.a.control.system.for.the.adaptive.mirror..he.other.part.of.the.light.with.a.corrected.wave-
front.passes.through.the.beam.splitter.and.is.imaged.onto.a.high-resolution.camera..(Credit:.Lawrence.Livermore.
National.Laboratory.and.NSF.Center.for.Adaptive.Optics.)
(Kolmogorov.1941)..he.structure.function.that.relates.the.mean-square.velocity.diference.between.two.
points.in.space.that.are.separated.by.a.displacement.vector.
r
.is.given.by
(
)
−
( )
2
.
D
=
v r
+
r
v r
v
r
1
r
1
he.coherence.length.is.called.the.Fried's.parameter.
r
0
,.or.the.“seeing.cell.size”.over.which.the.overall.
wavefront.distortion.is.limited.to.a.uniform.tilt,.and.is.deined.as.the.maximum.diameter.of.a.collector.
that.is.allowed.before.atmospheric.distortion.seriously.limits.performance.(Fried.March.1965a,.1965b,.
1966).. he. phase. structure. function,. which. describes. the. expected. variance. in. the. refractive. index.
between.two.points,.for.Kolmogorov.turbulence.for.plane.waves.is.given.as
5 3
r
r
.
D
∅
=
6 88
.
0
he.coherence.length.
r
0
.sets.the.number.of.degrees.of.freedom.of.an.astronomical.AO.system.(
Figure.8.11
)
..
he.primary.mirror.of.the.telescope,.with.diameter.
D
,.is.divided.into.“sub-apertures”.of.diameter.
r
0
..he.
number.of.subapertures.is.approximately.(
D
/
r
0
)
2
,.where.
r
0
.is.evaluated.at.the.desired.observing.wavelength..A.
typical.range.for.the.coherence.length.might.be.10-100.cm..he.largest.telescope.to.date,.the.Keck.Telescope.
on.the.peak.of.Mauna.Kea,.has.a.diameter.
D
.=.10.m,.so.that.the.number.of.degrees.of.freedom.required.for.
the.DM.is.on.the.order.of.100-10,000.depending.on.the.coherence.length.
A.DM.for.correcting.wavefront.aberrations.will.have.residual.wavefront.itting.error.depending.on.
the.type.of.DM.that.is.used.(Hardy.1998)..he.mean.square.“itting.error”.for.Kolmogorov.turbulence.
is.given.by
5 3
d
r
σ
F
2
=
a
rad
2
F
0
.
