Biomedical Engineering Reference
In-Depth Information
TABlE 8.1
Fitting.Error.Coeicient.for.Various.Types.of.Deformable.Mirrors
Coniguration
Coeicient
Actuators/Segment
Piston.only.(square.segments)
1.26
1
Piston.only.(circular.segments)
1.07
1
Piston.plus.tilt.(square.segments)
0.18
3
Piston.plus.tilt.(circular.segments)
0.14
3
Continuous.facesheet
0.28
1
Source:
. Hardy.1998.
square.segments.will.require.3(0.18/0.28)
6/5
.=.1.8.times.more.actuators..he.factor.of.3.is.because.a.pis-
ton.plus.tilt.mirror.requires.three.actuators.per.segment.to.achieve.the.tilting.motion.
In.addition.to.itting.error,.other.considerations.for.DMs.include.the.stroke.and.pitch.of.the.mirror,.
the. inluence. function. between. actuators,. and. the. response. time. that. sets. the. temporal. bandwidth..
he.stroke.of.mirror.is.the.magnitude.of.displacement.of.the.mirror.surface.that.can.be.obtained..he.
required.stroke.will.depend.on.the.magnitude.of.the.wavefront.aberrations.that.are.required..In.astron-
omy,.several.micrometers.are.required.for.the.10.m.Keck.telescope..As.the.telescope.diameter.increases,.
and.it.images.more.of.the.sky,.the.magnitude.of.correction.that.is.required.increases..he.required.mir-
ror.stroke.is.given.by
5 6
D
r
.
Stroke
=
(
)( )(
)
0 5 5 1 2
.
.
µ
0
he.factor.of.0.5.arises.because.the.wavefront.phase.is.twice.the.surface.phase.of.the.mirror..he.fac-
tor.of.5.is.from.the.number.of.RMS.standard.deviations.of.the.wavefront.error.that.must.be.corrected..
he. factor. of. 1.2. is. to. account. for. ≈20%. of. the. mirror. stroke. that. must. be. used. to. latten. the. mirror..
he.itting.coeicient,.μ,.depends.on.the.type.of.mirror.that.is.being.used.and.is.listed.in.Table.8.1..he.
stroke.speciications.for.the.30.m.telescope.that.is.currently.being.designed.calls.for.10-15.μm.of.stroke..
Vision.science.applications.also.require.10-20.μm.of.stroke,.where.the.stroke.requirements.depend.on.
the.population.of.the.subjects.that.are.corrected.
he.pitch.of.the.mirror,.or.the.spacing.between.actuators.
d
,.is.determined.by.the.root-mean-square.
itting.error.σ.for.light.with.a.wavelength.λ:
5 6
=
λ
d
r
.
σ
µ
f
2
π
0
he. early. DMs. used. in. astronomy. had. piezoelectric. actuators. with. an. inter-actuator. spacing. of.
5-7.mm,.resulting.in.large.mirror.when.a.large.number.of.actuators.are.required..he.trend.is.toward.
a.smaller.pitch.of.1.mm.and.a.higher.actuator.count..he.30.m.telescope.requires.an.array.of.100.×.100.
actuators.(10,000).
he.inluence.function.between.actuators.is.determined.by.how.much.the.mirror.surface.moves.at.a.
neighboring.site.when.an.actuator.is.“poked.”.A.segmented.mirror.will.have.no.coupling.between.actua-
tors.since.the.mirror.segments.are.independent,.while.a.continuous.facesheet.mirror.will.have.on.the.order.
of.20%.inluence.since.the.actuators.are.coupled.through.the.facesheet..his.coupling.needs.to.be.com-
prehended.in.the.sotware.that.is.used.to.control.the.mirror..Finally,.the.response.time.of.the.mirror.will.
determine.the.temporal.bandwidth.that.the.mirror.is.capable.of.correcting..In.astronomy,.this.is.deter-
mined.by.the.temporal.coherence.time.τ
0
,.the.timescale.over.which.atmospheric.variations.can.be.consid-
ered.to.be.static..his.is.given.by.the.coherence.length,.
r
0
,.divided.by.the.average.wind.velocity,.<
v
>,.in.a.
layer.of.the.atmosphere,.τ
0
.=.
r
0
/<
v
>..For.
r
0
.=.10.cm,.<
v
>.=.10.m/s,.the.coherence.time.τ
0
.would.be.10.ms.
