Biomedical Engineering Reference
In-Depth Information
Absolute mean 20
×
Absolute mean 40
×
0.04
0.05
0.02
0
0
0
10
Zernike mode
(a)
20
0
10
Zernike mode
20
(c)
RMS 20
×
RMS 40
×
0.04
0.02
0.02
0
0
0
10
Zernike mode
20
0
10
Zernike mode
20
(b)
(d)
FIGuRE 17.11
Zernike.statistical.data.for.the.measurements.in.
Table.17.1
.
.(a).and.(b).he.mean.of.the.absolute.
value.and.the.RMS.values.for.each.Zernike.mode.for.the.20×.objective.(0.40.NA),.respectively..(c).and.(d).he.mean.
of.the.absolute.value.and.the.RMS.values.for.each.Zernike.mode.for.the.40×.objective.(0.75.NA),.respectively.
was.10.ms.apart..Each.correction.was.done.using.the.light.coming.from.a.single.bead.to.directly.measure.
the.wavefront..he.measurement.was.then.fed.back.to.the.DM.by.using.a.proportional.gain.of.0.4,.which.
was.the.highest.possible.gain.for.this.sample.before.the.onset.of.oscillations.(Lyapunov.stability.criteria).
(Slotine.&.Li.1991)..he.AO.loop.gain.can.be.described.by.the.feedback.equation
W s
KD s G s
( )
( ) ( )
.
.
.
(17.6)
E s W s D s W s H s
( )
( )
( )
( )
( )
=
−
=
=
1
+
where.
E
(
s
).is.the.wavefront. error.measured.by.the.wavefront. sensor,.
W
(
s
).is.the.Fourier.transform.of.
the. input. wavefront. coming. from. the. sample,.
H
(
s
). is. the. transfer. function. of. the. AO. system,.
G
(
s
). is.
the. transfer. function. of. wavefront. sensor,.
D
(
s
). is. the. transfer. function. of. the. DM,. and.
K
. is. the. gain.
on.the.feedback.loop.(0.4)..he.goal.of.the.AO.system.is.to.reduce.the.diference.between.the.applied.
phase.on.the.mirror.and.the.incoming.wavefront,.the.error.
E
(
s
),.thus.lattening.the.wavefront.(Hardy.
1998;.Poyneer,.Gavel,.&.Brase.2002)..In.AO,.DM.correction.usually.requires.a.gradual.change.in.shape.
to. account. for. the. nonlinearity. of. the. wavefront. sensor. and. the. DM.. his. comes. about. mainly. due.
to. the. nonlinear. efects. of. the. DM. and. secondly. (usually. much. smaller). due. to. the. nonlinear. efects.
of. the. SHWF. sensor.. he. nonlinear. efects. of. the. DM. come. from. the. nonlinear. dependence. of. the.
electrostatic. actuation. force. on. the. applied. voltage. and. plate. separation. for. a. parallel. plate. actuator.
and.the.nonlinear.restoring.force.from.stretching.of.both.the.mechanical.spring.layer.and.the.mirror.
surface..
Figure 17.12a
.shows.the.original.PSF.of.the.microsphere.before.correction.taken.with.the.sci-
ence.camera..
Figure 17.12b
.
shows.the.result.of.correcting.for.40%.of.the.measured.wavefront.error.in.
Figure 17.12a
.
.hese.steps.were.repeated.until.there.was.no.additional.signiicant.reduction.in.wavefront.
error.(i.e.,.<7.nm)..
Figure.17.12e
.demonstrates.the.results.of.correcting.the.wavefront.ater.four.steps.
in. the. AO. loop.. Each. image. has. been. normalized. to. its. own. maximum. to. clearly. show. the. details. of.
the. PSF.. he.bar. in.
Figure 17.12c
.
is. approximately. equal.to. the. difraction. limit. of. the. 40×. objective,.
0.45 μm..he.improvement.in.Strehl.was.approximately.10×..he.relative.Strehl.ratio.
S
.was.obtained.by.
measuring.the.peak.intensity.in.
Figure.17.12a
.
divided.by.the.peak.intensity.in.
Figure.17.12e
.using.the.
same.integration.time.Δ
t
.for.each,.as.shown.in.Equation.17.7:
