Biomedical Engineering Reference
In-Depth Information
Once.the.values.of.α
i,j
.have.been.found.for.a.particular.sensorless.AO.system,.it.is.a.simple.mathemati-
cal.procedure.to.obtain.a.new.set.of.orthogonal.modes.that.are.optimal.for.that.system.
10.11 conclusion
We.have.explained.the.motivation.behind.sensorless.AO.based.on.modal.wavefront.sensing,.described.
the.basic.principles.of.the.approach,.and.provided.an.outline.of.its.mathematical.basis..We.presented,.
in.particular,.a.method.using.sequential.quadratic.maximization,.which.has.already.proven.to.be.efec-
tive.in.a.range.of.adaptive.microscopes..Central.to.this.approach.is.the.choice.of.aberration.expansion.
in.terms.of.modes.that.are.orthogonal,.where.the.deinition.of.orthogonality.depends.on.the.imaging.
properties.of.the.microscope.and.the.optimization.metric..his.means.that,.in.general,.diferent.sets.of.
optimum.modes.are.required.for.diferent.adaptive.microscopes.
he.sensorless.adaptive.schemes.are.designed.to.be.specimen-independent..Although.the.value.of.the.
optimization.metric.depends.on.both.the.aberrations.and.the.specimen.structure,.the.orthogonal.form.
of.the.metric.function.does.not.change.if.the.aberration.modes.are.appropriately.chosen..As.explained.
in.
Section.10.5
,.the.coeicients.of.the.metric.function.depend.on.factors.such.as.specimen.structure,.
illumination.intensity,.and.detection.eiciency..his.means.that.the.width.of.the.parabolic.function.can.
change.between.diferent.specimens.and.image.settings..However,.the.metric.function.retains.the.neces-
sary.form.that.permits.independent.optimization.of.each.aberration.mode.
It.should.be.emphasized.that.once.the.optimum.modes.have.been.determined,.the.aberration.mea-
surement. and. correction. process. is. fast,. limited. only. by. the. rate. at. which. images. can. be. acquired..
Calculations. are. not. usually. the. speed-limiting. factor,. as. neither. the. evaluation. of. the. quality. metric.
nor.the.maximization.calculation.of.Equation.10.4.is.time-consuming.
For.the.purposes.of.live.specimen.imaging,.it.is.also.important.to.consider.the.cumulative.exposure.
during. the. correction. process.. When. using. an. image. quality. metric. such. as. total. intensity,. the. value.
is.averaged.across.the.large.number.of.image.pixels..It.follows.that.the.image.quality.required.for.this.
measurement.could.be.considerably.lower.than.that.required.in.the.inal.image..he.sequence.of.images.
used.for.the.aberration.correction.process.can.be.acquired.at.higher.frame.rates.and.lower.illumination.
intensity.than.would.normally.be.required.for.imaging..As.an.example,.it.was.shown.by.Débarre.et.al..
(2009).in.an.adaptive.two-photon.microscope.that.the.total.cumulative.energy.dose.during.correction.
was.only.twice.the.energy.dose.used.in.the.inal.image.acquisition.
Eicient.optimization.algorithms.are.not.limited.to.the.sequential.quadratic.maximization.approach.
explained.here..In.some.systems,.it.is.possible.to.determine.the.aberrations.using.fewer.measurements..
For.example,.it.has.been.shown.that.the.system.in
.
Section.10.7
.
actually.requires.only.
N
.+.1.measure-
ments.to.ind.
N
.modal.coeicients.(Booth.2006)..As.it.is.based.on.the.approximation.of.Equation.10.11,.
the.method.is.limited.in.the.range.of.aberration.amplitudes.that.can.be.corrected..When.the.aberration.
amplitude.lies.near.but.outside.of.this.range.of.approximation,.the.method.still.provides.rapid.conver-
gence,.but.extra.iterations.may.be.required.before.acceptable.correction.is.obtained..Further.iterations.
may.also.be.required.if.the.modes.used.are.not.optimum,.according.to.the.deinition.we.have.used.here..
his. has. been. shown. in. confocal. and. harmonic. generation. microscopes,. where. Zernike. modes. were.
used. in. an. eicient. but. nonoptimum. sensorless. scheme. (Booth. et. al.. 2002;. Jesacher. et. al.. 2009).. he.
methods.described.here.could.also.be.combined.with.more.advanced.control.strategies.to.reine.perfor-
mance.in.practical.adaptive.systems.(Song.et.al..2010).
Acknowledgments
M..J..Booth.was.an.Engineering.and.Physical.Sciences.Research.Council.(EPSRC).Advanced.Research.
Fellow.supported.by.the.grant.EP/E055818/1.
