Biomedical Engineering Reference
In-Depth Information
system),. the. image. is. the. convolution. of. the. luorophore. distribution. in. the. object. and. the. intensity.
point.spread.function.(PSF).of.the.microscope..As.the.aberrations.afect.only.the.imaging.properties,.
the.sensorless.AO.scheme.must.be.able.to.separate.this.information.from.the.efects.of.the.object.struc-
ture..Phase.retrieval.methods.have.been.used.to.extract.aberration.information.from.a.single.image,.
but.these.methods.are.efective.only.if.the.object.structure.is.known.(e.g.,.if.the.specimen.is.a.single.
point-like.bead).(Kner.et.al..2010)..For.unknown.specimen.structures,.the.aberrations.can.be.deter-
mined.only.by.acquiring.more.images,.each.with.a.diferent.bias.aberration.introduced.by.the.adaptive.
element..Assuming.that.the.object.structure.is.unknown.but.does.not.change.measurements.between.
images,.then.comparisons.between.the.qualities.of.the.biased.images.should.reveal.the.efects.of.the.
aberrations.on.the.imaging.properties.of.the.microscope..his.information.about.image.quality.forms.
the.basis.for.the.determination.of.the.aberration.in.the.system.and.consequently.the.optimum.setting.
for.the.correction.element.
he. deinition. of. “image. quality”. is. somewhat. subjective.. However,. there. are. many. ways. in. which.
quality.can.be.reasonably.represented.by.a.mathematical.quantity..For.example,.in.the.confocal.luo-
rescence.microscope,.the.magnitude.of.the.intensity.PSF.is.reduced.as.the.size.of.aberration.increases;.
consequently,.the.total.image.intensity.(the.sum.of.all.pixel.values).is.also.reduced..It.is.straightforward.
to.show.that.for.most.object.structures,.the.total.image.intensity.is.maximum.when.aberrations.are.zero..
Hence,.the.total.image.intensity.is.an.appropriate.metric.for.the.representation.of.the.image.quality.in.
this.microscope.
Once.we.have.deined.an.appropriate.image.quality.metric,.we.can.consider.the.sensorless.AO.scheme.
as. a. mathematical. optimization. problem,. whose. objective. is. to. maximize. the. metric. function,. which.
we.denote.as. M ..he.maximum.of. M .corresponds.to.the.optimum.DM.setting.that.minimizes.the.total.
aberration.in.the.system..he.metric. M .is.a.function.of.input.parameters.that.determine.the.aberration.
applied.by.the.adaptive.element..hese.input.parameters.can.be.represented.by.the.set.of. P .control.sig-
nals. {
}
c c P .driving.the.actuators.of.the.DM..he.calculation.of.the.image.quality.for.each.applied.
aberration.is,.therefore,.equivalent.to.the.evaluation.of.the.metric.function.at.the.coordinates.given.by.
the.DM.control.signals..herefore,.the.objective.of.the.optimization.is.to.ind.the.values.of. c 1 ,.…,. c P .that.
maximize.
,
,
M c c P .
he.general.outline.of.this.optimization.procedure.is.shown.in. Figure.10.2 ..here.exist.many.difer-
ent.strategies.for.the.implementation.of.this.procedure,.including.the.various.heuristics.used.in.convex.
optimization.theory..One.possible.approach.is.to.use.model-free.stochastic.methods,.for.which.we.need.
to. assume. only. that. M . has. a. well-deined. maximum. value.. For. example,. one. could. test. all. possible.
shapes.of.the.DM.and.select.the.setting.with.optimum.image.quality—this.would.be.equivalent.to.an.
exhaustive.search.through.all.possible.aberrations.represented.by.all.possible.combinations.of.control.
signals..Although.from.a.mathematical.point.of.view.this.is.guaranteed.to.ind.the.optimum.correction,.
the.number.of.image.measurements.would.be.impractically.large.(Booth.2006)..Other.more-developed.
model-free. methods,. such. as. genetic. or. hill-climbing. algorithms,. have. been. demonstrated. (Sherman.
et al..2002;.Wright.et.al..2005)..Although.they.are.more.eicient.than.an.exhaustive.search,.they.typically.
require.a.large.number.of.image.measurements..Although,.in.principle,.the.acquisition.of.these.images.
is.possible,.there.are.several.reasons.why.this.is.incompatible.with.practical.microscopy..Specimens.are.
oten. sensitive. to. cumulative. light. exposure—live. specimens. sufer. from. phototoxic. efects. and. even.
ixed.luorescent.specimens.undergo.photobleaching..Many.multiple.exposures.are.clearly.undesirable.
in. each. of. these. cases.. Specimens. may. also. move. during. the. imaging. sequence,. hence. the. specimen.
structure.will.not.stay.constant..It.is,.therefore,.desirable.to.minimize.the.measurement.time.by.ensur-
ing.that.the.number.of.exposures.is.as.small.as.possible.
Using. the. mathematical. analogy,. each. specimen. exposure. (and. quality. metric. calculation). corre-
sponds. to. a. function. evaluation. in. the. optimization. problem.. It. follows. that. reducing. the. required.
number.of.exposures.is.equivalent.to.deriving.an.eicient.optimization.algorithm.that.minimizes.the.
number. of. function. evaluations.. his. can. be. achieved. using. a. priori. knowledge. of. how. .aberrations.
(
{
,
,
}
)
1
Search WWH ::




Custom Search