Biomedical Engineering Reference
In-Depth Information
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Individual actuator basis
(
~
100 channels)
Grouped actuator basis
(
~
25 channels)
Zernike polynomial basis
(33 channels)
FIGuRE 12.5
hree.control.bases.for.SPGD..Let:.diagonal.control.channels.are.highlighted.in.an.individual-
actuator. control. basis;. Center:. diagonal. control. channels. are. highlighted. in. the. grouped. actuator. control. basis;.
Right:.the.2nd-7th.of.Zernike.polynomial.shapes.in.the.Zernike.basis.
chosen. for. SPGD. control. parameters.. In. this. approach,. the. actuators. are. perturbed. in. a. coordinated.
fashion,.corresponding.to.superposition.of.Zernike.polynomial.shapes.
Booth.and.Wilson.demonstrated.in.theory.that.only.a.few.Zernike.terms.need.to.be.corrected.with.
AO. to. improve. optical. quality. signiicantly. in. two-photon. microscopy. [28].. In. practice,. the. irst. 35.
Zernike. terms,. without. the. lowest. two,. which. afect. only. image. shit,. are. used. as. the. control. basis..
Figure 12.5.shows.the.three.choices.of.the.control.basis.
With.the.appropriate.perturbation.step.size.selected.for.each.candidate.SPGD.control.basis,.each.was.
used.to.optimize.the.luorescent.signal.from.the.microsphere.bead.embedded.in.a.mouse.skull.at.200.μm.
below.the.surface,.under.control.of.the.AO.loop..For.each.control.test,.the.SPGD.algorithm.was.run.for.
over.100.iterations..
Figure.12.6
.
shows.the.metric.response.during.control.for.each.of.the.three.control.
basis..he.metric.value,.luorescence.intensity.(vertical.scale),.is.normalized.by.the.metric.value.at.the.
initial.state.(mirror.in.neutral,.lat.state)..he.best.control.basis.is.the.one.that.converges.to.the.highest.
metric. value.. Clearly,. the. Zernike-based. controller. produced. the. best. results. out. of. the. three. control.
bases.. he. controller. produced. 40%. improvement. in. the. metric.. By. contrast,. the. grouped. actuator-
based.controller.produced.~4%.improvement,.and.the.individual.actuator-based.controller.produced.
essentially.no.improvement.
he.SPGD.algorithm.for.AO.in.an.actual.luorescence.microscopy.experiment.in.deep-tissue.imaging.
performed.best.when.the.control.basis.was.Zernike.polynomials.with.perturbations.applied.as.changes.
in.the.Zernike.polynomial.coeicients..Key.factors.in.the.efectiveness.of.the.Zernike.control.basis.in.
this.SPGD.application.were.that.the.Zernike.polynomials.closely.approximate.the.expected.aberrations.
in. the. microscope,. and. the. Zernike-based. controller. required. fewer. control. degrees. of. freedom.. To.
represent.Zernike.polynomial.shapes.on.the.DM.accurately,.it.is.also.necessary.to.drive.each.actuator.
precisely.for.the.desired.delection.proile..his.is.nontrivial,.since.the.fundamental.electrostatic.actua-
tion.mechanism.is.nonlinear..An.empirical.calibration.procedure.is.used.to.derive.a.voltage.map.to.drive.
the.DM.into.Zernike.shapes.[29].
12.3.2 Metric Selection for Stochastic Parallel Gradient Descent Algorithm
We.chose.to.use.the.average.luorescence.intensity.over.the.whole.scanning.ield.as.the.feedback.metric.
in.the.SPGD.closed-loop.AO..he.selection.of.this.metric.is.based.on.the.assumption.that.stronger.two-
photon.luorescence.intensity.can.be.generated.in.the.excitation.process.from.an.aberration-free.optical.
setup.than.that.from.aberrated.optical.setup.
