Biomedical Engineering Reference
In-Depth Information
estimation. is. independent. of. the. number. of. control. channels,. which. is. a. signiicant. advantage. in. the.
control.eiciency.over.the.sequential.gradient.method..However,.there.is.a.signiicant.drawback.in.the.
multi-dithering.method..he.signal-to-noise.ratio.in.the.measurement.channel.decreases.proportionally.
with.the.number.of.control.channels.[27]..A.high.signal-to-noise.system.is.required.in.this.application..
Unfortunately,. two-photon. luorescence. imaging. is. inherently. a. low-light. imaging. modality,. particu-
larly.at.depths.for.which.aberration.correction.is.required..hus,.signal-to-noise.ratios.are.relatively.low.
12.3.1 Stochastic Parallel Gradient Descent Algorithm
with Zernike Polynomial Basis
he. stochastic. parallel. gradient. descent. (SPGD). algorithm. maximizes. or. minimizes. a. metric. signal.
corresponding.to.system.performance.in.an.iterative.control.loop.based.on.randomized.perturbations.
of.the.system's.controllable.inputs..he.control.loop.for.AO.includes.temporarily.changing.the.mirror.
shape. by. applying. perturbations. on. its. independent.control. inputs. (e.g.,.DM. actuators),. .assessing. the.
efect. of. these. perturbations. on. the. metric. (e.g.,. luorescence. intensity),. estimating. a. metric. .gradient.
with.respect.to.control.input.perturbations,.and.inally.updating.the.mirror.shape.to.a.state.that.should.
incrementally.increase.the.metric..A.block.diagram.is.shown.in.Figure.12.3..First,.the.current.delection.
state.of.each.input.channel.of.the.DM.is.perturbed.by.a.unit.amount,.in.a.direction.that.is.randomly.
signed.for.each.input.channel..Note.that.the.obvious.basis.for.input.to.the.DM.is.the.DM.actuators,.with.
each.actuator's.input.serving.as.an.independent.control.channel..Other.basis.sets.can.be.established.as.
well..For.example,.one.could.control.the.DM.based.on.basis.sets.coordinated.over.all.actuators,.with.
independent.inputs.corresponding.to.Zernike.modes..he.luorescence.signal.is.measured.and.stored.
as.the.metric.value..hen.the.control.channels.are.perturbed.in.the.opposite.direction,.and.the.metric.
is.recorded.again..he.diference.in.recorded.metrics.for.positive.and..negative.perturbations.provides.
a. gradient. in. the. multidimensional. input. basis. space,. and. a. new. state. for. the. DM. is. determined. by.
multiplying.each.input.channel's.signed.perturbation.by.the.global.gradient.and.adding.this.value.to.
the.previous.input.channel.state..When.the.measured.metric.reaches.a.steady.state,.the.loop.is.stopped.
Figure.12.4
.
shows.the.concept.of.the.application.of.AO.in.a.luorescence.microscope..he.AO.loop.
utilizes.the.measured.luorescence.intensity.as.the.metric.and.builds.the.DM.iteratively.based.on.the.
gradient.information.from.each.loop.cycle.
Assign DM shape (
S
1..140
)
Perturb DM in step size of
ds
1..140
:
S
1..140
+ =
S
1..140
+
ds
1..140
•
random_sign
1..140
Measure fluorescence intensity as metric: J
+
Perturb DM:
S
1..140
- =
S
1..140
-
ds
1..140
•
random_sign
1..140
Measure fluorescence intensity as metric: J
-
Access the metric gradient:
dj
=
sign
((
J
+
)
-
(
J
-
))
DM shape update:
S
1..140
=
S
1..140
+
k
•
dj
•
ds
1..140
(k is the controller gain)
FIGuRE 12.3
he.low.chart.of.stochastic.parallel.gradient.descent.algorithm.
