Biomedical Engineering Reference
In-Depth Information
he.phase.can.be.varied.only.from.0.to.2π.without.phase.wrapping,.so.it.is.limited.in.the.amount.of.
wavefront.correction.that.it.is.capable.of.correcting,.usually.being.used.as.a.“tweeter”.to.make.low-
amplitude,.high-order.wavefront.corrections..he.change.in.orientation.of.the.liquid.crystal.is.limited.
to. approximately. 100. Hz,. so. it. is. limited. in. bandwidth. for. rapidly. varying. wavefront. corrections..
Nonetheless,.the.pixel.size.on.an.SLM.can.be.very.small,.allowing.for.very.high-order.corrections.to.
be.made..In.addition,.since.each.pixel.can.be.controlled.independently,.there.is.no.inluence.of.one.
actuator.on.another.
he.use.of.SLMs.in.optical.microscopy.has.recently.been.reviewed.by.Maurer.et.al..(2011)..hey.have.
been.used.for.wavefront.shaping.for.both.correction.of.refractive.image.aberrations.and.scattering..hey.
have.also.been.used.as.dynamic.spatial.Fourier.ilters.in.the.imaging.path.
For. correction. of. refractive. image. aberrations,. LC-SLMs. have. been. used. to. precorrect. the. illu-
mination. wavefront. to. overcome. shits. in. the. wavefront. as. it. propagates. through. the. sample. (Ji.
2009;.Milkie.2011)..his.approach.is.described.in.detail.in.Chapter.13.and.is.shown.schematically.in.
Figure 8.3..For.a.sample.with.a.homogeneous.index.of.refraction,.as.shown.in.Figure.8.3a,.a.plane.
wave.that.ills.the.back.aperture.of.an.objective.lens.is.brought.to.a.focal.spot.within.the.sample..he.
objective.lens.creates.a.spherically.converging.wavefront.with.each.normal.to.the.wavefront.interfer-
ing. constructively. at. the. focus.. For. a. sample. with. a. spatially. varying. index. of. refraction,. the. light.
rays. are. refracted. and. the. wavefront. phase. is. shited. by. the. sample. inhomogeneities. as. shown. in.
Figure.8.3b,.so.that.they.no.longer.reach.a.common.focus.in.phase.for.constructive.interference..To.
overcome.this,.the.pupil.can.be.segmented.into. N .subregions.by.an.LC-SLM,.and.the.tilt.and.phase.
of.each.subregion.varied.to.optimize.constructive.interference.at.the.focus,.as.shown.in.Figure.8.3c..
When.the.wavefront.tilts.and.phases.have.been.optimized,.the.optical.rays.intersect.at.the.same.point.
with. the. appropriate. phase. for. constructive. interference.. To. perform. the. optimization,. a. reference.
image.using.all.of.the.beamlets.is.irst.acquired..hen.all.but.one.of.the.beamlets.are.removed.with.
a. binary. phase. pattern. that. delects. them. toward. a. ield. stop.. An. image. is. then. acquired. with. the.
remaining.beamlet..Any.inhomogeneities.along.the.path.of.the.beamlet.that.delect.it.from.the.ideal.
focal.point.are.evidenced.as.a.shit.in.this.image.relative.to.the.reference.image..Once.the.image.shit.
has.been.determined,.the.delection.angle.can.be.calculated.and.an.equal.but.opposite.angle.can.be.
imparted.to.the.beamlet.by.application.of.an.appropriate.phase.ramp.at.the.corresponding.subregion.
of.the.SLM..his.is.then.repeated.for.each.beamlet,.one.by.one,.until.all.of.the.beamlets.intersect.at.
a. common. focal. point.. To. bring. all. of. the. beamlets. into. phase. for. constructive. interference. at. the.
Microscope
Microscope
Microscope
(a)
(b)
(c)
FIGuRE 8.3 A. simple. model. for. the. formation. of. an. optical. focus.. (a). An. ideal. microscope. converts. a. planar.
wavefront.to.a.converging.spherical.one.in.a.sample..Propagation.vectors.or.“rays”,.deined.by.the.direction.normal.
to.the.wavefront,.converge.at.a.common.point.and,.being.in.phase,.constructively.interfere.there.to.create.an.opti-
mal.focus..Sinusoidal.curves.denote.the.phase.variation.along.each.ray..(b).Inhomogeneities.in.the.refractive.index.
of.the.sample.change.the.directions.and.phases.of.the.rays,.leading.to.a.distorted.wavefront.and.an.enlarged.focal.
volume.with.lower.peak.intensity..(c).Controlling.the.input.wavefront.using.an.active.optical.element.(not.shown).
can.cancel.these.aberrations,.recovering.a.difraction-limited.focus..(From.Ji,.N.,.D..E..Milkie,.and.E..Betzig,. Nat
Methods ,.7,.141-147,.2009.)
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