Biomedical Engineering Reference
In-Depth Information
aberration. in. the. pupil. plane. because. the. source. of. the. aberrations. is. close. to. the. light. source.. hus,.
they.will.vary.across.the.ield.of.view..he.area.in.the.ield.of.view.that.can.be.corrected.at.one.time.will.
depend.on.the.source.of.the.aberrations.and.is.referred.to.as.the.isoplanatic.patch..To.correct.the.entire.
ield.of.view.in.wide-ield.microscopy,.we.need.to.take.diferent.images.with.the.correction.optimized.
for.diferent.patches..he.corrected.isoplanatic.patches.from.each.image.would.then.be.stitched.together.
to.correct.the.entire.ield.of.view..In.confocal.and.multiphoton.microscopy,.there.is.the.possibility.of.
correcting.each.pixel.in.the.image.independently.because.these.are.raster.scanning.techniques,.but.in.
some. reports. this. has. been. determined. to. be. too. time-consuming,. and. the. wavefront. correction. has.
been.set.only.once.for.each.focal.depth.(Marsh.et.al..2003)..Many.biological.samples.have.a..cylindrical.or.
spherical.shape,.and.the.overall.shape.of.the.sample.will.also.be.a.signiicant.contribution.to.the.sample.
aberrations.(Schwertner.et.al..2004a,b).
15.1.2 earlier correction Approaches
Many.diferent.approaches.to.correcting.or.eliminating.aberrations.have.been.developed.over.the.years..
As. already. mentioned,. cell. ixation. and. clearing. techniques. can. remove. sample-induced. aberrations.
and.scattering.(Tuchin.2007)..he.refraction.index.of.ixed.cells.can.be.matched.to.that.of.the.immersion.
medium.to.minimize.depth.aberration..his.can.be.carried.out.by.changing.the.immersion.medium.or.
by.ixing.the.cells..Glycerol.and.water-immersion.lenses.have.slightly.smaller.NAs.than.oil-immersion.
objectives.but.reduce.the.refractive.index.mismatch.with.live.specimens.and.therefore.also.the..resulting.
depth.aberration..Ater.ixing.cells,.their.sample.refractive.index.will.closely.match.the.ixation-medium.
index..Using.a.higher.refractive-index.ixation.medium.allows.the.imaging.system.to.efectively.use.a.
higher. NA.. Recently,. a. new. high-refractive-index. ixation. medium. has. been. developed. that. permits.
imaging.with.the.full.NA.of.an.oil-immersion.lens.(Staudt.et.al..2007).
Using.an.immersion.oil.with.refractive.index,.
n
.=.1.518,.we.can.ind.that.a.point.image.50.μm.below.
the.cover.glass.in.glycerol.(
n
.=.1.4746,.refractive.index.diference,.δ
n
.=.0.0434).has.similar.distortions.
as.a.point.image.12.μm.inside.a.volume.of.a.typical.biological.bufer.medium.(
n
.=.1.341,.δ
n
.=.0.177)..
he.corresponding.peak.intensity.is.about.four.times.lower.than.that.would.be.detected.for.an.identical.
point.source.right.under.the.cover.glass..For.a.water-immersion.objective.imaging.into.tissue.(
n
.=.1.41,.
δ
n
.=.0.077),.comparable.distortions.will.appear.at.28.μm.depth.
he.depth.aberrations.resulting.from.variations.in.cover-glass.thickness.can.be.corrected.to.a.great.
extent. by. adjustable. collars. built. into. some. objectives. (King. and. Cogswell. 2004).. Adjustment. of. the.
immersion.oil.refractive.index.has.been.shown.to.produce.similar.correction.(Hiraoka.et.al..1990)..By.
incorporating.a.special.telescope.before.the.imaging.detector,.optimization.of.the.correction.without.
disturbance.of.the.objective.or.the.specimen.can.be.achieved,.as.shown.in.
Figure.15.4
.
(Kam.et.al..1997)..
In. essence,. these. methods. shit. the. imaged. plane. above. or. below. the. designed. focal. plane,. adding. or.
subtracting.a.phase.that.varies.approximately.as.second.order.with.the.angle.of.emergence.from.a.point.
in.the.sample.at.focus..However,.it.should.be.stressed.that.all.these.methods.provide.only.second-order.
corrections.that.may.not.be.suiciently.good.for.light.entering.at.high.NAs.
Another.approach.to.addressing.depth.aberrations.is.to.deconvolve.the.images.with.a.depth-.dependent.
PSF..In.deconvolution,.the.luorophore.density,.
f x y z
,
( )
,.is.estimated.by.mathematically.inverting.the.
imaging.process.of.the.microscope,.which.is.the.convolution.of.the.instrument.response,.the.PSF,.with.
f x y z
(
,
,
)
..For.the.case.of.a.space.invariant.PSF,.
h x y z
(
,
,
)
,.the.image,.
g x y z
(
,
,
)
,.can.be.expressed.as
(
)
=
(
) (
)
∫∫∫
g x y z
,
,
h x
−
x y
,
−
y z
,
−
z
f x y z
,
,
d d d
z
0
x y
.
(15.3)
.
.
0
0
0
0
0
0
0
0
here. are. many. deconvolution. approaches. to. inverting. this. equation. to. get. the. best. estimate. of.
f x y z
,
( )
..Because.Equation.15.3.is.a.convolution,.it.can.be.calculated.rapidly.using.fast.Fourier.trans-
form.algorithms..But,.clearly,.if.the.PSF.is.not.spatially.invariant,.as.is.the.case.when.aberrations.are.
present,.Equation.15.3.is.not.correct,.and.the.inversion.will.not.result.in.a.good.estimate.of.the.object..
