Biomedical Engineering Reference
In-Depth Information
(a)
(b)
(c)
FIGuRE 15.4
Point.spread.functions.(PSFs).measured.from.focal.series.images.of.0.1-μm-diameter.luorescent spheres.
using.a.100×/1.3.objective..he.bead.centers.were.found,.the.three-dimensional.PSFs.were.cylindrically.averaged.and.
presented.as.a.vertical.section.through.the.optical.axis..he.intensity.scale.is.logarithmic.to.depict.the.faint.out-of-focus.
patterns..Images.were.taken.in.focal.steps.of.0.25.μm,.and.pixel.was.replicated.four.times.along.the.optical.axis.to.have.
the.radial.and.axial.pixel.size.roughly.equal..he.scale.bars.are.5.μm..he.Galilean.telescope.version.was.used..he.beads.
are.in.an.agarose.layer.with.an.estimated.refractive.index.of.1.4..(a).PSFs.for.three.beads:.one.right.under.the.coverslip.
(
F
.=.0),.one.at.
F
.=.−5.μm,.and.one.at.
F
.=.−15.μm.below.the.coverslip..An.increasingly.aberrated.pattern.is.obtained.for.
deeper.beads..(b).PSFs.for.the.same.three.beads.ater.adjusting.the.telescope.ring.to.
Z
.=.−2.(arbitrary.units).and.focusing.
with.
F
..he.nonaberrated.plane.of.focus.is.now.−5.μm.below.the.coverslip,.and.opposite.signs.of.the.aberrated.patterns.
are.obtained.above.and.below.this.plane..Top.bead:.
F
.=.−3.5.μm;.middle.bead:.
F
.=.−8.5.μm,.lower.bead:.
F
.=.−18.5 μm..
(c).PSFs.for.the.same.three.beads.now.taken.with.both.
F
.and.
Z
.adjusted.to.minimize.aberration.at.all.three.depths..Top.
bead:.
F
.=.0,.
Z
.=.0;.middle.bead:.
F
.=.0−8.5.μm,.
Z
.=.−2;.lower.bead:.
F
.=.−26.μm,.
Z
.=.−4..From.Kam.et.al..(1997).
When.depth.aberrations.are.present,.the.PSF.will.be.a.function.of.both.the.imaging.plane,.
z
,.and.the.
object.plane,.
z
0
,.independently..Now,
(
)
=
∫∫∫
(
) (
)
g x y z
,
,
h x
−
x y
,
−
y z z
,
,
f x y z
,
,
d d d
z
0
x y
.
(15.4)
.
.
0
0
0
0
0
0
0
0
here.are.approaches.to.approximating.and.inverting.Equation.15.4,.but.Equation.15.4.is.much.more.
computationally.intensive.than.Equation.15.3,.and.these.methods.are.correspondingly.intensive,.because.
the. image. must. be. calculated. many. times. (Kam. et. al.. 2001;. Preza. and. Conchello. 2004;. Arigovindan.
et al. 2010)..Equation.15.4.can.in.principle.be.extended.to.the.case.where.the.PSF.varies.with.lateral.as.
well.as.axial.position.to.account.for.aberrations.other.than.the.depth.aberration,.but.this.will.make.the.
problem.even.more.intractable..Because.deconvolution.is.a.post-acquisition.process,.it.cannot.restore.the.
signal-to-noise.ratio.that.is.degraded.through.the.lower.peak.intensities.because.of.the.aberrated.PSF.
15.2 Microscope Design
Later.we.describe.the.design.and.construction.of.a.microscope.to.correct.for.depth.aberration.and.focus..
he. microscope. layout. used. at. University. of. California,. San. Francisco,. is. shown. in.
Figure. 15.5
.
. he.
microscope.uses.a.60×.oil-immersion.objective.(Olympus.1.42.NA.PlanApo.N).and.Olympus.tube.lens.
(
f
tl
,. focal. length. 180. mm). in. a. custom-built. open. microscope. coniguration. assembled. on. an. optical.
table..he.back.pupil.plane.of.the.objective.is.reimaged.onto.the.deformable.mirror.(DM).using.the.tube.
lens.and.achromat.
f
1
.chosen.so.that.the.desired.NA.ills.the.15.mm.diameter.of.the.DM.
f
f
2
NA
f
1
1
.
φ
DM
=
2
NA
f
=
.
(15.5)
obj
M
tl
