Biomedical Engineering Reference
In-Depth Information
TABlE 5.1
Statistical.Properties.of.the.Measured.Specimen-Induced.Focal.Spot.
Displacements
Specimen.No.
NA
Std.Dev.(
X
)
Std.Dev.(
Y
)
Std.Dev.(
Z
)
Max.Dev.(total)
1
1.2
0.065
0.202
0.173
0.521
0.6
0.053
0.200
0.418
1.563
2
1.2
0.118
0.125
0.118
0.672
0.6
0.288
0.326
0.569
2.080
3
1.2
0.076
0.107
0.162
0.491
0.6
0.093
0.150
0.473
1.440
4
1.2
0.052
0.057
0.146
0.457
0.6
0.087
0.075
0.297
1.090
5
1.2
0.186
0.102
0.133
0.713
0.6
0.281
0.139
0.495
1.911
6
1.2
0.076
0.107
0.162
0.423
0.6
0.093
0.099
0.390
1.270
Units.are.in.micrometers
Average slope across pupil at NA = 1.2
Average slope across pupil at NA = 0.6
Spherical aberr. (1st) dominates at NA =1.2
Defocus dominates at NA = 0.6
Pupil size
NA
=
1.2
NA
=
1.2
NA
=
1.2
NA
=
0.6
NA
=
0.6
NA
=
0.6
(r)
(r)
r
r
r
0
0
0
Phase function
(a)
(b)
(c)
FIGuRE 5.5
Illustration.of.the.dependence.of.the.specimen-induced.distortions.and.other.aberrations.on.the.NA..
Please.see.text..(a).If.the.phase.function.is.a.constant.slope.function.the.average.wavefront.tilt.across.the.pupil.is.the.
same.for.the.lower.NA.of.0.6.and.the.higher.NA.of.1.2.(b).A.more.typical.aberration.pattern.can.lead.to.a.dependence.
of.the.specimen-induced.distortion.on.the.NA.shown.here.for.lateral.distortion..(c).For.axial.distortion.
of.1.2,.while.the.quadratic.term,.indicating.axial.displacement,.is.only.minor..his.is.exactly.opposite.at.
lower.NA,.where.the.axial.displacement.(quadratic.component).dominates.while.the.spherical.aberra-
tion.component.is.very.small..his.example.also.coincides.with.the.general.observation.that.larger.NAs.
lead.to.higher.spatial.frequencies.in.the.aberration.function.and,.therefore,.require.higher.aberration.
orders.for.the.appropriate.description.and/or.correction.
Another.representation.of.the.results.for.an.NA.of.0.6.is.also.shown.in.
Figure.5.6
..Here.the.imaging.of.
a.regular.square.grid.underneath.the.specimen.is.simulated.and.the.mesh.knots.of.the.regular.grid.are.
displaced.according.to.the.measured.deviations..Note.that.the.efect.is.exaggerated.in.the.drawing—the.
mesh.knot.displacement.is.drawn.ive.times.larger.at.the.scale.of.the.grid.
When.a.relative.measurement.within.a.3D.data.set.is.done,.both.the.absolute.errors.of.the.two.indi-
vidual.spot.position.measurements.contribute.to.the.inaccuracy.of.the.relative.position.measurement..In.
the.worst.case,.the.individual.distortions.will.add.up..he.data.imply.that.the.efect.of.specimen-induced.
aberrations.can.easily.lead.to.a.distance.measurement.inaccuracy.on.the.order.of.1-2.μm..Considering.
that.typical.cell.dimensions.are.in.the.range.from.5.to.20.μm,.this.can.lead.to.large.relative.errors..If,.for.
example,.a.distance.of.approximately.5.μm.has.to.be.measured.within.a.cell.and.the.uncertainty.of.the.dis-
tance.measurement.is.1.μm,.the.expected.relative.error.is.20%.and.hence.these.efects.cannot.be.neglected.
