Biomedical Engineering Reference
In-Depth Information
be.placed.at.the.plane.of.best.focus.or.circle.of.least.confusion.for.the.best.image.result..For.a.simple.thin.
lens.or.a.relective.spherical.mirror,.the.spherical.aberration.is.inversely.proportional.to.the.cube.of.
F
/#.
(Equation.9.4)..As.the.focal.length.gets.smaller,.the.spherical.aberration.also.increases.rapidly:
K
F
s
/#
3
.
S
∝
.
(9.4)
(
)
where.
S
.is.the.spherical.aberration.and.
K
s
.is.a.constant.
Coma.is.an.of-axis.aberration..Coma.is.absent.on.the.axis.and.the.magnitude.increases.with.the.ield.
angle.and.decreases.with.the.square.of.F-number..Coma.limits.the.ield.of.view.of.an.optical.system..For.
a.simple.thin.lens.or.a.relective.spherical.mirror,.the.coma.is.given.by
K
F
c
/#
2
.
C
∝
(
.
(9.5)
)
where.
C
.is.the.coma.and.
K
c
.is.a.constant..A.shit.in.focus.does.not.improve.a.comatic.image.unlike.the.
case.with.spherical.aberrations..In.testing.an.optical.system,.coma.may.appear.on.axis,.where.it.should.
be.zero..his.indicates.tilted.or.decentered.optical.components.in.the.system.due.to.the.misalignment.
Astigmatism.is.caused.by.lens.asymmetry.or.of-axis.object..Rays.focus.at.diferent.points.for.horizontal.
or.vertical.rays.as.shown.in.
Figure.9.4d
.
.In.a.system.where.astigmatism.exists,.a.detector.should.be.placed.
at.the.plane.in.between.the.two.focal.planes.for.horizontal.and.vertical.rays.for.best.focus.and.best.image.
quality..For.ininite.conjugates,.the.astigmatism.of.a.thin.lens.or.relective.spherical.mirror.is.given.by
K
F
a
/#
.
A
∝
(
.
(9.6)
)
where.
A
.is.the.astigmatic.aberration.and.
K
a
.is.a.constant.
Astigmatism.is.introduced.by.relective.relay.telescopes.due.to.of-axis.relection,.and.it.is.more.severe.
in.a.compact.system.with.shorter.focal-length.optics..A.cylindrical.lens.can.be.inserted.in.the.optical.
system.to.compensate.the.astigmatism.introduced.by.the.of-axis.relective.telescopes..Oten,.however,.
when.images.show.severe.asymmetry.over.the.entire.ield.of.view,.it.indicates.the.optical.system.is.mis-
aligned.or.badly.reassembled.
Field.curvature.is.the.aberration.where.the.sharpest.focus.is.on.a.curved.surface.in.the.image.space.
rather.than.a.plane..Objects.in.the.center.and.edges.of.the.ield.are.not.in.focus.simultaneously.as.shown.
in.
Figure.9.4e
.
.With.a.lat.detector,.it.can.never.focus.all.the.points.at.once..Again,.the.best.focus.is.the.
best.compromise.for.the.best.image.quality..Field.curvature.is.not.directly.related.to.the.F-number.of.
the.optical.system.and.it.is.mainly.noticeable.at.the.edges.of.the.ield..Most.microscope.objectives.and.
eyepieces.are.designed.to.be.well.corrected.for.ield.curvature,.especially.for.the.wide-ield.microscopes.
Distortion.happens.when.parts.of.the.image.are.more.magniied.than.others,.so.the.optical.system.
cannot.create.a.rectilinear.image.of.the.object..Distortion.does.not.modify.the.sharpness.of.the.image.
but. deforms. its. shape. as. shown. in.
Figure. 9.4f
.
. Distortion. occurs. quite. oten. in. microscope. eyepieces.
using. thick. lenses.. It. can. be. corrected. using. post-image. processing. if. necessary.. Field. curvature. and.
distortion.cannot.be.improved.by.moving.the.image.plane.or.by.better.alignment.
Chromatic.aberrations.are.diferent.from.the.preceding.aberrations.as.they.are.not.caused.by.imperfect.
surfaces.or.surface.errors..Chromatic.aberrations.happen.only.when.polychromatic.light.is.used.in.the.optical.
system,.whereas.other.aberrations.occur.with.a.single.color.of.light..When.diferent.colors.of.light.propagate.in.
a.medium,.they.travel.at.diferent.speeds..he.refractive.index.is.thus.wavelength.dependent,.which.is.known.
as.dispersion..Chromatic.aberrations.are.those.departures.from.perfect.imaging.that.are.due.to.dispersion.
here. are. two. types. of. chromatic. aberrations:. longitudinal. and. transverse. chromatic. aberrations..
Longitudinal.chromatic.aberration.causes.the.variation.of.focus.or.image.plane.with.wavelengths..Lateral.
chromatic.aberration.causes.images.to.be.diferent.sizes.for.diferent.colors.or.wavelengths..Chromatic.aber-
rations.oten.limit.the.performance.of.otherwise.well-corrected.optical.systems..Longitudinal.chromatic.
aberration.reduces.the.image.sharpness.whereas.lateral.chromatic.aberration.gives.rise.to.colored.fringes.
