Biomedical Engineering Reference
In-Depth Information
2.7 Aberrations
he.restriction.of.the.thin.lens.analysis.to.monochromatic.paraxial.rays.leads.to.optical.aberrations.for.
real.lenses..For.an.extended.lens.that.admits.light.rays.away.from.the.axis,.the.paraxial.approximation.
used.in.Equation.2.4.is.no.longer.valid..In.general,.the.optical.surface.obtained.from.the.principle.of.
least.time.is.no.longer.a.spherical.surface,.but.rather.a.higher-order.surface.than.a.sphere..Nonetheless,.
a.spherical.surface.is.much.easier.to.fabricate.by.grinding.and.polishing.than.an.aspherical.surface,.
and.therefore,.lenses.with.spherical.surfaces.are.oten.used..As.the.light.rays.become.further.removed.
from.the.optical.axis,.they.no.longer.come.to.a.focus.at.one.point,.but.rather.focus.at.diferent.points.
depending.on.their.distance.from.the.axis..he.resulting.aberration.is.known.as.spherical.aberration,.
since. it. results. from. the. spherical. surface. of. the. lens.. An. example. is. shown. in. Figure. 2.10.. he. light.
rays.at.the.edge.of.the.lens.come.to.a.focus.closer.to.the.lens.than.those.from.the.paraxial.region.near.
the.optical.axis.
In.addition.to.the.spherical.shape.of.the.lens,.spherical.aberration.can.arise.from.index.mismatches.
between.the.lens.and.the.sample..When.the.light.travels.between.regions.of.diferent.indices.of.refrac-
tion,.the.light.rays.can.be.bent.at.the.interface.according.to.Snell's.law,.as.described.in.Equation.2.3..his.
aberration.can.be.the.dominant.aberration.when.imaging.deeply.into.a.specimen.since.it.increases.with.
depth.into.the.sample.
Another.aberration.is.caused.by.the.wavelength.dependence.of.the.index.of.refraction.
n
..Chromatic.
aberration.arises.when.multiwavelength.light.is.refracted.at.an.interface.between.two.regions.with.dif-
ferent.indices.of.refraction..he.diferent.colors.of.light.can.be.refracted.by.difering.amounts,.as.shown.
in. Figure. 2.11.. A. familiar. example. is. the. decomposition. of. white. light. by. a. prism. or. water. droplet,.
which.forms.the.familiar.colored.rainbow.when.sunlight.is.decomposed.into.its.spectral.components..
he.cause.for.the.spectral.decomposition.is.the.wavelength.dependence.of.the.index.of.refraction..he.
Spherical aberration
FIGuRE 2.10
Spherical.aberration..he.light.rays.that.are.farther.from.the.optical.axis.come.to.a.focus.at.diferent.
distances.from.the.lens..(Credit:.Wiki.)
Chromatic aberration
FIGuRE 2.11
Chromatic. aberration.. Diferent. colors. of. light. are. refracted. by. diferent. amounts. when. passing.
through.regions.with.diferent.indices.of.refraction..his.is.because.the.index.of.refraction.depends.on.the.wave-
length.of.light..(Credit:.Wiki.)
