Biomedical Engineering Reference
In-Depth Information
3
Theory of Image
Formation
3.1.
.Introduction:.Imaging.Properties.and.Point.
.
Spread.Function.(PSF)........................................................................43
3.2.
Difraction.of.Light.............................................................................43
3.3.
Amplitude.PSF.of.a.hin.Lens...........................................................45
3.4.
.Efective.PSF.and.Image.Formation.in.a.
.
Confocal.Microscope..........................................................................46
Michael Schwertner
confovis GmbH
3.5.
PSF.for.an.Ideal.Lens.and.Difraction.Limited.Imaging...............47
3.1 introduction: imaging Properties and
Point Spread Function (PSF)
his.chapter.briely.mentions.some.aspects.of.the.scalar.theory*.of.the.difraction.of.light.and.image.
formation..One.of.the.main.results.is.the.point.spread.function.(PSF).of.a.lens.which.in.turn.is.impor-
tant.in.the.context.of.lateral.and.axial.resolution.and.the.efects.of.aberrations.in.confocal.microscopy.
If.we.want.to.understand.and.model.an.imaging.system,.we.have.to.ask.what.optical.ield.(or.intensity.
distribution/image).it.will.produce.for.a.given.input.(object)..In.confocal.microscopy.we.are.interested.
in.the.quality.of.the.focal.spot..It.turns.out.that.the.PSF,.which.is.the.image.of.a.single.object.point.(see.
Figure. 3.1
),. characterizes. the. system. completely.. his. is. because. the. output. of. the. optical. system. can.
be. understood. as. the. superposition. of. the. optical. ields. caused. by. the. object. points.. In. the. following.
.sections.we.will.give.expressions.for.the.PSF.of.a.lens..hese.may.be.derived.from.irst.principles.
3.2 Diffraction of Light
he.theory.of.difraction.for.coherent.light.is.based.on.the.Huygens-Fresnel.principle.as.discussed.in.
Chapter.1,.stating.that.every.unobstructed.point.of.a.wavefront.serves.as.a.source.of.spherical.second-
ary.wavelets.of.the.same.frequency..Now.the.amplitude.of.the.optical.ield.at.any.point.beyond.is.the.
superposition.of.all.these.wavelets.taking.their.phase.and.amplitude.into.account.(Hecht.1987)..his.is.
mathematically.equivalent.to.Goodman.(1996):
∞
∞
)
exp(
−
jkR
jR
)
.
∫
∫
.
(3.1)
U x y
(
,
)
≈
U x y
(
,
d d
y
1
x
2
2
2
1
1
1
1
λ
−∞
−∞
*
.
A.transversal.electromagnetic.wave,.such.as.light,.is.described.by.its.amplitude,.phase,.and.plane.of.polarization..Scalar.
theory.means.that.only.the.phase.and.amplitude.are.considered,.and.polarization.efects.are.neglected.
43
