Biomedical Engineering Reference
In-Depth Information
Δ
p
θ
D
p
p
FIGuRE 1.10
Difraction.as.a.consequence.of.the.Heisenberg.uncertainty.principle.
FIGuRE 1.11
Ocean.waves.at.the.entrance.to.the.Panama.canal.
Now. a. plane. wave. constrained. to. pass. through. an. aperture. of. size.
D
. has. its. position. uncertainty.
constrained.(in.that.direction).to.the.region.
D
..hus,.the.momentum.in.the.direction.orthogonal.to.the.
original.propagation.direction.is.uncertain.to.the.order.of.
h
/
D.
.With.that.in.mind,.one.can.see.that.the.
uncertainty.in.the.direction.of.the.emerging.wave,.Δ
p
/
p
,.is.on.the.order.λ/
D
,.which.corresponds.exactly.
to.what.is.observed.in.difraction.by.such.an.aperture.(Figure.1.10).
So.the.fact.that.difraction.is.observed.is.not,.ater.all,.a.discriminator. between.a.wave.theory.and.
a.particle.theory.of.light!.With.this.in.mind,.we.are.driven.to.use.the.Copenhagen.interpretation.with.
roles.played.by.both.waves.and.particles.at.the.appropriate.time,.as.our.best.theory.of.light.to.date.
We.conclude.this.section.with.a.photograph.that.illustrates.the.classic.wave.phenomena.with.ocean.
waves..Taken.from.above,.the.photo.shows.waves.incident.on.the.opening.of.a.harbor.(in.this.case,.the.
Atlantic.side.entrance.to.the.Panama.canal)..he.planar.open.ocean.waves.difract.as.they.pass.through.
the.“slit”.formed.by.the.two.breakwaters..Looking.closely,.one.can.also.see.that.each.ship.is.a.source.of.
scattered.waves.(Figure.1.11).
1.4 Analytic Methods for Light Wave Propagation and Analysis
1.4.1
Huygens Wavelets
In.1678,.Huygens.proposed.an.analytical.theory.to.describe.light.wave.propagation..he.theory.starts.
with.a.basic.idea.that.the.wave.ield.in.3-space.is.formed.by.a.sum.of.point.source.emitters.each.radi-
ating. spherical. waves. symmetrically. into. 3-space.. he. phase. of. each. spherical. wave. wiggles. once. per.
