Biomedical Engineering Reference
In-Depth Information
δ
D
Δ
x
<
λ
/2
f
FIGuRE 1.20
Consideration.of.Maréchal's.criterion.sets.the.depth.of.focus.of.a.beam.
the Maréchal.plates.of.the.actual.wave,.they.must.be.bright..Basic.geometry.and.the.formula.for.a.
circle.reveal
2
f
D
.
=
(
)
2
∆
z
≅
2
λ
2
f
/#
λ
that.is,.the.depth.of.focus.is.also.set.by.the.
f
/#.and.wavelength.of.the.beam,.this.time.with.a.square.law.
dependence.on.
f
/#.
Once.again,.the.physical.limit.of.resolution.is.about.one.wavelength..his.combined.with.the.difrac-
tion.limit.sets.the.resolution.limit.in.all.three.spatial.dimensions.to.about.a.wavelength.
1.5.6 rayleigh range
In. applications. where. beams. must. travel. signiicant. distances,. it. is. important. to. understand. when.
simple.ray.tracing.will.no.longer.predict.where.the.light.will.go..For.short.distances,.aperture.plane.
waves.generally.stay.intact..At.longer.distances,.however,.they.will.be.dominated.by.wave.difraction.
and.the.light.will.diverge.away.from.the.nominal.beam.line..Focused.spherical.waves.exhibit.a.similar.
behavior.where.they.remain.spherical.until.they.get.to.near.the.depth.of.focus.region.around.the.center.
of.curvature.
For.a.plane.wave,.the.
Rayleigh range
.is.the.propagation.distance,.
L
,.at.which.the.aperture.
D
.is.one.
Fresnel.zone.
λ
D
.in.size..hat.is,
D
2
λ
.
L
=
here. is. no. lens. in. this. deinition,. just. an. aperture. limiting. a. plane. wave.. But. notice. that. at. the.
Rayleigh.range.it.makes.no.diference.if.we.use.a.lens—the.difraction.of.the.aperture.alone.is.as.large.
as.the.difraction.limit.of.a.lens.with.focal.length.
L
,.that.is.(rearranging.the.above.equation),.
L
D
λ
=
.
he.Fresnel.number.is.a.measure.of.progress.of.a.beam.toward.the.Rayleigh.range..It.is.deined.as.the.
number.of.Fresnel.zones.in.the.aperture.plane.wave,.as.a.function.of.distance.from.the.aperture:
D
D
L D
D
L
2
.
N
=
=
λ
/
λ
