Biomedical Engineering Reference
In-Depth Information
is.useful.for.evaluating.the.spatial.frequency.performance.of.the.imaging.system.since
{
}
=
{
}
.
2
2
( )
( )
(
)
F
i x
OTF
u F o x
′
t
that.is,.the.imaging.system's.ability.to.reproduce.spatial.frequencies.in.the.object.is.determined.by.the.
OTF..In.practical.use,.the.OTF.is.normalized.to.one.at.
u
.=.0.so.as.to.make.it.independent.of.overall.
source. brightness.. he. OTF. is. typically. complex. valued,. but. from. the. deinition.it. can. be. seen. that. a.
symmetric.pupil.will.produce.a.real.OTF.
he.optics.within.the.system.and.the.propagating.medium.in.between.optical.elements.can.introduce.
aberration.on.the.propagating.beam..hese.are.accounted.for.by.introducing.phase.factors.on.the.pupil.
function,.as.in
.
( )
=
( )
( )
P u
A u
i u
e
ϕ
Transmissivity.variations.can.likewise.be.incorporated.in.the.amplitude.factor.
he.plot.in.Figure.1.24.shows.a.radial.slice.of.the.OTF.for.a.circular.aperture..For.a.circularly.sym-
metric.aperture,.the.OTF.is.also.circularly.symmetric..Some.apertures.have.asymmetries,.such.as.the.
structural.supports.obscuring.portions.of.the.aperture.of.modern.relective.telescopes,.and.these.asym-
metries.will.produce.asymmetries.in.the.OTF.so.that.detailed.evaluation.will.need.to.consider.the.entire.
2D.function..For.simpliication,.most.common.optical.designs.have.circularly.symmetric.or.nearly.sym-
metric.apertures.so.we.can.glean.information.from.the.radial.slice.of.the.OTF.
he.horizontal.axis.is.the.spatial.frequency,.in.inverse.meters..A.difraction-limited.system.has.the.
highest. spatial. frequency. transfer. coeicients,. but. as. can. be. seen,. these. fall. to. zero. at. the. spatial. fre-
quency.
D
/λ..his.corresponds.to.spatial.variations.in.the.object.intensity.that.are.iner.than.the.optical.
system's.difraction.limit..hese.are.ultimately.blurred.together.by.the.difraction-limited.PSF.
Aberrations. within. the. system. suppress. the. response. to. spatial. frequency,. most. oten. severe. aber-
rations. tend. to. suppress. the. high. spatial. frequency. response—efectively. reducing. the. optical. system.
resolution.to.that.of.a.smaller.aperture.
he. integral. of. the. OTF. relative. to. the. integral. of. the. difraction-limited. OTF. is. the.
Strehl ratio
,.
named.ater.the.German.physicist.Karl.Strehl..he.Strehl.ratio.has.a.value.from.zero.to.one.and.is.oten.
used.as.a.single.number.score.of.the.quality.of.an.optical.system..From.the.deinition.of.the.OTF,.one.
1.0
0.8
0.6
0.4
0.2
0.0
0
D
/
λ
Spatial frequency
FIGuRE 1.24
Examples. of. optical. transfer. functions. (OTF,. radial. average).. he. upper. curve. is. the. OTF. of. a.
circular.aperture.of.diameter.
D
..he.lower.curves.are.those.of.systems.with.increasingly.severe.phase.aberrations.
