Biomedical Engineering Reference
In-Depth Information
wavelength),.falling.in.neither.the.Mie.scattering.regime.( r .⨠.λ,.where. r .is.the.radius.of.
object).nor.the.Raleigh.scattering.regime.( r =.λ)..Although.no.accurate.theoretical.model.is.
available.in.this.regime,.it.hardly.impedes.the.rapid.growth.of.research.interest.and.prac-
tice.on.the.trapping.and.manipulation.of.these.objects.with.optical.tweezers.(Mofitt.et.al..
2008)..Several.optical.tweezers.instruments.such.as.BioRyx.(from.Arryx.Incorporated).and.
PALM.(from.Zeiss,.Inc).are.now.commercially.available,.although.their.major.capability.
is.largely.restricted.to.particle.trapping.and.molecular.force.measurement..Other.home-
made.systems.offer.some.lexibility.and.new.functions,.which.help.broaden.their.applica-
tions.in.various.ields.involving.cells.and.other.live.systems.
19.2 Optical Trap Mechanism
As.aforementioned,.optical.tweezers.trapping.requires.the.use.of.one.or.multiple.highly.
focused.laser.beams..These.laser.beams.are.guided.through.an.optical.objective.and.strike.
the.target.objects.such.as.dielectric.microparticles..When.a.particle.approaches.the.focus.
center. of. the. incident. beam,. the. scattering. of. photons. exerts. two. types. of. force. on. the.
particle:.a.gradient.force.in.the.direction.of.the.light.intensity.gradient.that.pulls.objects.
toward.its.spatial.focus.point.(the.gradient.direction).and.a.scattering.force.in.the.direction.
of.light.propagation.that.pushes.objects.along.the.propagation.direction,.as.illustrated.in.
Figure.19.1.(Ashkin.et.al..1986).
19.2.1  Optical Trapping in Mie Scattering regime
If.the.particle.size.is.substantially.larger.than.the.wavelength.of.the.trapping.laser.( r .⨠.λ),.
that.is,.in.the.Mie.scattering.regime,.the.optical.forces.can.be.calculated.directly.from.ray.
optics..Under.light.illumination,.the.refraction.from.the.particle.(assuming.to.be.in.a.spher-
ical.shape).results.in.a.momentum.change.of.light..Simultaneously,.an.equal,.but.opposite.
momentum.change.(and.force).is.exerted.back.on.the.particle..The.resultant.force.on.the.
particle.lies.in.the.direction.of.the.focus.of.the.light.while.its.actual.orientation.depends.
on.the.ratio.of.the.refraction.index.of.the.particle.to.that.of.the.surrounding.medium.( m ):.
it. points. toward. (when. m .>.1). or. against. (when. m .<.1). the. direction. of. the. light. intensity.
gradient..The.magnitude.of.such.optical.force.can.be.calculated.from.the.momentum.lux.
( S ).that.enters.and.leaves.the.particle.surface:
n
c
∫∫ (
m
F
=
S
S
)
dA
.
(19.1)
in
out
.
where
n m .is.the.refraction.index.of.the.medium
c .is.the.speed.of.light.in.vacuum
With. a. 100%. relecting. mirror,. S out .=.− S in . and. F .=.2( n m / c ) I ,. where. I . is. the. intensity. of. the.
incident. light.. For. most. light. sources,. the. magnitude. of. this. optical. force. is. very. small.
and. negligible.. However,. if. a. laser. beam. is. highly. focused. through. an. objective. with. a.
high.numerical.aperture.(NA),.such.optical.force.may.become.large.enough.to.overcome.
 
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