Biomedical Engineering Reference
In-Depth Information
Shack-Hartmann.sensor..In.addition,.more.reference-arm.light.is.necessary,.since.the.reference.beam.
remains.collimated.on.the.camera.while.the.sample.beam.is.focused.
In.contrast,.the.virtual.SHS.relies.on.the.fact.that.amplitude.and.phase.of.the.electromagnetic.ield.
to.be.analyzed.have.already.been.determined.interferometrically..By.performing.Fourier.transforms.on.
small.rectangles.of.the.electromagnetic.ield,.the.lenslets.of.a.real.SHS.can.be.simulated,.and.the.resulting.
intensity.analyzed.exactly.as.in.a.real.SHS..With.respect.to.sotware.requirements,.the.only.additional.
step.a.vSHS.needs.compared.to.a.real.SHS.is.the.small.fast.Fourier.transforms.(FFTs).for.each.sublens,.
which.can.be.parallelized.and/or.performed.on.a.graphics.processing.unit.(GPU).if.speed.is.of.concern.
However,.the.vSHS.has.several.advantages.for.CGWS.with.respect.to.a.real.SHS..Since.coherence.gat-
ing.inherently.has.to.deal.with.a.strong.incoherent.background.from.backscattering.outside.the.coher-
ence.length,.a.high-dynamic-range.camera.is.necessary..With.a.real.SHS,.the.sample.light.from.the.CV.
would.be.focused.into.small.spots.on.the.camera,.which.would.further.increase.the.dynamic.range.nec-
essarily..In.contrast,.the.vSHS.camera.measures.the.electromagnetic.ield.in.a.plane.where.the.intensity.
is.distributed.as.homogeneously.as.possible,.minimizing.the.dynamic.range.needed.
Furthermore,.with.a.vSHS,.no.tedious.calibration.and.alignment.between.lenslet.array.and.camera.
are.necessary..he.size.and.number.of.lenslets.can.be.changed.rapidly.in.sotware;.the.same.data.can.
even.be.analyzed.several.times.with.diferent.parameters.if.necessary.
Note.that.the.strength.of.aberrations.that.can.be.correctly.analyzed.by.a.real.Shack-Hartmann.sensor.
is.limited.by.the.focal.length.of.the.lenslets..If.the.tilt.on.one.sublens.is.strong.enough,.the.corresponding.
spot.on.the.camera.will.be.laterally.displaced.far.enough.to.leave.the.region.of.the.camera.associated.with.
this.particular.sublens..his.can.cause.the.sotware.algorithm.analyzing.the.data.to.misinterpret.which.
spot.corresponds.to.which.sublens..Similarly,.the.strength.of.aberrations.that.can.be.analyzed.by.a.vSHS.
is.limited.by.the.sampling.of.the.camera—that.is,.by.the.pixel.size.of.the.camera..Since.the.phase.is.deter-
mined.only.modulo.2π,.only.phase.slopes.with.a.magnitude.below.π/pixel.are.determined.correctly..When.
the.tilt.becomes.strong.enough.that.the.phase.change.between.two.adjacent.pixels.is.below.-π.or.exceeds.π,.
aliasing.occurs,.and.the.tilt.between.these.pixels.will.be.over-.or.underestimated.by.a.multiple.of.2π/pixel.
14.4.3 Measurement Procedure
Summing.up.the.steps.described.earlier,.the.procedure.for.wavefront.measurement.in.scattering.tissue.is.
as.follows..A.quadruplet.of.phase-shited.interferograms.is.acquired,.which,.using.Equation.14.1,.allows.
the.calculation.of.the.electromagnetic.ield.in.the.BFP.of.the.objective..he.aperture.of.the.BFP.is.divided.
into.quadratic.subregions,.and.the.Fourier.transform.of.the.electromagnetic.ield.for.each.subregion,.is.
calculated,.simulating.the.efect.of.a.real.sublens.perfectly.aligned.with.this.pixel.region..he.squared.
amplitude. of. the. FFT. result. corresponds. to. the. intensity. of. the. difraction. pattern,. which. would. have.
been.measured.on.the.camera.of.a.real.SHS..To.quantify.the.local.wavefront.tilt,.the.displacement.of.the.
difraction.pattern.is.determined.by.centroid.estimation..Using.all.local.wavefront.tilts,.the.full.wavefront.
in.terms.of.Zernike.modes.can.be.determined..Since.this.reconstructed.wavefront.still.contains.speckle,.
the.whole.procedure.from.phase.shiting.to.Zernike.modes.is.repeated.in.several.laterally.adjacent.posi-
tions. of. the. CV.. All. resulting. Zernike. coeicient. vectors. can. be. averaged,. corresponding. to. ensemble.
averaging.described.earlier,.to.determine.the.inal.wavefront.estimate.with.minimized.speckle.error.
Since.centroid.estimation,.Zernike.reconstruction,.and.averaging.are.all.linear,.a.minor.speed.gain.
can.be.achieved.by.averaging.the.difraction.patterns.directly.and.performing.centroid.estimation.and.
Zernike.reconstruction.on.the.averaged.difraction.patterns.for.all.lenslets.(as.described.in.
Figure 14.7
).
Note.that.averaging.must.not.be.performed.before.the.calculation.of.the.virtual.difraction.pattern,.
since. the. Fourier. transform. and. subsequent. absolute. square. are. nonlinear. operations.. For. example,.
averaging.of.the.reconstructed.complex.electromagnetic.ield.corresponds.to.coherently.summing.the.
signal.of.all.scatterers,.which.implies.that.speckle.contrast.remains.maximal..If.averaging.is.performed.
even.earlier.on.the.level.of.image.quadruplets.taken.for.diferent.scatterer.distributions,.no.electric.ield.
can.be.reconstructed.since.this.would.average.away.the.speckle.present.in.the.individual.quadruplets.
