Biomedical Engineering Reference
In-Depth Information
where.ƒ
LA
.is.the.focal.length.of.the.lenslet.array,.Δ
x
.and.Δ
y
.are.the.slope.measurements.at.the..subaperture.
i
.in.the.
x
.and.
y
.directions,.respectively,.and.
w
(
x
i
,
y
i
).is.the.wavefront.at.the.point.
x
i
.and.
y
i
.
17.1.3 cross-correlation centroiding
Many.astronomy.AO.systems.use.a.quad-cell.detector.in.the.SHWF.sensor.to.determine.the.mean.slope.
at. each. subaperture. (Hardy. 1998).. Although. the. quad. cell. may. be. very. easy. to. implement,. it. images. the.
sub.aperture.into.four.pixels,.so.it.can.be.used.to.detect.only.approximately.half.a.wavelength.of.tilt.at.each.
subaperture..To.overcome.the.limitations.of.the.quad.cell,.more.pixels.per.subaperture.are.needed.to.better.
sample.the.Hartmann.spots..Introducing.more.pixels.does.have.the.negative.efect.of.increasing.the.efects.of.
noise,.which.current.detectors.have.not.managed.to.overcome..On.the.other.hand,.there.are.many.algorithms.
that.help.overcome.the.efects.of.noise.(homas.et.al..2006;.Adkin,.Azucena,.&.Nelson.2006;.Poyneer.2003).
he.cross-correlation.algorithm.requires.a.reference.Hartmann.spot.with.which.all.the.Hartmann.
spots. will. be. compared. to.. he. reference. image. shown. in. Figure. 17.2. is. irst. analyzed. to. acquire. the.
image. of. a. Hartmann. spot.. Figure. 17.3. shows. the. average. Hartmann. spot. of. the. reference. image. in.
Figure.17.12
.
.In.a.real.time.AO.system,.the.reference.spot.should.not.be.oversampled.too.much,.since.a.
lot.of.resources.are.required.to.analyze.the.data..homas.et.al..(2006).suggested.that.the.Hartmann.spot.
FIGuRE 17.2
SHWF.sensor.image.with.a.microsphere.as.the.reference.source..
Let
:.he.raw.WFS.data;.
Right
:.he.
same.image.with.the.subapertures.separated.
Reference image
2
4
6
8
10
12
14
16
18
20
22
5
10
x
(pixels)
15
20
FIGuRE 17.3
Average.Hartmann.spot,.obtained.by.inding.the.maximum.of.each.subaperture.in.Figure.17.2.and.
adding.all.the.images.around.their.corresponding.maxima.
