Adaptive Optics in Wide-Field Microscopy - Adaptive Optics for Biological Imaging - page 290

1.0

90

0.8

45

0.6

0

0.4

- 45

0.2

- 90

0.0

(a) (b)

FIGuRE 15.20 Wavefront.in.the.back.pupil.plane.of.a.1.42.NA.system.calculated.from.the.three-dimensional.image.
of.a.200.nm.yellow-green.luorescent.bead..(a).Amplitude,.normalized.to.a.maximum.of.1..(b).Phase.(in.degrees).

Figure.15.20.shows.the.results.of.phase.retrieval.on.a.system.without.AO..his.image.was.taken.on.a.
well-corrected.Olympus.IX71.microscope.with.a.1.42.NA.60×.oil.objective.(Olympus.PLAPON)..he.
Strehl.ratio.calculated.from.the.retrieved.wavefront.was.0.70..It.was.calculated.as

2

( )

∫

A k k , d d k k

x y x y

. S

) .

.(15.14)

=

( )

((

( )

2

∫ ∫

A k k , d d k k d d k k

x y x y x y

where.the.integral.is.over.the.pupil.for.the.nominal.NA.of.the.microscope..he.Strehl.ratio.is.formulated.
this.way.to.account.for.the.possibility.of.a.lat.wavefront.that.does.not.ill.the.full.microscope.NA..Phase.
retrieval.also.works.well.on.signiicantly.distorted.PSFs,.as.shown.later.
he.retrieved.wavefront.can.be.easily.decomposed.into.Zernike.modes..Here.we.use.an.algorithm.that.
decomposes.the.gradients.of.the.wavefront.onto.a.set.of.orthonormal.vector.polynomials.derived.from the.
set.of.Zernike.functions.(Zhao.and.Burge.2007.and.2008)..An.important.advantage.of.this.algorithm.is.
that.the.phase.changes.in.the.gradient.are.signiicantly.smaller.than.those.in.the.wavefront.itself.so.that.
phase. wrapping. is. not. an. issue.. he. Zernike. decomposition. also. presents. an. easy. way. to. convert. from.
the.size.of.the.phase-retrieved.back.pupil.plane.to.that.of.the.array.used.to.set.the.DM..For.the.following.
results,.the.phase.retrieval.was.performed.on.an.image.stack.with.256.×.256.pixel.lateral.size.and.the.DM.
was.set.with.the.wavefront.measured.by.an.SHWFS,.which.is.32.×.32.pixels.and.not.perfectly.centered..
A.let-right.inversion.of.the.phase-retrieved.pupil.was.performed.to.account.for.the.imaging.of.the.back.
pupil.plane.on.the.wavefront.sensor.
To. demonstrate. the. accuracy. of. phase. retrieval. and. to. test. the. open-loop. control. with. the. mirror,.
we.set.the.DM.shape.to. Z 2 .(0°.astigmatism).with.amplitudes.between.-0.5.and.0.5.microns.and.mea-
sured.the.phase.in.the.back.pupil.plane.using.phase.retrieval..he.phase.was.then.decomposed.into.the.
Zernike.polynomials.(as.described.above).to.test.the.linearity.and.cross-talk.of.the.system. . Figure.15.21a .
shows.the.retrieved.amplitude.of. Z 2 .and. Z 2 − .(45°.astigmatism).versus.the.amplitude.of. Z 2 .set.by.the.DM..
For. Z 2 ,.the.slope.is.0.96.and.the.root-mean-square.error.(RMSE).is.20.9.nm..For. Z 2 − ,.the.slope.is.0.01.
and.the.RMSE.is.10.nm..Here.the.slope.is.1%.of.the.value.for. Z 2 ,.indicating.only.weak.cross.talk.between.
the. Zernike. modes.. We. tested. the. linearity. for. setting. other. Zernike. modes. on. the. DM. with. similar.
results..he.exception.was.in.setting.tip,.tilt,.and.focus. Z

( , , .and. Z 0 ) ..With.these.modes,.stage.drit.
can.cause.substantial.variations.from.measurement.to.measurement.. Figure.15.21b .shows.the.retrieved.
amplitudes.of. Z 1 − ,. Z 1 ,.and. Z 0 .versus.setting. Z 2 .
Figure.15.22 . shows.the.results.of.using.the.retrieved.phase.to.set.the.DM..Column.1.shows.the.PSF.
with.all.the.actuators.on.the.DM.set.to.0.V..he.PSF.is.strongly.distorted.with.a.calculated.Strehl.ratio.

1 1

Z

1