Adaptive Optics in Wide-Field Microscopy - Adaptive Optics for Biological Imaging - page 291

of.0.005..(Although.for.such.a.strongly.distorted.PSF,.the.Strehl.ratio.is.not.that.meaningful.since.the.
peak.intensity.is.not.at.the.center.of.the.PSF.).Column.2.shows.the.results.ater.correcting.the.DM.with.
the.retrieved.phase..he.PSF.is.dramatically.improved..he.Strehl.ratio.is.0.2,.a.40-fold.improvement..
Another.round.of.correction.improves.the.Strehl.ratio.to.0.75..We.let.the.loop.run.through.two.more.
cycles,.but.the.Strehl.ratio.did.not.substantially.improve,.ultimately.reaching.0.78..Because.of.imperfec-
tions.in.the.microscope.objective.and.surface.roughness.in.the.various.optical.elements,.a.perfect.Strehl.
ratio.of.1.is.never.achieved.in.practice..A.Strehl.ratio.of.0.78.corresponds.to.an.RMS.wavefront.error.of.
roughly.40.nm.and.indicates.a.difraction-limited,.well-corrected.optical.system.
For.Figure.15.22,.each.image.stack.was.256.×.256.pixels.with.21.slices.from.2.0.microns.below.focus.
to. 2.0. microns. above. focus. in. 0.2. micron. steps.. he. phase. retrieval. ran. for. 64. iterations,. which. took.

0.6

1.2

Z - 1
Z 1
Z 0

1

1
1
2

0.4
0.2
0

0.8
0.6
0.4
0.2
0

- 0.2
- 0.4 - 0.2

- 0.4
- 0.6
- 0. - 0.5

- 0.6
- 0.8
- 0.5

0
Amplitude set on DM
(a)

0
Amplitude of Z 2 set on DM (microns)

0.5

0.5

(b)

FIGuRE 15.21 (a).Plot.of.the.amplitude.of. Z 2 .(circles).and. Z 2 − (squares).determined.by.phase.retrieval.versus.the.
amplitude.of. Z 2 .set.on.the.DM..he.solid.lines.are.linear.its.to.the.data..he.slope.of.the.it.to. Z 2 .is.0.96,.and.the.
root-mean-square.error.(RMSE).is.20.9.nm..he.slope.of.the.it.to. Z 2 − .is.0.0097.and.the.RMSE.is.9.9 nm..(b).Plot.
of.the.amplitude.of. Z 1 − ,. Z 1 ,.and. Z 0 .determined.by.phase.retrieval.versus.the.amplitude.of.set.on.the.DM..here.is.
substantial.drit.from.measurement.to.measurement.

3
2
1

0.05 3

2
1

0.65 3

2
1

3
2
1

1.00 1.00 3

2
1

1.00

0

0 0 0 0

- 1
- 2
- 3

- 1
- 2
- 3

- 1
- 2
- 3

- 1
- 2
- 3

- 1
- 2
- 3

0.00

0.00

0.00 0.00 0.00

- 3 - 2 - 1 0 1 2 3 - 3 - 2 - 1 0 1 2 3 - 3 - 2 - 1 0 1 2 3 - 3 - 2 - 1 0 1 2 3 - 3 - 2 - 1 0 1 2 3

3
2
1

0.00

- 1.00 3

2
1

3
2
1

0.00

0.00 3

2
1

0.00 3

2
1

0

0 0 0 0

- 1
- 2
- 3

- 1
- 2
- 3

- 1
- 2
- 3

- 1 - 1

- 2
- 3

- 2
- 3

- 3.50

- 3.00 - 3.00 - 3.00 - 3.00

- 3 - 2 - 1 0 1 2 3 - 3 - 2 - 1 0 1 2 3 - 3 - 2 - 1 0 1 2 3 - 3 - 2 - 1 0 1 2 3 - 3 - 2 - 1 0 1 2 3

3.14 3.14 3.14 3.14 3.14

- 3.14 - 3.14 - 3.14 - 3.14 - 3.14

FIGuRE 15.22 Iterative. correction. of. the. microscope. PSF.. Top. row:. in. focus. image. of. the. PSF,. linear. scale..
Second.row:.same.as.irst.row.but.on.a.log.scale..hird.row:.phase.in.the.back.pupil.plane.calculated.from.phase.
retrieval.with.the.tip,.tilt,.and.focus.terms.removed..First.column:.before.correction;.DM.actuators.all.set.to.0.V..
Each..successive.column.is.ater.a.round.of.iteration.