aurélie facomprez , pierre mahou , emmanuel beaurepaire · aurélie facomprez1, pierre mahou1,...

Delphine Débarre1,2, Jun Zeng1, Nicolas Olivier1,

Aurélie Facomprez1, Pierre Mahou1, Emmanuel Beaurepaire1

1 Lab. for Optics and Biosciences, Ecole Polytechnique, Palaiseau, France

2 Lab. for Interdisciplinary Physics, Grenoble, France

www.lob.polytechnique.edu

3D mapping and correction of aberrations in nonlinear microscopy using modal image-based approaches

Nonlinear microscopy and aberrations

Principles of modal adaptive optics

Accuracy of correction

Time and exposure

3D resolved aberration mapping

Spatial variations of aberrations

Strategies for 3D resolved aberration correction

Modal image-based adaptive optics for nonlinear microscopy

Nonlinear (=multiphoton) microscopy

Multiphoton processes occur onlywhere the intensity is highest,

i.e. near the focus of the objective.

Confinedexcitation

F I2

(0.5 × 2µm)

Multiphoton microscopy : Cornell Univ (NY, USA) 1990

2‐photon excitation 1‐photon excitation

Pulsed laser

488 nm

520 nm F I

900 nm

520 nm F I2

CW laser 2PEF : two‐photon excitedfluorescence

B Am

os

near‐infrared femtosecondpulses 100 fs, 80MHz.

The laser beam is focused inside the sample.It is then scanned in 2D and 3D with mobile mirrors, to record an image.

pixel = 3µs. image 2D= 0.5‐2s. image 3D = 20‐120s.

Anim

T. Savy

Examples of applications

Olivier et al, Science 2010Polytechnique LOB / CNRS N&D Gif

Dev biology: THG imaging of a zebrafish embryo

Neuroscience: 2PEF imaging of “brainbow” labelled mouse brain tissue

Thick / live tissue imaging

Mahou et al, Nat Methods 2012Polytechnique LOB / Inst Vision Paris

THG

2PEF

Optical aberrations in microscopy

Flat wave front

Biological sample

Aberrated focus

Objective lens

Diffraction-limited focus

Sources of aberrations

Optical system elements

Specimen

Effects of aberrations

Enlarged focal spot

Sources of aberrations

Optical system elements

Specimen

Effects of aberrations

Enlarged focal spot

Loss of resolution

Decrease in signal

Limited penetration depth

Unstained zebrafish embryo development,THG microscopy, 4 different imaging planes


Principle of modal adaptive optics

coll. N. Peyriéras, CNRS N&D Gif




Time and exposure





A typical adaptive optics system…

Wavefrontsensor

Beam splitter

Correction element

Aberratedwavefront

Corrected wavefront

Control system


Principle of adaptive optics

…developed for astronomy

Direct aberration measurement is more complicated than in astronomy!


Principle of adaptive optics

A typical adaptive optics system…

Wavefrontsensor

Beam splitter

Correction element

Aberratedwavefront

Corrected wavefront

Control system

Pre-aberrated wave front

Objective lens

Specimen

Adaptive element

Flat wave front

Apply aberration

Acquire image

Calculate quality metric

Estimate correction

phase

Apply correction

Choose aberration

Optimisation algorithm

Aberration representation

Image quality metric

Adaptive optics for microscopy

Iterative aberration correction algorithm: modal approaches

Confocal: Booth et al, PNAS, 20022PEF: Débarre et al, Opt. Lett. 34, 2495, 2009

THG/2PEF: Olivier et al Opt Lett 34, 2145, 2009Accuracy analysis: Facomprez et al, Opt Exp, 2012Aberration maps: Zeng et al, Biomed Opt Exp, 2012

See work by M Booth, D Débarre, T Wilson (Oxford)

The wavefront shape is decomposed on an aberration basis :

= 0.3 - 0.7 - 0.5 + 0.3

Zernike modes (n=1 to 4)

The basis is chosen to appropriately describe

the aberrations

Example :

defocus astigmatism

comaspherical aberration

Modal aberration decomposition


1 2

3 4 5 6 7

8 9 10 11

X X X

2-photon fluorescence imaging

Correction of a single aberration mode (astigmatism)

Metric = image intensity

Maximisation using three image measurements with applied aberrations

Image

Metric

Initial

Applied aberration

Initial - b Initial + b Corrected

known curve calculated maximum

Coefficient retrieval - one aberration mode


2PEF2 Photon Excited

Fluorescence

THGThird Harmonic

Generation

Lily pollen grain

Olivier et al,Opt. Lett. 34, 3145 (2009)

THG correction 2PEF correction

Multimodal nonlinear microscopy


2PEF2 Photon Excited

Fluorescence




Time and exposure





Range of accurate correction

Exposure/time required

• Number of measurements per mode

• Type of algorithm

• Number of iterations

• Signal intensity

Experimental investigation


sample

1 iteration

2 iterations

3 iterations


Number of iterations of the correction algorithm

A practical case

•Efficient correction with 5N algorithm

•2-3 iterations can futher improveaccuracy

(here: for aberrations up to 1.8 rad)

-> precision and limiting factor ?

(Zernike modes have non-independent influence).

Facomprez et al., Opt. Express 20, 2598 (2012)

what we need:

• Very little signal is required to correct for aberrations

what we use:

Number of photons used for correction


Red = starting with 0 rad aber., 3 iterationsBlue = adding 1 rad aberration

E NNtot PB

F(E0)

Number of modes

Number of points/mode

Detector noise

“Modulation depth”

Number of photons/mode

measured

Metric modulation over image

(prop. to signal)

Only free parameter

Faco

mpr

ez e

t al.,

Opt

. Exp

ress

20,

259

8 (2

012)

THG imaging of a developing drosophila embryo

Unc

orre

cted

Cor

rect

ed

. 1 correction update every minute

. Signal x2.5

. Extra-illumination +150%Olivier et al, Opt Lett 34, 2145 (2009)

Time-resolved correction on live samples





Time and exposure





Spatially averaged measurement

Spatially resolved measurement



Measured aberration map -

System aberration map


Sample aberrations

-0.4 0.4Aberration amplitude (rad)

100 µm


Aberration maps : ex vivo human skin

Ex vivo human skin samplemounted in PBS, 2PEF/SHG signals

depth : 80µm


With M‐C. Schanne‐Klein (X‐LOB),A‐M Pena (l’Oreal)

Note – Here, aberrations originatemostly from surface folds

Zeng

et a

l., B

iom

ed. O

pt. E

xpre

ss 3

, 189

8 (2

012)

Fixed mouse brain slice in PBS. Endogenous

fluorescence, 2PEF

100 µm

depth = 80µm below surface

astigmatism coma spherical ab.

Aberration maps : fixed mouse hippocampus


Note – Here, aberrations appear in volume, with imaging depthZeng et al., Biomed. Opt. Express 3, 1898 (2012)

Samples preparation: J. Livet, K. Matho

(Inst Vision)


Aberrations and refractive index distribution


• n2 > n3 > n1

• Only n3 is fitted (withinrealistic values) to match the mesures.

• Simulations confirm the validity of the measures.

• Volumetric opticalproperties account for the aberrations

Fixed mouse brain slice in

PBS. Endogenous fluorescence,

2PEF

1.39

1.3551.33

100 µm

Zeng

et a

l., B

iom

ed. O

pt. E

xpre

ss

3, 1

898

(201

2)

Aberration maps : effect of index matching

100µm

fixed

mou

se b

rain

slic

e in

Vec

tash

ield

, CFP

labe

lling

+ au

toflu

ores

cenc

e, 2

PE

F im

agin

g


Correction over a small region of isoplanetism

fixed

mou

se b

rain

slic

e, C

FP la

belli

ng+

auto

fluor

esce

nce,

2P

EF

imag

ing

20µm


With index matching, aberrations are homogeneousover ~50µm «aplanetism» zones.

-> local correction is possible

… what about correcting over larger zones ?

Zeng et al., Biomed. Opt. Express 3, 1898 (2012)

Correction over a small region of isoplanetism - limit

100µm

Strehl ratio afteraverage correction

Strehl ratio aftercorrection on green area


Zeng

et a

l., B

iom

ed. O

pt. E

xpre

ss

3, 1

898

(201

2)

Spatially resolved correction

# subregions = 1 # subregions = 9 # subregions = 25 # subregions = 64

• Adaptive scanning pattern + slowly changing correction

• (Multiconjugate adaptive optics)

Challenge : the number of measurements scales as the number of subregions…


Spatially-resolved correction despite slow mirrors?

… simpler estimation?

Pixel = 3µs. Line ~msImage 2D= 0.5-2s.

fixed

mou

se b

rain

slic

e,

auto

fluor

esce

nce,

2P

EF

imag

ing


Aberrations and refractive index distribution


Another possibility:

Simulations confirm the validity of the measures.-> predictive (progressive) correction may be possible

• Model‐based AO permitsmeasurement/correction over a large range of aberrations

• Accuracy and precision can be assessed from the experimental parameters

• Time and exposure required for a single correction are compatible with biologicalimaging

• Spatial variations of aberrations restrict correction to a small region of aplanetism

• Predictive aberration correction could permit spatially resolved correction

Conclusion and Outlook

Note 1 ‐ The wavefront is decomposed on a truncated aberration basis:

= 0.3 ‐ 0.7 ‐ 0.5 + 0.3 …correction device can generate a finite number of aberration modes

n1

n2> n1

Note 2 ‐ Only limited phase gradients can be compensated for:

…the limit is set by the excitation NA

Laboratory for Optics and Biosciences

Delphine Débarre

NicolasOlivier

PierreMahou

AurélieFacomprez

JunZeng

Acknowledgements

www.lob.polytechnique.edu

Time-resolved correction on a developing sample:Olivier et al., Opt. Lett. 34, 3145-47 (2009)

Accuracy of modal correction:Facomprez et al., Opt. Express 20, 2598-2612 (2012)

3D aberration mapping:Zeng et al., Biomed. Opt. Express 3, 1898-1913 (2012)

Additional thanks: • Marie-Claire Schanne-Klein (LOB), • Maxwell Zimmerley (LOB),• Thibault Vieille (LOB)• Ana-Maria Pena (L’Oréal),• Jean Livet, Katie Matho (Inst de la Vision Paris)• Nadine Peyriéras (CNRS N&D Gif)• MicAdO consortium (ESPCI, ENS, Imagine Optic)

+ ANR RIB 2007

aurélie facomprez , pierre mahou , emmanuel beaurepaire · aurélie facomprez1, pierre mahou1,...

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