Optouidic adaptive optics in multi-photon microscopy Maximilian Sohmen 1Juan D. Mu noz-Bola nos 1Pouya Rajaeipour 2 Monika Ritsch-Marte 1C a glar Ataman 2 3and Alexander Jesacher1

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Optoﬂuidic adaptive optics in multi-photon microscopy

Maximilian Sohmen ,

1, ∗

Juan D. Mu˜noz-Bola˜nos ,

Pouya Rajaeipour ,

Monika Ritsch-Marte ,

1C¸

a˘glar Ataman ,

2, 3

and Alexander Jesacher

Institute for Biomedical Physics, Medical University of Innsbruck, 6020 Innsbruck, Austria

Phaseform GmbH, 79110 Freiburg, Germany

Microsystems for Biomedical Imaging Laboratory,

Department of Microsystems Engineering, University of Freiburg, 79110 Freiburg, Germany

(Dated: 21st April 2023)

Adaptive optics in combination with multi-photon techniques is a powerful approach to image

deep into a specimen. Remarkably, virtually all adaptive optics schemes today rely on wavefront

modulators which are reﬂective, diﬀractive, or both. This, however, can pose a severe limitation

for applications. Here, we present a fast and robust sensorless adaptive optics scheme adapted for

transmissive wavefront modulators. We study our scheme in numerical simulations and in experiments

with a novel, optoﬂuidic wavefront shaping device which is transmissive, refractive, polarisation-

independent and broadband. We demonstrate scatter correction of two-photon-excited ﬂuorescence

images of microbeads as well as brain cells and benchmark our device against a liquid-crystal spatial

light modulator. Our method and technology could open new routes for adaptive optics in scenarios

where previously the restriction to reﬂective and diﬀractive devices may have staggered innovation

and progress.

I. INTRODUCTION

Optical microscopy is a potent and indispensable tool

in many branches of science, in particular for biomed-

ical research. However, due to light scattering inside the

sample, conventional light microscopy is typically lim-

ited to the sample’s most superﬁcial tens of micrometres.

Prominent approaches to lift this limitation and increase

the imaging depth include multi-photon techniques [

]

and adaptive optics (AO) [

]. For the present work,

we rely on a combination of both, two-photon excited

ﬂuorescence (TPEF) microscopy as well as sensorless AO

– an approach that has been followed successfully in a vari-

ety of diﬀerent ways in the recent past, by many groups

worldwide [4–11], including ours [12–14].

AO relies on active shaping of a light ﬁeld’s wavefront

to improve image quality. The overwhelming majority of

wavefront shaping devices on the market today – such as

deformable mirrors, liquid-crystal-on-silicon spatial light

modulators (LCoS-SLMs), or microoptoelectromechani-

cal systems (MOEMS) [

] – operates in reﬂection

rather than transmission of a light ﬁeld. In addition,

many of these devices (of the above, e.g., LCoS-SLMs

and MOEMS) are diﬀractive rather than reﬂective op-

tical elements. While being reﬂective or diﬀractive is no

fundamental problem in numerous cases, in others – some

of them very relevant for applications – it can present a

serious challenge.

A novel kind of transmissive, refractive wavefront mod-

ulator that may present a well-suited alternative for such

scenarios is the deformable phase plate (DPP), a transpar-

ent multi-electrode optoﬂuidic device recently developed

∗Correspondence should be addressed to

maximilian.sohmen@i-med.ac.at

by some of us [

–

]. The following three aspects may

help to illustrate where the DPP can oﬀer advantages

compared to established wavefront modulators.

First, device integration: compared to a reﬂective

device, integrating the DPP into a pre-existing (e.g., com-

mercial) imaging system is much easier and does not

require additional beam folding optics. Similarly, stack-

ing several wavefront modulators in series (as, e.g., in

woofer-tweeter arrangements [

] or for multi-conjugate

AO) is far more straightforward using transmissive ele-

ments. Second, polarisation independence: whereas, e.g.,

liquid-crystal SLMs can only shape light that is linearly

polarised along a speciﬁc direction, the DPP can shape

light of arbitrary polarisation. This allows, on the one

hand, to freely combine the DPP with polarisation-optical

elements or, on the other hand, to shape unpolarised light

such as the ﬂuorescence from a microscopy sample. Third,

low chromatic dispersion: whereas, by principle, pixelated

holograms – displayed, e.g., on a liquid-crystal SLM or a

MOEMS – are highly dispersive and typically only allow to

shape wavelengths up to some tens of nanometres around

a chosen design value, the DPP – with a dispersion as low

as less than 1 mm of fused silica [

] – enables broadband

operation. Two immediate beneﬁts are evident: on the

one hand, in applications involving short laser pulses, a

drastic reduction of optical peak intensity due to pulse

dispersion can be avoided. On the other hand, in the

imaging context, broadband operation oﬀers, e.g., to ad-

dress diﬀerent ﬂuorophore classes in parallel using several

excitation wavelengths, or to route both excitation light

and returning (even multi-photon-excited) ﬂuorescence

signal through the device on a shared path (e.g., when

imaging back onto a pinhole as in confocal microscopy).

In our opinion, a practical AO approach that seeks to

fully exploit the beneﬁts of the DPP should therefore be

guided by the following key criteria: (i) simple integration

arXiv:2210.02100v3 [physics.optics] 20 Apr 2023

– maintaining the possibility to easily insert the DPP into

the optical path of a microscope; (ii) high speed – car-

rying out a complete AO correction run should be fast

(timescale seconds or less); (iii) accuracy – measuring and

compensating aberrations as accurately as possible; (iv)

robustness and user-friendliness – the corrections should

converge reliably without requiring parameter tweaking

by the user, ideally over a wide range of aberration sever-

ity [14].

This work is structured as follows. In Section II, we

present our approach to meet the above criteria (i)–(iv),

including a brief description of the DPP device, our wave-

front sensing strategy, and sketches of the optical layout

as well as our AO algorithm. In Section III A, we com-

pare diﬀerent algorithm variants in numerical simulations.

In Section III B, we experimentally demonstrate correc-

tion of strong aberrations through combination of our

sensorless AO algorithm with DPP wavefront shaping.

To this end, we present TPEF microscope images of two

kinds of samples, standardised ﬂuorescent beads as well

as ﬂuorescence-labelled brain cells. Finally, we discuss

our main ﬁndings (Section IV), give a brief Summary

and Outlook (Section V), and provide information on our

Materials and Methods (Section VI).

II. GENERAL APPROACH

Before we proceed to our numerical simulations and

experimental results, we will sketch our general approach

and the design considerations that have guided us in our

development process.

A. The deformable phase plate (DPP)

The DPP is a transparent optoﬂuidic device designed

for wavefront modulation of a light ﬁeld in transmis-

sion [

–

]. The DPP’s ﬂuid chamber is formed by a

micro-machined ring spacer, placed on a glass substrate

and spanned by a deformable polymeric membrane (see

Fig. 1). Channels in the glass substrate through which the

chamber is ﬁlled with liquid are sealed after manufacture.

On the glass substrate, contact pads in the periphery

individually connect to 63 transparent electrodes in and

around the central aperture. Application of a voltage

between any of these electrodes and the grounded, con-

ductive membrane gives rise to an electrostatic force which

deforms the membrane. If, consequently, the ﬂuid cham-

ber’s local thickness changes from

+ ∆

, the

corresponding phase shift for a transmitted light ﬁeld

of wavelength

is ∆

= 2

(∆

`/λ

)∆

, where ∆

the according diﬀerence in refractive index between the

ﬂuid and air. While electrostatic actuation alone would

only enable a unidirectional pulling of the membrane,

hydro-mechanical coupling by the liquid inside the sealed

chamber establishes a bidirectional push-pull mechanism,

where a positive displacement in one membrane portion

Figure 1:

The deformable phase plate (DPP).

(a) Top-

view drawing. Each of the transparent electrodes in the centre

region can be set to an individual electric potential through

connected contact pads. (b) Cross-sectional drawing and prin-

ciple of operation. A voltage between an array electrode and

the grounded membrane results in a membrane deformation.

The locally varying optical path length leads to a wavefront

modulation of an oncoming light ﬁeld. (c) Photograph of

the DPP naked and (d) readily assembled in its 30-mm cage-

compatible housing.

leads to a negative displacement in the other portions,

and vice versa.

The DPP action is independent of polarisation, free

from diﬀractive losses, nearly non-dispersive, gravity-

neutral (see Methods), and shows no observable hyster-

esis, allowing for operation with open-loop control. For

wavelengths between 400 and 2200 nm, the present DDP

(Delta 7, Phaseform GmbH, Freiburg i. Br., Germany)

shows

>85 %

transmission of power, limited primarily by

Fresnel reﬂection at uncoated surfaces; only below 400 nm

absorption by the polymeric membrane becomes appre-

ciable. The maximum stroke of the DPP is highest for

low-order Zernike modes, e.g., about

m (peak-valley)

optical path diﬀerence for a defocus aberration at 632 nm

wavelength. The rise time (10 % to 90 % of set value) of

the DPP is about 50 ms, limited by ﬂuid ﬂow.

B. Wavefront sensing strategy

The idea of sensorless AO is to conduct many cycles

of applying test modes to the wavefront modulator while

measuring their eﬀect on the target signal (e.g., ﬂuores-

cence intensity) and to construct a wavefront correction

pattern from this information [

]. In our case, however,

faced with the comparatively long switching time of the

DPP, it is desirable to follow a wavefront sensing strategy

where taking fast measurements of individual modes is

decoupled from the limited wavefront modulator speed.

Focus Scanning Holographic Aberration Probing

SHARP), as introduced by Papadopoulos et al. [

was one of the ﬁrst methods to employ such a decoup-

ling. The basic principle of F

SHARP is to split the

laser beam for ﬂuorescence excitation in an interferometer

and to vary the angle between the two interferometer

arms – a stronger, static reference beam and a weaker,

scanned probe beam – using a fast piezo mirror. The

recorded interferogram then directly reveals the aberra-

tions accumulated along the optical path to the sample

plane, which can in turn be compensated by a wavefront

modulator. The wavefront modulator itself is kept con-

stant during the (fast) piezo scanning operation and only

has to be switched once per algorithm iteration (after

the aberration ﬁeld has been determined), wherefore the

wavefront modulator switching time is in general not too

limiting for the total algorithm speed. Besides this speed

advantage, F

SHARP exhibits a very robust operation:

in contrast, e.g., to modal wavefront sensing techniques

[

], the F-SHARP algorithm converges reliably even if

the aberrations are comparatively strong [10].

To-date, F

SHARP-type methods have been used ex-

clusively in combination with LCoS-SLMs [

–

], i.e.,

wavefront modulators that are reﬂective and diﬀractive.

Here, we present and test a novel variant ﬁt for use in

combination with transmissive (and, as in case of the

DPP, refractive) wavefront modulators.

C. Optical layout

A schematic of our optical setup is presented in Fig. 2.

This setup is based on the original F

SHARP implementa-

tion [

], yet with two crucial modiﬁcations. First, instead

of a Mach-Zehnder, our setup features a Michelson inter-

ferometer, bearing the advantage that distances which

are not common path between the two arms can be kept

as short as possible, helping to minimise relative vibra-

tions, drifts, and alignment maintenance. Second, instead

of shaping only the static reference beam, in our DPP

version both, static reference and scanned probe beam are

wavefront-shaped.

These two modiﬁcations greatly simplify integrating

SHARP into pre-existing optical setups: the Michel-

son interferometer, on the one hand, can be designed

as a highly stable and compact add-on module in the

early excitation path; the DPP, on the other hand, being

transmissive, can be inserted almost everywhere along the

downstream optical path. In our case, the DPP is located

close to a pupil-conjugate plane (within some millimetres

accuracy).

D. Algorithm outline

Figure 3provides a diagrammatic overview over im-

portant algorithm steps shared and diﬀering between the

original and our variant of F-SHARP.

Figure 2:

Sketch of the optical layout.

BSC = (non-

polarising) beam splitter cube, DPP = deformable phase plate,

PMT = photomultiplier tube, SLM = spatial light modulator.

In Step 1, the phase correction mask is initialised ﬂat.

In Step 2, by phase-stepping the piezo in the probe arm

at a range of diﬀerent tip/tilt angles and measuring the

TPEF intensity generated in the object plane, we inter-

ferometrically obtain an estimate of the aberrations in

the excitation path. In Step 3, the ﬁeld obtained through

interferometry is propagated numerically to the wavefront

modulator location (in our case, where the DPP is pupil-

conjugate, this corresponds to a Fourier transform). In

Step 4, the old phase mask (from a previous iteration)

is either replaced by the negative new mask in case only

the static beam is shaped (as for F

SHARP with SLM;

Figure 3:

Diagrammatic algorithm outline

. Overview of

critical steps shared and diﬀering between the original and

our F

SHARP variant. Functions with names ending with an

exclamation mark modify their argument.

FT!(. . .)

: Fourier

transform;

optimise(. . .)

: ﬁnd the voltages that optimally

reproduce a target phase mask (e.g., in Zernike basis) at given

constraints [

denotes the inﬂuence matrix,

u lim

the

voltage limit of the DPP electrodes (see main text).

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Optouidicadaptiveopticsinmulti-photonmicroscopyMaximilianSohmen,1,JuanD.Mu~noz-Bola~nos,1PouyaRajaeipour,2MonikaRitsch-Marte,1CaglarAtaman,2,3andAlexanderJesacher11InstituteforBiomedicalPhysics,MedicalUniversityofInnsbruck,6020Innsbruck,Austria2PhaseformGmbH,79110Freiburg,Germany3MicrosystemsforB...

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Optouidic adaptive optics in multi-photon microscopy Maximilian Sohmen 1Juan D. Mu noz-Bola nos 1Pouya Rajaeipour 2 Monika Ritsch-Marte 1C a glar Ataman 2 3and Alexander Jesacher1

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