Super-resolved imaging based on spatiotemporal wavefront shaping Guillaume Noetinger1Samuel M etais2Geoﬀroy Lerosey3 Mathias Fink1S ebastien M. Popoﬀ1and Fabrice Lemoult1

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Super-resolved imaging based on spatiotemporal wavefront shaping

Guillaume Noetinger,1Samuel M´etais,2Geoﬀroy Lerosey,3

Mathias Fink,1S´ebastien M. Popoﬀ,1and Fabrice Lemoult1

1Institut Langevin, ESPCI Paris, Universit´e PSL, CNRS, 75005 Paris, France

2Aix Marseille Universit´e, CNRS, Centrale Marseille, Institut Fresnel, Marseille, France

3Greenerwave, 75002 Paris, France

(Dated: October 24, 2022)

A novel approach to improving the performances of confocal scanning imaging is proposed. We

experimentally demonstrate its feasibility using acoustic waves. It relies on a new way to encode

spatial information using the temporal dimension. By moving an emitter, used to insonify an object,

along a circular path, we create a temporally modulated waveﬁeld. Due to the cylindrical symmetry

of the problem and its temporal periodicity, the spatiotemporal input ﬁeld can be decomposed

into harmonics corresponding to diﬀerent spatial vortices, or topological charges. Acquiring the

back-reﬂected waves with receivers which are also rotating, multiple images of the same object

with diﬀerent Point Spread Functions (PSFs) are obtained. Not only is the resolution improved

compared to a standard confocal conﬁguration, but the accumulation of information also allows

building images beating the diﬀraction limit. The topological robustness of the approach promises

good performances in real life conditions.

Imaging devices exploit waves to retrieve information

about an object. Ultrasound imaging devices or optical

microscopes are two widespread commercially-available

technologies relying on diﬀerent waves, both oﬀering

key insights for medical diagnosis and scientiﬁc research.

While having diﬀerent properties, those approaches rely

on the same principles, and their resolution is limited

by the same diﬀraction eﬀects to a distance of the order

of the wavelength. More speciﬁcally, in optical full-ﬁeld

microscopy, a sample is uniformly illuminated and the

waves scattered oﬀ an object are collected with a micro-

scope objective. The ﬁnite aperture of the optical system

ﬁlters out waves corresponding to high scattering angles

and thus the smaller details [1]. The image of a point,

i.e. the Point-Spread Function (PSF) of the system, is

an Airy spot whose ﬁrst zero is located at a distance

1.22 λ

2NA from the focus (where λis the operating wave-

length and NA the numerical aperture). The Rayleigh

criterion states that two point-like objects closer than

this distance cannot be distinguished [2].

Overcoming this limitation is the domain of super-

resolution imaging and many techniques have already

been proposed [3–12]. As any label-free imaging scheme

can be decomposed in two main steps, i.e. acquiring data

and processing the acquired data, those techniques can

be divided in two diﬀerent classes.

The ﬁrst strategy consists in shaping the illumination

and/or the collection of waves. The simplest implementa-

tion is the well-known confocal microscope [13, 14], where

both the illumination and the detection correspond to a

diﬀraction-limited volume. In addition to suppressing

out-of-focus signals, it enhances the maximum transmit-

ted spatial frequency by a factor of two [15]. Neverthe-

less, such improvement is diﬃcult to observe experimen-

tally due to a poor gain for high spatial frequencies. The

increase in lateral resolution is usually considered to be

on the order of roughly 40%. Other approaches were pro-

posed, all relying on engineering the illumination or the

collection scheme, such as diﬀractive tomography [16, 17],

ptychography [18], structured illumination [19] or other

PSF-engineering [20, 21]. However, all these techniques

remain ultimately limited in resolution by the diﬀraction.

The second strategy consists in developing algorithms

for reconstructing the image. Indeed, the Rayleigh cri-

terion is somewhat an arbitrary rule. In particular, it

assumes any spatial frequency outside of the transmitted

bandwidth is deﬁnitely lost. Nonetheless, strong argu-

ments exist to claim that the resolution can be limited

only by the signal-to-noise ratio [22, 23]. However, the

presence of noise in real life experiments makes the prob-

lem ill-posed, forbidding a direct inversion of the mathe-

matical equations. Various algorithms were developed to

regularize the system by compensating for unknown or

noisy information using strong priors [24–27].

In this letter, we propose an approach combining wave-

front shaping and mathematical deconvolution for im-

proving the resolution. It consists in using dynamic wave-

front shaping to rotate an illumination wavefront, thus

using the temporal domain as an additional way to en-

code information. We show that it is equivalent to mea-

suring the image of an object with multiple imaging sys-

tems with diﬀerent orthogonal PSFs, corresponding to

diﬀerent harmonics of the received signals. The addition

of information provided by those images allows increas-

ing the eﬀective signal to noise ratio and thus improving

the resolution. We experimentally demonstrate this con-

cept in acoustics in a confocal-like conﬁguration by re-

constructing the image of two small scatterers. Using a

simple deconvolution process we show that two scatterers

can be distinguished below the diﬀraction limit.

The fundamental idea of the proposal relied on creating

a singularity that would allow discriminating precisely

arXiv:2210.12010v1 [physics.optics] 21 Oct 2022

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Super-resolvedimagingbasedonspatiotemporalwavefrontshapingGuillaumeNoetinger,1SamuelMetais,2GeoroyLerosey,3MathiasFink,1SebastienM.Popo,1andFabriceLemoult11InstitutLangevin,ESPCIParis,UniversitePSL,CNRS,75005Paris,France2AixMarseilleUniversite,CNRS,CentraleMarseille,InstitutFresnel,Marseille,F...

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Super-resolved imaging based on spatiotemporal wavefront shaping Guillaume Noetinger1Samuel M etais2Geoﬀroy Lerosey3 Mathias Fink1S ebastien M. Popoﬀ1and Fabrice Lemoult1.pdf

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Super-resolved imaging based on spatiotemporal wavefront shaping Guillaume Noetinger1Samuel M etais2Geoﬀroy Lerosey3 Mathias Fink1S ebastien M. Popoﬀ1and Fabrice Lemoult1

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