Polarization-resolved microscopy through scattering media via wavefront shaping
aa r X i v : . [ phy s i c s . op ti c s ] N ov Polarization-resolved microscopy through scattering media via wavefront shaping.
Hilton B. de Aguiar, ∗ Sylvain Gigan, and Sophie Brasselet † Aix-Marseille Universit´e, CNRS, Centrale Marseille,Institut Fresnel UMR 7249, 13013 Marseille, France Laboratoire Kastler Brossel, UMR 8552 of CNRS and Universit´e Pierre et Marie Curie, 24 rue Lhomond, 75005 Paris, France
Wavefront shaping has revolutionized imaging deep in scattering media , being able tospatially and temporally refocus light through or inside the medium. However, wavefrontshaping is not compatible yet with polarization-resolved microscopy given the need of polarizingoptics to refocus light with a controlled polarization state. Here, we show that wavefront shapingis not only able to restore a focus, but it can also recover the injected polarization state withoutusing any polarizing optics at the detection. This counter-intuitive effect occurs up to severaltransport mean free path thick samples, which exhibit a speckle with a completely scrambledstate . Remarkably, an arbitrary rotation of the input polarization does not degrade the qualityof the focus. This unsupervised re-polarization — out of the originally scrambled polarization state— paves the way for polarization-resolved structural microscopy at unprecedented depths. Weexploit this phenomenon and demonstrate second harmonic generation (SHG) structural imagingof collagen fibers in tendon tissues behind a scattering medium. FIG. 1.
Illustration of polarization state scrambling during propagation in a scattering medium and principleof polarization revival via wavefront shaping . When light propagates in a scattering medium, the wavefront is rapidlydeformed into a speckle pattern, but polarization scrambling occurs on a different length scale. In the forward scatteringregime (as typically found in biological tissues), when the thickness L is much less the transport mean free path l t , forwardscattering events mainly conserves the initial polarization state. In the diffusive regime L > l t , (a) for an unshaped wavefront,the polarization of the speckle gradually scrambles and lacks any resemblance with the input one. The bottom panel illustrateshow during propagation each forward scattering conserves polarization (continuous line) and how polarization is mixed whenentering the diffusive regime (dashed). In contrast, we observe that (b) an optimal wavefront shaped by a spatial light modulator(SLM) is not only able to refocus light, but also recovers the original polarization state even without polarizing optics in thedetection. Accessing the structural organization of molecular assemblies is an important aspect of biological imaging. Forinstance, this organization determines important functions such as the formation of bio-filaments, but also contributesto disorders such as in the formation of amyloids in neurodegenerative diseases. Polarization-resolved microscopies areable to provide molecular structural insights beyond the diffraction-limited scale , and, being non-invasive and non-destructive, could in principle be used for deep in-vivo structural imaging. Unfortunately, light propagation throughmultiply scattering media, like thick biological tissues, inherently scrambles polarization states. After injection of awell-defined polarization state and wavevector direction, each successive scattering event rotates the polarization .Thus, after multiple scattering events the polarization is ultimately scrambled and the wavefront concomitantlydistorted generating a speckle (schematically sketched in Fig. 1.a). This unavoidable scrambling makes molecularstructural imaging impossible deep in biological media. Most importantly, it is highly detrimental for polarization-resolved studies because no predetermined relation with the incoming polarization state exists anymore: this is indeeda prerequisite for the analysis of the polarized response and its relation to structural modeling .Wavefront shaping has been introduced to overcome penetration depths limits in scattering media . By coherentlycontrolling the speckle pattern generated from multiple scattering events, one can increase the energy density attargeted positions building a constructive interference locally. Wavefront shaping allows refocusing light through ,or inside , scattering media thanks to the manipulation of the wavefront phase or amplitude . Nevertheless,the analysis of polarization effects on wavefront shaping experiments has been often disregarded because, in principle,there are no correlations among the t ijmn elements of the vectorial transmission matrix t , relating input field E in with polarization state i to output field E jm with polarization state j . Thus, in order to control the output polarizationstate, one needs to perform polarization sensitive measurements of the transmission matrix .Here, we demonstrate an effect which enables polarization-resolved imaging through scattering media, and formsthe basis for prospective deep structural molecular imaging: polarization revival out of a polarization-state-scrambledspeckle (Fig. 1.b).We first discuss aspects related to the speckle without wavefront shaping. We performed experiments at controlledoptical thickness ( L/l t ) using phantoms with scattering properties similar to biological media (see Methods). To aidthe discussion, the inset of Fig. 2.a shows simplified schematics of the polarization state combinations used. Fig. 2.a(red dashed) shows the spatially output-averaged Degree of Linear Polarization (DOLP= (cid:0) I k − I ⊥ (cid:1) / (cid:0) I k + I ⊥ (cid:1) , whereI is intensity) of the speckle observed outside the medium. As L/l t increases, the speckle polarization state decreasesits correlation with the initial linearly polarized one as evidenced by the decrease in h DOLP i .Conversely, when performing wavefront shaping the outcome is very different. To find the optimal wavefronts,a broadband transmission matrix is first acquired (see Methods) without any selection of output polarization state using the experimental layout shown in Fig. 4.a (Fig. 2.a inset, continuous line). In practice, this is equivalent toacquire experimental transmission matrix elements t ( exp ) mn = t xxmn + t yxmn . Once the transmission matrix is known, wecan selectively refocus light at targeted positions (Fig. 2.a, upper right panel). Surprisingly, upon rotation of theinput polarization state the refocus does not degrade. We further quantified this resilience to a change in input stateas intensity ratio between the two injected polarization states (I ⊥ / I k ) shown in Fig. 2.a (continuous line). Clearly,only minute degradation of the refocus intensity ratio is seen reaching depths in the diffusive regime ( L/l t > t xxmn ≈ t yymn . These correlations are formally shown in Fig. 3 as cross-correlation of anotherset of measurements where t xxmn and t yymn are independently measured for the same realization of disorder (with thepolarization state combination used shown in Fig. 3 left panels). In this analysis, which procedure is explained inSupplementary Section 2, the peak above the noise confirms that the diagonal elements of the vectorial transmissionmatrix are highly correlated. We conclude from these observations that t ( exp ) mn ≡ t xxmn , since the speckle from t yxmn hasa smaller contrast and is moreover weakly correlated with t xxmn (see Supplementary Section 2 for correlation amongelements). We further explored the reason for these effects and found out that the transmission matrix correlationsand polarization state revival are related to the broadband nature of the acquired transmission matrix. Indeed,these effects are considerably decreased when the transmission matrix is taken with a monochromatic source, asexpected (see Supplementary Section 3 for similar experiments performed with monochromatic light).We then exploited these correlations for demonstrating nonlinear structural imaging. Fig. 4 shows the experimentallayout and representative results of a wavefront shaping experiment. In a first step, a polarization combination isused where analyzer and incoming polarization state are aligned together, that is, a configuration measuring the t xxmn elements. Note that the presence of the analyzer is not necessary for a wavefront shaping experiment, but it supportsan unambiguous proof of structural imaging (see below). After acquiring the broadband transmission matrix (seeMethods), we spatially refocus light in a raster scanning fashion and acquire in parallel the enhanced SHG signalfrom nanocrystals of potassium titanyl phosphate (nanoKTP). The dipolar character of nanoKTP ensures that noambiguity exists in the polarization state evaluation. The refocused light generates efficient SHG from the nanoscopicsources as seen by the two nanoparticles in Fig. 4.b (left panel). In a second step, a second imaging scan using thevery same optimal wavefronts is taken (Fig. 4.b, right panel), however with the incoming polarization state rotated90 ◦ . The refocus after the scattering medium still persists and highlights the second particle revealing the orientation- FIG. 2.
Experimental quantification of polarization revival . (a) Left panel: averaged degree of linear polarizationof the speckle ( h DOLP i , red squares) and refocus polarization ratio after wavefront shaping ( I ⊥ I k , corresponding to the samewavefront but rotated input polarization, green circles), as a function of optical depths L/l t . Polarization scrambling of thespeckle occurs for length of the order of l t . Nevertheless, at depths of several l t , after shaping, the refocus intensity survives achange of 90 ◦ of the input polarization. (Right panels) speckle image after (top) and before (bottom) the wavefront shapingprocedure. The scattering media are made of 5 µ m-diameter polystyrene beads. (b) Similar experiments performed usingopaque 1 mm-thick acute brain slice coronal cross section as scattering medium. (top left panel) Non-analyzed refocus intensity(green circles) upon rotation of the excitation field. (right panels) Images show the refocus at two input polarization state( ⊥ and k ) with the same intensity scale. (bottom left panel) The refocus polarization state purity is evaluated by placing ananalyzer and observing an extinction (black circles). Scale bars: 1 µ m. dependent nonlinear efficiency. This highlights the presence of nanoKTP crystals with different orientations, whichare identified using the same wavefront. Any oriented nonlinear source could be probed in the same way, highlightingits molecular order organization in a scattering medium. A similar situation is found, for example, in coherent Ramanimaging of biological membranes or myelin sheath in neurons .The implication of these observations for structural nonlinear imaging in biologically relevant specimens are shownin Fig. 5. In order to mimic a nonlinear microscopy experiment, we showcase SHG imaging of collagen fibers placedafter the scattering medium with a characterized transmission matrix. Different from the previous experiment, herewe exploit the memory effect to raster scan the refocus . This methodology is able to provide highly contrastedSHG images of rat tendon specimens where clear fibers can be seen running along the diagonal of the images (Fig. 5,left panel). In this demonstration, we do not use an analyzer to detect the SHG: in an eventual refocusing inside ascattering medium the nonlinearly generated photons polarization state would be scrambled . Therefore, structuralimaging is only insightful if performed in a non-analyzed configuration. By fixing the refocus position in a fiber androtating the excitation polarization state, we can still perform a polarization-resolved study . Fig. 5 (right panel)shows the measured SHG intensity (green circles) and a fit (black continuous line). The retrieved nonlinear opticalconstants of collagen are in excellent agreement with previously reported values (see Supplementary Section 4 forfurther information on the SHG analysis).Finally, we expect these correlations to have profound implications for deep structural imaging in various approaches.For instance, acoustic-based methods are able to refocus in the diffuse regime ( L > l t ) with cellular resolution.This means that the acoustic signal from the obtained refocus could be able to perform structural analysis: If theabsorbers are organized in an ordered way, a rotation of the refocus optical polarization, using the very same wavefront, FIG. 3.
Experimental quantification of vectorial transmission matrix correlations . Cross-correlation of vectorialtransmission matrix elements with polarization combinations xx and yy for L/l t ≈
6. The peak confirms strong correlationbetween the matrix elements thus explaining the resilience of the focus to a polarization state change.FIG. 4.
Demonstration of structural imaging through scattering media exploiting transmission matrix corre-lations . (a) Simplified experimental layout. Ultrashort pulse wavefronts are shaped by a SLM and focused on the scatteringmedium. The speckle transmitted by the scattering medium excites the nonlinear sources (nanoKTP) placed at a plane furtherimaged on a complementary metal-oxide semiconductor camera (CMOS) and a photomultiplier tube (PMT). (b) Polarization-resolved SHG images. In a first step, the vectorial transmission matrix elements t xxmn are acquired and used for raster scanningthe refocus thus generating the SHG images (left panel). The inset in (a) shows the brightfield (BF) image at the same regionof interest (ROI) where two particles can be seen. In a second step, only the excitation polarization is rotated and a secondscan is taken (right panel, 5x rescaled) using the very same t xxmn elements. Scale bar: 1 µ m. should lead to a change in the acoustic signal. METHODS
Optical set-up . Ultrashort pulses (130 fs, 800 nm, 76 MHz repetition rate, Mira, Coherent) are steered onto a256 ×
256 pixels reflective SLM (Boulder Nonlinear Systems). The SLM is imaged on the back focal plane of thefocusing lens (achromatic lens, f=19 mm, AC127-019-B-ML, Thorlabs) with the scattering medium placed after it.The nanoKTP crystals are imaged by an objective (40X, 0.75 NA, Nikon) on a 12-bit CMOS camera (Flea3, PointGrey) and on a large area photon counting PMT (MP 953, PerkinElmer). The SHG signal is spectrally separatedwith suitable dichroic mirror (560 nm longpass, AHF Analysentechnik), shortpass (700 nm, FESH0700, Thorlabs) and
FIG. 5.
Applications of transmission matrix correlations for biological specimens nonlinear structural imaging. (left panel) Raster scanning using the memory effect generates SHG images from rat tail collagen tendon placed after a thindiffuser with a known transmission matrix. (right panel) By refocusing on a specific fiber, the intensity response of the SHGsignal is recorded as the input angle varies. The continuous line (black) is a fit to the data (green circles) from which we retrievethe nonlinear susceptibilities values of the collagen fiber. The retrieved nonlinear susceptibilities reveals the molecular order ofthe fibers and are in excellent agreement with previous observations (see Supplementary Section 4). bandpass (400 ±
10 nm, Chroma Technology) filters. Additionally, a longpass filter (650 nm, FELH0650, Thorlabs)and a zero-order half-wave plate (46-555, Edmund Optics) — placed in a motorized rotation stage — are used forthe excitation beam before the focusing lens. An analyser (WP25M-UB, Thorlabs) is used to select the detectedpolarization state whenever stated.
Broadband transmission matrix measurement, wavefront shaping and nonlinear imaging methodol-ogy . A thorough description of the methods used for acquisition of the transmission matrix can be found elsewhere .It consists of a two-step process: first the broadband transmission matrix of the system is acquired using ultrashortpulses. Once acquired, the transmission matrix elements are used for selective refocusing in a ROI. Briefly, for eachinput-output channel, phase and amplitude of the corresponding transmission matrix element are obtained by phase-shifting interferometry. The wavefront phase of a Hadamard base (input channel) is shifted in respect to a referencefield in the range [0 − π ] with its intensity recorded by a CMOS pixel (output channel). A Fourier transform isapplied on the output channel interferogram of the n th Hadamard basis thus retrieving its phase and amplitude.Once all the Hadamard basis are measured, an unitary transformation is applied to obtain the transmission matrixin the canonical basis . For acquiring the nonlinear images two methodologies were used. In Fig. 4, we raster scanthe refocus at each spatial position in the ROI containing the nanoKTP and, in parallel, collecting the SHG signalintegrated within the imaged plane with the large area PMT. In Fig. 5, we raster scan the refocus using the memoryeffect: a linear phase ramp is added to the wavefront, thus displacing the refocus in the image plane (with the SHGsignal acquired in parallel). Number of controlled SLM segments for the experiments: 2 (Fig. 4) and 2 (Figs. 2,3, 5) Sample preparation . Various types of scattering media were used: dispersions of 5 µ m-diameter polystyrenebeads (Fig. 2.a and 3), 1-mm thick brain slice (Fig. 2.b) — both fixed in agarose solution — 1 mm-thick parafilmfilm (Fig. 4) and a commercial diffuser (Fig. 5, 10 ◦ Light Shaping Diffuser, Newport). The rat tendon (Fig. 5)was placed between two coverlips separated by a 120 µ m-thick spacer and filled with agarose solution. The 1 mm-thick mouse brain coronal cross-section (Fig. 2.b) followed the same protocol, except the spacer was 1 mm-thick.The nanoKTP crystals (150 nm diameter) were previously characterized by various methods and were drop caston a coverslip (170 µ m-thickness). The scattering mean free path, l s , of the scattering media in Fig. 2.a and 3( l s = 53 − µ m) were determined by measuring the extinction of the laser through a thin dispersion slab of knownthickness, with scattered light and ballistic light spatially isolated in the Fourier space . Anisotropy values g forcalculating l t = l s / (1 − g ) were obtained using the scattering pattern from Mie theory. ACKNOWLEDGEMENTS
The authors thank Esben Andressen and Herve Rigneault for fruitful discussions and support, Arnaud Malvacheand Rosa Cossart for providing the brain slices, Thierry Gacoin and Ludovic Meyer for providing the nanoKTP parti-cles. This work has been supported by the FEMTO Network and contracts ANR-10-INBS-04-01 (France-BioImaginginfrastructure network), ANR-11-INSB-0006 (France Life Imaging infrastructure network), and the A*MIDEX projectANR-11-IDEX-0001-02. S.G. is funded by the European Research Council (grant 278025 - COMEDIA).
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