3D resolved mapping of optical aberrations in thick tissues

Active image optimization for lattice light sheet microscopy in thick samples

Lattice light-sheet microscopy (LLSM) is a very efficient technique for high resolution 3D imaging of dynamic phenomena in living biological samples. However, LLSM imaging remains limited in depth due to optical aberrations caused by sample-based refractive index mismatch. Here, we propose a simple and low-cost active image optimization (AIO) method to recover high resolution imaging inside thick biological samples. AIO is based on (1) a light-sheet autofocus step (AF) followed by (2) an adaptive optics image-based optimization. We determine the optimum AIO parameters to provide a fast, precise and robust aberration correction on biological samples. Finally, we demonstrate the performances of our approach on sub-micrometric structures in brain slices and plant roots.

Closed-loop wavefront sensing and correction in the mouse brain with computed optical coherence microscopy

Optical coherence microscopy (OCM) uses interferometric detection to capture the complex optical field with high sensitivity, which enables computational wavefront retrieval using back-scattered light from the sample. Compared to a conventional wavefront sensor, aberration sensing with OCM via computational adaptive optics (CAO) leverages coherence and confocal gating to obtain signals from the focus with less cross-talk from other depths or transverse locations within the field-of-view. Here, we present an investigation of the performance of CAO-based aberration sensing in simulation, bead phantoms, and ex vivo mouse brain tissue. We demonstrate that, due to the influence of the double-pass confocal OCM imaging geometry on the shape of computed pupil functions, computational sensing of high-order aberrations can suffer from signal attenuation in certain spatial-frequency bands and shape similarity with lower order counterparts. However, by sensing and correcting only low-order aberrations (astigmatism, coma, and trefoil), we still successfully corrected tissue-induced aberrations, leading to 3× increase in OCM signal intensity at a depth of ∼0.9 mm in a freshly dissected ex vivo mouse brain.

Raster adaptive optics for video rate aberration correction and large FOV multiphoton imaging

Removal of complex aberrations at millisecond time scales over millimeters in distance in multiphoton laser scanning microscopy limits the total spatiotemporal imaging throughput for deep tissue imaging. Using a single low resolution deformable mirror and time multiplexing (TM) adaptive optics, we demonstrate video rate aberration correction (5 ms update rate for a single wavefront mask) for a complex heterogeneous distribution of refractive index differences through a depth of up to 1.1 mm and an extended imaging FOV of up to 0.8 mm, with up to 167% recovery of fluorescence intensity 335 µm from the center of the FOV. The proposed approach, termed raster adaptive optics (RAO), integrates image-based aberration retrieval and video rate removal of arbitrarily defined regions of dominant, spatially varied wavefronts. The extended FOV was achieved by demonstrating rapid recovery of up to 50 distinct wavefront masks at 500 ms update rates that increased imaging throughput by 2.3-fold. Because RAO only requires a single deformable mirror with image-based aberration retrieval, it can be directly implemented on a standard laser scanning multiphoton microscope.

Advances in adaptive optics-based two-photon fluorescence microscopy for brain imaging

Deep tissue imaging using two-photon fluorescence (TPF) techniques have revolutionized the optical imaging community by providing in depth molecular information at the single-cell level. These techniques provide structural and functional aspects of mammalian brain at unprecedented depth and resolution. However, wavefront distortions introduced by the optical system as well as the biological sample (tissue) limit the achievable fluorescence signal-to-noise ratio and resolution with penetration depth. In this review, we discuss on the advances in TPF microscopy techniques for in vivo functional imaging and offer guidelines as to which technologies are best suited for different imaging applications with special reference to adaptive optics.

3-photon fluorescence imaging of sulforhodamine B-labeled elastic fibers in the mouse skin in vivo

Elastic fibers are key constituents of the skin. The commonly adopted optical technique for visualizing elastic fibers in the animal skin in vivo is 2-photon microscopy (2 PM) of autofluorescence, which typically suffers from low signal level. Here we demonstrate a new optical methodology to image elastic fibers in animal models in vivo: 3-photon microscopy (3 PM) excited at the 1700-nm window combining with preferential labeling of elastic fibers using sulforhodamine B (SRB). First, we demonstrate that intravenous injection of SRB can circumvent the skin barrier (encountered in topical application) and preferentially label elastic fibers, as verified by simultaneous 2 PM of both autofluorescence and SRB fluorescence from skin structures. Then through 3-photon excitation property characterization, we show that 3-photon fluorescence can be excited from SRB at the 1700-nm window, and 1600-nm excitation is most efficient according to our 3-photon action cross section measurement. Based on these results and using our developed 1600-nm femtosecond laser source, we finally demonstrate 3 PM of SRB-labeled elastic fibers through the whole dermis in the mouse skin in vivo, with only 3.7-mW optical power deposited on the skin surface. We expect our methodology will provide novel optical solution to elastic fiber research.

Adaptive optics light-sheet microscopy based on direct wavefront sensing without any guide star

We propose an adaptive optics light-sheet fluorescence microscope (AO-LSFM) for closed-loop aberrations' correction at the emission path, providing intrinsic instrumental simplicity and high accuracy when compared to previously reported schemes. The approach is based on direct wavefront sensing, i.e., not on time-consuming iterative algorithms, and does not require the use of any guide star, thus reducing instrumental complexity and/or sample preparation constraints. The design is based on a modified Shack-Hartmann wavefront sensor providing compatibility with extended sources such as images from optical sectioning microscopes. We report an AO-LSFM setup based on such sensors, including characterization of the sensor performance, and demonstrate for the first time to the best of our knowledge a significant contrast improvement on neuronal structures of the ex vivo adult drosophila brain in depth.

Local wavefront mapping in tissue using computational adaptive optics OCT

The identification and correction of wavefront aberrations is often necessary to achieve high-resolution optical images of biological tissues, as imperfections in the optical system and the tissue itself distort the imaging beam. Measuring the localized wavefront aberration provides information on where the beam is distorted and how severely. We have recently developed a method to estimate the single-pass wavefront aberrations from complex optical coherence tomography (OCT) data. Using this method, localized wavefront measurement and correction using computational OCT was performed in ex vivo tissues. The computationally measured wavefront varied throughout the imaged OCT volumes and, therefore, a local wavefront correction outperformed a global wavefront correction. The local wavefront measurement was also used to generate tissue aberration maps. Such aberration maps could potentially be used as a new form of tissue contrast.

Adaptive optics microspectrometer for cross-correlation measurement of microfluidic flows

Mapping flows in vivo is essential for the investigation of cardiovascular pathologies in animal models. The limitation of optical-based methods, such as space-time cross correlation, is the scattering of light by the connective and fat components and the direct wave front distortion by large inhomogeneities in the tissue. Nonlinear excitation of the sample fluorescence helps us by reducing light scattering in excitation. However, there is still a limitation on the signal-background due to the wave front distortion. We develop a diffractive optical microscope based on a single spatial light modulator (SLM) with no movable parts. We combine the correction of wave front distortions to the cross-correlation analysis of the flow dynamics. We use the SLM to shine arbitrary patterns of spots on the sample, to correct their optical aberrations, to shift the aberration corrected spot array on the sample for the collection of fluorescence images, and to measure flow velocities from the cross-correlation functions computed between couples of spots. The setup and the algorithms are tested on various microfluidic devices. By applying the adaptive optics correction algorithm, it is possible to increase up to 5 times the signal-to-background ratio and to reduce approximately of the same ratio the uncertainty of the flow speed measurement. By working on grids of spots, we can correct different aberrations in different portions of the field of view, a feature that allows for anisoplanatic aberrations correction. Finally, being more efficient in the excitation, we increase the accuracy of the speed measurement by employing a larger number of spots in the grid despite the fact that the two-photon excitation efficiency scales as the fourth power of this number: we achieve a twofold decrease of the uncertainty and a threefold increase of the accuracy in the evaluation of the flow speed.

Grid-Free Localization Algorithm Using Low-rank Hankel Matrix for Super-Resolution Microscopy

Localization microscopy, such as STORM / PALM, can reconstruct super-resolution images with a nanometer resolution through the iterative localization of fluorescence molecules. Recent studies in this area have focused mainly on the localization of densely activated molecules to improve temporal resolutions. However, higher density imaging requires an advanced algorithm that can resolve closely spaced molecules. Accordingly, sparsitydriven methods have been studied extensively. One of the major limitations of existing sparsity-driven approaches is the need for a fine sampling grid or for Taylor series approximation which may result in some degree of localization bias toward the grid. In addition, prior knowledge of the point-spread function (PSF) is required. To address these drawbacks, here we propose a true grid-free localization algorithm with adaptive PSF estimation. Specifically, based on the observation that sparsity in the spatial domain implies a low rank in the Fourier domain, the proposed method converts source localization problems into Fourier-domain signal processing problems so that a truly gridfree localization is possible. We verify the performance of the newly proposed method with several numerical simulations and a live-cell imaging experiment.

Combined hardware and computational optical wavefront correction

In many optical imaging applications, it is necessary to overcome aberrations to obtain high-resolution images. Aberration correction can be performed by either physically modifying the optical wavefront using hardware components, or by modifying the wavefront during image reconstruction using computational imaging. Here we address a longstanding issue in computational imaging: photons that are not collected cannot be corrected. This severely restricts the applications of computational wavefront correction. Additionally, performance limitations of hardware wavefront correction leave many aberrations uncorrected. We combine hardware and computational correction to address the shortcomings of each method. Coherent optical backscattering data is collected using high-speed optical coherence tomography, with aberrations corrected at the time of acquisition using a wavefront sensor and deformable mirror to maximize photon collection. Remaining aberrations are corrected by digitally modifying the coherently-measured wavefront during imaging reconstruction. This strategy obtains high-resolution images with improved signal-to-noise ratio of in vivo human photoreceptor cells with more complete correction of ocular aberrations, and increased flexibility to image at multiple retinal depths, field locations, and time points. While our approach is not restricted to retinal imaging, this application is one of the most challenging for computational imaging due to the large aberrations of the dilated pupil, time-varying aberrations, and unavoidable eye motion. In contrast with previous computational imaging work, we have imaged single photoreceptors and their waveguide modes in fully dilated eyes with a single acquisition. Combined hardware and computational wavefront correction improves the image sharpness of existing adaptive optics systems, and broadens the potential applications of computational imaging methods.

Wavefront measurement using computational adaptive optics

In many optical imaging applications, it is necessary to correct for aberrations to obtain high quality images. Optical coherence tomography (OCT) provides access to the amplitude and phase of the backscattered optical field for three-dimensional (3D) imaging samples. Computational adaptive optics (CAO) modifies the phase of the OCT data in the spatial frequency domain to correct optical aberrations without using a deformable mirror, as is commonly done in hardware-based adaptive optics (AO). This provides improvement of image quality throughout the 3D volume, enabling imaging across greater depth ranges and in highly aberrated samples. However, the CAO aberration correction has a complicated relation to the imaging pupil and is not a direct measurement of the pupil aberrations. Here we present new methods for recovering the wavefront aberrations directly from the OCT data without the use of hardware adaptive optics. This enables both computational measurement and correction of optical aberrations.

Adaptive optical microscopy for neurobiology

With the ability to correct for the aberrations introduced by biological specimens, adaptive optics-a method originally developed for astronomical telescopes-has been applied to optical microscopy to recover diffraction-limited imaging performance deep within living tissue. In particular, this technology has been used to improve image quality and provide a more accurate characterization of both structure and function of neurons in a variety of living organisms. Among its many highlights, adaptive optical microscopy has made it possible to image large volumes with diffraction-limited resolution in zebrafish larval brains, to resolve dendritic spines over 600μm deep in the mouse brain, and to more accurately characterize the orientation tuning properties of thalamic boutons in the primary visual cortex of awake mice.

Single-Cell Optical Distortion Correction and Label-Free 3D Cell Shape Reconstruction on Lattices of Nanostructures

Imaging techniques can be compromised by aberrations. Especially when imaging through biological specimens, sample-induced distortions can limit localization accuracy. In particular, this phenomenon affects localization microscopy, traction force measurements, and single-particle tracking, which offer high-resolution insights into biological tissue. Here we present a method for quantifying and correcting the optical distortions induced by single, adherent, living cells. The technique uses periodically patterned gold nanostructures as a reference framework to quantify optically induced displacements with micrometer-scale sampling density and an accuracy of a few nanometers. The 3D cell shape and a simplified geometrical optics approach are then utilized to remap the microscope image. Our experiments reveal displacements of up to several hundred nanometers, and in corrected images these distortions are reduced by a factor of 3. Conversely, the relationship between cell shape and distortion provides a novel method of 3D cell shape reconstruction from a single image, enabling label-free 3D cell analysis.

Optimizing the metric in sensorless adaptive optical microscopy with fluorescence fluctuations

Adaptive optics (AO) strategies using optimization-based, sensorless approaches are widely used, especially for microscopy applications. To converge rapidly to the best correction, such approaches require that a quality metric and a set of modes be chosen optimally. Fluorescence fluctuations microscopy, a family of methods that provides quantitative measurements of molecular concentration and mobility in living specimen, is in particular need of adaptive optics, since its results can be strongly biased by optical aberrations. We examined two possible metrics for sensorless AO, measured in a solution of fluorophores diffusing in 3D: the fluorescence count rate and the molecular brightness (or number of photons detected per molecule in the observation volume). We studied their respective measurement noise and sensitivity to aberrations. Then, AO correction accuracy was experimentally assessed by measuring the residual aberration after correcting a known wavefront. We proposed a theoretical framework to predict the correction accuracy, knowing the metric measurement noise and sensitivity. In the small aberration range, the brightness allows more accurate corrections when fluorophores are few but bright, whereas the count rate performs better in more concentrated solutions. When correcting large aberrations, the count rate is expected to be a more reliable metric.

Improving Focal Photostimulation of Cortical Neurons with Pre-derived Wavefront Correction

Recent progress in neuroscience to image and investigate brain function has been made possible by impressive developments in optogenetic and opto-molecular tools. Such research requires advances in optical techniques for the delivery of light through brain tissue with high spatial resolution. The tissue causes distortions to the wavefront of the incoming light which broadens the focus and consequently reduces the intensity and degrades the resolution. Such effects are detrimental in techniques requiring focal stimulation. Adaptive wavefront correction has been demonstrated to compensate for these distortions. However, iterative derivation of the corrective wavefront introduces time constraints that limit its applicability to probe living cells. Here, we demonstrate that we can pre-determine and generalize a small set of Zernike modes to correct for aberrations of the light propagating through specific brain regions. A priori identification of a corrective wavefront is a direct and fast technique that improves the quality of the focus without the need for iterative adaptive wavefront correction. We verify our technique by measuring the efficiency of two-photon photolysis of caged neurotransmitters along the dendrites of a whole-cell patched neuron. Our results show that encoding the selected Zernike modes on the excitation light can improve light propagation through brain slices of rats as observed by the neuron's evoked excitatory post-synaptic potential in response to localized focal uncaging at the spines of the neuron's dendrites.

Large-field-of-view imaging by multi-pupil adaptive optics

For in vivo deep imaging at high spatiotemporal resolutions, we developed Multi-Pupil Adaptive Optics (MPAO) which enables simultaneous wavefront correction over a large imaging field-of-view. The current implementation improves correction area by nine times over that of conventional methods. MPAO’s capability of spatially independent wavefront control further enables 3D nonplanar imaging. We applied MPAO to in vivo structural and functional imaging of biological dynamics in mammalian brain.

Image-based adaptive optics for in vivo imaging in the hippocampus

Adaptive optics is a promising technique for the improvement of microscopy in tissues. A large palette of indirect and direct wavefront sensing methods has been proposed for in vivo imaging in experimental animal models. Application of most of these methods to complex samples suffers from either intrinsic and/or practical difficulties. Here we show a theoretically optimized wavefront correction method for inhomogeneously labeled biological samples. We demonstrate its performance at a depth of 200 μm in brain tissue within a sparsely labeled region such as the pyramidal cell layer of the hippocampus, with cells expressing GCamP6. This method is designed to be sample-independent thanks to an automatic axial locking on objects of interest through the use of an image-based metric that we designed. Using this method, we show an increase of in vivo imaging quality in the hippocampus.

Correlative nonlinear optical microscopy and infrared nanoscopy reveals collagen degradation in altered parchments

This paper presents the correlative imaging of collagen denaturation by nonlinear optical microscopy (NLO) and nanoscale infrared (IR) spectroscopy to obtain morphological and chemical information at different length scales. Such multiscale correlated measurements are applied to the investigation of ancient parchments, which are mainly composed of dermal fibrillar collagen. The main issue is to characterize gelatinization, the ultimate and irreversible alteration corresponding to collagen denaturation to gelatin, which may also occur in biological tissues. Key information about collagen and gelatin signatures is obtained in parchments and assessed by characterizing the denaturation of pure collagen reference samples. A new absorbing band is observed near the amide I band in the IR spectra, correlated to the onset of fluorescence signals in NLO images. Meanwhile, a strong decrease is observed in Second Harmonic signals, which are a structural probe of the fibrillar organization of the collagen at the micrometer scale. NLO microscopy therefore appears as a powerful tool to reveal collagen degradation in a non-invasive way. It should provide a relevant method to assess or monitor the condition of collagen-based materials in museum and archival collections and opens avenues for a broad range of applications regarding this widespread biological material.

Characterisation of the effects of optical aberrations in single molecule techniques

Optical aberrations degrade image quality in fluorescence microscopy, including for single-molecule based techniques. These depend on post-processing to localize individual molecules in an image series. Using simulated data, we show the impact of optical aberrations on localization success, accuracy and precision. The peak intensity and the proportion of successful localizations strongly reduces when the aberration strength is greater than 1.0 rad RMS, while the precision of each of those localisations is halved. The number of false-positive localisations exceeded 10% of the number of true-positive localisations at an aberration strength of only ~0.6 rad RMS when using the ThunderSTORM package, but at greater than 1.0 rad RMS with the Radial Symmetry package. In the presence of coma, the localization error reaches 100 nm at ~0.6 rad RMS of aberration strength. The impact of noise and of astigmatism for axial resolution are also considered. Understanding the effect of aberrations is crucial when deciding whether the addition of adaptive optics to a single-molecule microscope could significantly increase the information obtainable from an image series.

Simple wavefront correction framework for two-photon microscopy of in-vivo brain

We present an easily implemented wavefront correction scheme that has been specifically designed for in-vivo brain imaging. The system can be implemented with a single liquid crystal spatial light modulator (LCSLM), which makes it compatible with existing patterned illumination setups, and provides measurable signal improvements even after a few seconds of optimization. The optimization scheme is signal-based and does not require exogenous guide-stars, repeated image acquisition or beam constraint. The unconstrained beam approach allows the use of Zernike functions for aberration correction and Hadamard functions for scattering correction. Low order corrections performed in mouse brain were found to be valid up to hundreds of microns away from the correction location.

High-resolution in vivo imaging of mouse brain through the intact skull

Multiphoton microscopy is the current method of choice for in vivo deep-tissue imaging. The long laser wavelength suffers less scattering, and the 3D-confined excitation permits the use of scattered signal light. However, the imaging depth is still limited because of the complex refractive index distribution of biological tissue, which scrambles the incident light and destroys the optical focus needed for high resolution imaging. Here, we demonstrate a wavefront-shaping scheme that allows clear imaging through extremely turbid biological tissue, such as the skull, over an extended corrected field of view (FOV). The complex wavefront correction is obtained and directly conjugated to the turbid layer in a noninvasive manner. Using this technique, we demonstrate in vivo submicron-resolution imaging of neural dendrites and microglia dynamics through the intact skulls of adult mice. This is the first observation, to our knowledge, of dynamic morphological changes of microglia through the intact skull, allowing truly noninvasive studies of microglial immune activities free from external perturbations.

Correction of depth-induced spherical aberration for deep observation using two-photon excitation fluorescence microscopy with spatial light modulator

We demonstrate fluorescence imaging with high fluorescence intensity and depth resolution in which depth-induced spherical aberration (SA) caused by refractive-index mismatch between the medium and biological sample is corrected. To reduce the impact of SA, we incorporate a spatial light modulator into a two-photon excitation fluorescence microscope. Consequently, when fluorescent beads in epoxy resin were observed with this method of SA correction, the fluorescence signal of the observed images was ∼27 times higher and extension in the direction of the optical axes was ∼6.5 times shorter at a depth of ∼890 μm. Thus, the proposed method increases the depth observable at high resolution. Further, our results show that the method improved the fluorescence intensity of images of the fluorescent beads and the structure of a biological sample.

Quantitative analysis of light scattering in polarization-resolved nonlinear microscopy

Polarization resolved nonlinear microscopy (PRNM) is a powerful technique to gain microscopic structural information in biological media. However, deep imaging in a variety of biological specimens is hindered by light scattering phenomena, which not only degrades the image quality but also affects the polarization state purity. In order to quantify this phenomenon and give a framework for polarization resolved microscopy in thick scattering tissues, we develop a characterization methodology based on four wave mixing (FWM) process. More specifically, we take advantage of two unique features of FWM, meaning its ability to produce an intrinsic in-depth local coherent source and its capacity to quantify the presence of light depolarization in isotropic regions inside a sample. By exploring diverse experimental layouts in phantoms with different scattering properties, we study systematically the influence of scattering on the nonlinear excitation and emission processes. The results show that depolarization mechanisms for the nonlinearly generated photons are highly dependent on the scattering center size, the geometry used (epi/forward) and, most importantly, on the thickness of the sample. We show that the use of an un-analyzed detection makes the polarization-dependence read-out highly robust to scattering effects, even in regimes where imaging might be degraded. The effects are illustrated in polarization resolved imaging of myelin lipid organization in mouse spinal cords.

Determination of collagen fibril size via absolute measurements of second-harmonic generation signals

The quantification of collagen fibril size is a major issue for the investigation of pathological disorders associated with structural defects of the extracellular matrix. Second-harmonic generation microscopy is a powerful technique to characterize the macromolecular organization of collagen in unstained biological tissues. Nevertheless, due to the complex coherent building of this nonlinear optical signal, it has never been used to measure fibril diameter so far. Here we report absolute measurements of second-harmonic signals from isolated fibrils down to 30 nm diameter, via implementation of correlative second-harmonic-electron microscopy. Moreover, using analytical and numerical calculations, we demonstrate that the high sensitivity of this technique originates from the parallel alignment of collagen triple helices within fibrils and the subsequent constructive interferences of second-harmonic radiations. Finally, we use these absolute measurements as a calibration for ex vivo quantification of fibril diameter in the Descemet's membrane of a diabetic rat cornea.

Optimization-based wavefront sensorless adaptive optics for multiphoton microscopy

Optical aberrations have detrimental effects in multiphoton microscopy. These effects can be curtailed by implementing model-based wavefront sensorless adaptive optics, which only requires the addition of a wavefront shaping device, such as a deformable mirror (DM) to an existing microscope. The aberration correction is achieved by maximizing a suitable image quality metric. We implement a model-based aberration correction algorithm in a second-harmonic microscope. The tip, tilt, and defocus aberrations are removed from the basis functions used for the control of the DM, as these aberrations induce distortions in the acquired images. We compute the parameters of a quadratic polynomial that is used to model the image quality metric directly from experimental input-output measurements. Finally, we apply the aberration correction by maximizing the image quality metric using the least-squares estimate of the unknown aberration.

Snapshot coherence-gated direct wavefront sensing for multi-photon microscopy

Deep imaging in turbid media such as biological tissue is challenging due to scattering and optical aberrations. Adaptive optics has the potential to compensate the tissue aberrations. We present a wavefront sensing scheme for multi-photon scanning microscopes using the pulsed, near-infrared light reflected back from the sample utilising coherence gating and a confocal pinhole to isolate the light from a layer of interest. By interfering the back-reflected light with a tilted reference beam, we create a fringe pattern with a known spatial carrier frequency in an image of the back-aperture plane of the microscope objective. The wavefront aberrations distort this fringe pattern and thereby imprint themselves at the carrier frequency, which allows us to separate the aberrations in the Fourier domain from low spatial frequency noise. A Fourier analysis of the modulated fringes combined with a virtual Shack-Hartmann sensor for smoothing yields a modal representation of the wavefront suitable for correction. We show results with this method correcting both DM-induced and sample-induced aberrations in rat tail collagen fibres as well as a Hoechst-stained MCF-7 spheroid of cancer cells.

Correction of cell-induced optical aberrations in a fluorescence fluctuation microscope

We describe the effect of optical aberrations on fluorescence fluctuations microscopy (FFM), when focusing through a single living cell. FFM measurements are performed in an aqueous fluorescent solution and prove to be a highly sensitive tool to assess the optical aberrations introduced by the cell. We demonstrate an adaptive optics (AO) system to remove the aberration-related bias in the FFM measurements. Our data show that AO is not only useful when imaging deep in tissues but also when performing FFM measurements through a single cellular layer. This work paves the way for the application of FFM to complex three-dimensional multicellular samples.