Rotational memory effect of a multimode fiber

Imaging through a square multimode fiber by scanning focused spots with the memory effect

The existence of a shift-shift memory effect in square waveguides, whereby any translation of the input field induces translations in the output field in four symmetrical directions, has been previously observed by correlation measurements. Here we demonstrate that this memory effect is also observed in real space and can be put to use for imaging purposes. First, a focus is created at the output of a square-core multimode fiber, by wavefront shaping based on feedback from a guide-star. Then, because of the memory effect, four symmetrical spots can be scanned at the fiber output by shifting the wavefront at the fiber input. We demonstrate that this property can be exploited to perform fluorescence imaging through the multimode fiber, without requiring the measurement of a transmission matrix.

Speckle-correlation imaging through a kaleidoscopic multimode fiber

Speckle-correlation imaging techniques are widely used for noninvasive imaging through complex scattering media. While light propagation through multimode fibers and scattering media share many analogies, reconstructing images through multimode fibers from speckle correlations remains an unsolved challenge. Here, we exploit a kaleidoscopic memory effect emerging in square-core multimode fibers and demonstrate fluorescence imaging with no prior knowledge on the fiber. Experimentally, our approach simply requires to translate random speckle patterns at the input of a square-core fiber and to measure the resulting fluorescence intensity with a bucket detector. The image of the fluorescent object is then reconstructed from the autocorrelation of the measured signal by solving an inverse problem. This strategy does not require the knowledge of the fragile deterministic relation between input and output fields, which makes it promising for the development of flexible minimally invasive endoscopes.

Polarization-based intensity correlation of a depolarized speckle pattern

A different kind of intensity correlation, denoted as polarization-based intensity correlation (PBIC), is proposed and demonstrated to investigate the correlation between different polarizations of a depolarized speckle pattern (DSP), which has non-uniform spatial polarization distribution. It is shown both theoretically and experimentally that the range of the PBIC for any polarization of the DSP depends on the spatial average intensity of the speckles corresponding to that particular polarization. The experimentally determined nature of the change of the range of the PBIC for different polarization components, due to the variation in the average intensity, is found to be matching well with the theoretical prediction. The existence of non-zero correlation between two orthogonally polarized speckle patterns, filtered from a partially DSP, is also observed. This study may be useful in exploiting the PBIC for different applications such as speckle cryptography.

Optical memory effect in square multimode fibers

We demonstrate experimentally the existence of a translational optical memory effect in square-core multimode fibers. We found that symmetry properties of square-core waveguides lead to speckle patterns shifting along four directions at the fiber output for any given shift direction at the input. A simple theoretical model based on a perfectly reflective square waveguide is introduced to predict and interpret this phenomenon. We report experimental results obtained with 532-nm coherent light propagating through a square-core step-index multimode fiber, demonstrating that this translational memory effect can be observed for shift distances up to typically 10 µm after propagation through several centimeters of fiber.

Characterization of the spectral memory effect of scattering media

The optical memory effect is an interesting phenomenon exploited for deep-tissue optical imaging. Besides the widely studied memory effects in the spatial domain to accelerate point scanning speed, the spectral memory effect is also important in multispectral wavefront shaping. Although being theoretically analyzed for decades, quantitative studies of spectral memory effect on a variety of scattering media including biological tissue were rarely reported. In practice, quantifying the range of the spectral memory effect is essential in efficiently shaping broadband light, as it determines the optimum spectral resolution in realizing spatiotemporal focus through scattering media. In this work, we analyze the spectral memory effect based on a diffusion model. An explicit analytical expression involves the illumination wavelength, the diffusion constant, and the sample thickness is derived, which is consistent with the one in the literature. We experimentally quantified the range of spectral correlation for two types of biological tissue, tissue-mimicking phantoms with different concentrations, and diffusers. Specifically, for tissue-mimicking phantoms with calibrated scattering parameters, we show that a correction factor of more than 20 should be inserted, indicating that the range of spectral correlation is much larger than one would expect. This finding is particularly beneficial to multispectral wavefront shaping, as stringent requirements on the spectral resolution could be alleviated by at least one order of magnitude.

Memory effect assisted imaging through multimode optical fibres

When light propagates through opaque material, the spatial information it holds becomes scrambled, but not necessarily lost. Two classes of techniques have emerged to recover this information: methods relying on optical memory effects, and transmission matrix (TM) approaches. Here we develop a general framework describing the nature of memory effects in structures of arbitrary geometry. We show how this framework, when combined with wavefront shaping driven by feedback from a guide-star, enables estimation of the TM of any such system. This highlights that guide-star assisted imaging is possible regardless of the type of memory effect a scatterer exhibits. We apply this concept to multimode fibres (MMFs) and identify a 'quasi-radial' memory effect. This allows the TM of an MMF to be approximated from only one end - an important step for micro-endoscopy. Our work broadens the applications of memory effects to a range of novel imaging and optical communication scenarios.

Compressively sampling the optical transmission matrix of a multimode fibre

The measurement of the optical transmission matrix (TM) of an opaque material is an advanced form of space-variant aberration correction. Beyond imaging, TM-based methods are emerging in a range of fields, including optical communications, micro-manipulation, and computing. In many cases, the TM is very sensitive to perturbations in the configuration of the scattering medium it represents. Therefore, applications often require an up-to-the-minute characterisation of the fragile TM, typically entailing hundreds to thousands of probe measurements. Here, we explore how these measurement requirements can be relaxed using the framework of compressive sensing, in which the incorporation of prior information enables accurate estimation from fewer measurements than the dimensionality of the TM we aim to reconstruct. Examples of such priors include knowledge of a memory effect linking the input and output fields, an approximate model of the optical system, or a recent but degraded TM measurement. We demonstrate this concept by reconstructing the full-size TM of a multimode fibre supporting 754 modes at compression ratios down to ∼5% with good fidelity. We show that in this case, imaging is still possible using TMs reconstructed at compression ratios down to ∼1% (eight probe measurements). This compressive TM sampling strategy is quite general and may be applied to a variety of other scattering samples, including diffusers, thin layers of tissue, fibre optics of any refractive profile, and reflections from opaque walls. These approaches offer a route towards the measurement of high-dimensional TMs either quickly or with access to limited numbers of measurements.

Visual data detection through side-scattering in a multimode optical fiber

Light propagation in optical fibers is accompanied by random omnidirectional scattering. The small fraction of coherent guided light that escapes outside the cladding of the fiber forms a speckle pattern. Here, visual information imaged into the input facet of a multimode fiber with a transparent buffer is retrieved, using a convolutional neural network, from the side-scattered light at several locations along the fiber. This demonstration can promote the development of distributed optical imaging systems and optical links interfaced via the sides of the fiber.

Speckle-Correlation Scattering Matrix Approaches for Imaging and Sensing through Turbidity

The development of optical and computational techniques has enabled imaging without the need for traditional optical imaging systems. Modern lensless imaging techniques overcome several restrictions imposed by lenses, while preserving or even surpassing the capability of lens-based imaging. However, existing lensless methods often rely on a priori information about objects or imaging conditions. Thus, they are not ideal for general imaging purposes. The recent development of the speckle-correlation scattering matrix (SSM) techniques facilitates new opportunities for lensless imaging and sensing. In this review, we present the fundamentals of SSM methods and highlight recent implementations for holographic imaging, microscopy, optical mode demultiplexing, and quantification of the degree of the coherence of light. We conclude with a discussion of the potential of SSM and future research directions.

Structured light beams created through a multimode fiber via virtual Fourier filtering based on digital optical phase conjugation

Digital optical phase conjugation (DOPC) is a newly developed technique in wavefront shaping to control light propagation through complex media. Currently, DOPC has been demonstrated for the reconstruction of two- and three-dimensional targets and enabled important applications in many areas. Nevertheless, the reconstruction results are only phase conjugated to the original input targets. Herein, we demonstrate that DOPC could be further developed for creating structured light beams through a multimode fiber (MMF). By applying annular filtering in the virtual Fourier domain of the acquired speckle field, we realize the creation of the quasi-Bessel and donut beams through the MMF. In principle, arbitrary amplitude and/or phase circular symmetry filtering could be performed in the Fourier domain, thus generating the corresponding point spread functions. We expect that the reported technique can be useful for super-resolution endoscopic imaging and optical manipulation through MMFs.

Long-range spatio-temporal correlations in multimode fibers for pulse delivery

Long-range correlations play an essential role in wave transport through disordered media, but have rarely been studied in other complex systems. Here we discover spatio-temporal intensity correlations for an optical pulse propagating through a multimode fiber with strong random mode coupling. Positive long-range correlation arises from multiple scattering in fiber mode space and depends on the statistical distribution of arrival times. By optimizing the incident wavefront of a pulse, we maximize the power transmitted at a selected time, and such control is significantly enhanced by the long-range spatio-temporal correlation. We provide an explicit relation between the correlation and the power enhancement, which agrees with experimental results. Our work shows that multimode fibers provide a fertile ground for studying complex wave phenomena. The strong spatio-temporal correlation can be employed for efficient power delivery at a well-defined time.

Long-range correlations play a role in wave transport through disordered media but have rarely been studied in other systems. Here, the authors discover long-range spatio-temporal correlations in multimode fibers with strong random mode mixing, revealing the possibility of utilizing such correlations for effective pulse delivery through the fiber.

Snapshot fiber spectral imaging using speckle correlations and compressive sensing

Snapshot spectral imaging is rapidly gaining interest for remote sensing applications. Acquiring spatial and spectral data within one image promotes fast measurement times, and reduces the need for stabilized scanning imaging systems. Many current snapshot technologies, which rely on gratings or prisms to characterize wavelength information, are difficult to reduce in size for portable hyperspectral imaging. Here, we show that a multicore multimode fiber can be used as a compact spectral imager with sub-nanometer resolution, by encoding spectral information within a monochrome CMOS camera. We characterize wavelength-dependent speckle patterns for up to 3000 fiber cores over a broad wavelength range. A clustering algorithm is employed in combination with l₁-minimization to limit data collection at the acquisition stage for the reconstruction of spectral images that are sparse in the wavelength domain. We also show that in the non-compressive regime these techniques are able to accurately reconstruct broadband information.

Compressive imaging through a multimode fiber

We propose and experimentally demonstrate a new concept of endo-microscopy: compressive multimode (MM) fiber imaging. We show that the speckle patterns generated in a MM fiber represent an excellent basis for compressive sensing. We demonstrate high-resolution compressive imaging through a fiber probe with the total number of measurements 20 times less than what is required for the standard raster scanning approach to endo-microscopy. Moreover, we show that the inherent optical sectioning of a MM fiber can help to overcome the main problem of compressive sensing and can be used for the imaging of bulk structures. Compressive MM fiber imaging does not require complex wavefront shaping and significantly increases the pre-calibration and imaging speed, creating a new approach to endo-microscopy.

Single-shot memory-effect video

Imaging through opaque scattering media is critically important in applications ranging from biological and astronomical imaging to metrology and security. While the random process of scattering in turbid media produces scattered light that appears uninformative to the human eye, a wealth of information is contained in the signal and can be recovered using computational post-processing techniques. Recent studies have shown that statistical correlations present in the scattered light, known as ‘memory effects’, allow for diffraction-limited imaging through opaque media without detailed knowledge of (or access to) the source or scatterer. However, previous methods require that the object and/or scatterer be static during the measurement. We overcome this limitation by combining traditional memory effect imaging with coded-aperture-based computational imaging techniques, which enables us to realize for the first time single-shot video of arbitrary dynamic scenes through dynamic, opaque media. This has important implications for a wide range of real-world imaging scenarios.

Aberrations of the point spread function of a multimode fiber due to partial mode excitation

We investigate the point spread function of a multimode fiber. The distortion of the focal spot created on the fiber output facet is studied for a variety of the parameters. We develop a theoretical model of wavefront shaping through a multimode fiber and use it to confirm our experimental results and analyze the nature of the focal distortions. We show that aberration-free imaging with a large field of view can be achieved by using an appropriate number of segments on the spatial light modulator during the wavefront-shaping procedure. The results describe aberration limits for imaging with multimode fibers as in, e.g., microendoscopy.

Calibration-free imaging through a multicore fiber using speckle scanning microscopy

The images produced by multicore endoscopes are pixelated, and their resolution is limited by the core-to-core spacing. Lenses can be used to improve the resolution, but this reduces the field of view proportionally. Lensless endoscopy through multicore fibers can be achieved by using wavefront shaping techniques. This requires a calibration step, and the conformation of the fiber must remain constant over time. Here we demonstrate that, without a calibration step and in the presence of core-to-core coupling, we can obtain fluorescence images with a resolution better than the core-to-core spacing. This is accomplished by taking advantage of the memory effect present in these kinds of fibers.

Investigation on sensitivity enhancement for optical fiber speckle sensors

We present a detailed theoretical and experimental study on the sensitivity enhancement for multimode fiber (MMF) speckle sensor. Using mode coupling theory, we derive an expression showing that the sensitivity of the MMF speckle sensor depends on the intensity profile of the MMF modes. Particularly, we use our theory to study the influence of the spatial filtering window on the sensitivity, and the experimental results have found a good agreement with the theory. Our results suggest that the sensitivity of an MMF speckle sensor can be greatly enhanced by adjusting the size and location of the spatial filtering window. An 80-fold improvement on sensitivity was achieved in our experiment, as compared with the conventional MMF speckle sensor with the filtering window placed at the center of the speckle field.

High-resolution wavefront shaping with a photonic crystal fiber for multimode fiber imaging

We demonstrate that a high-numerical-aperture photonic crystal fiber allows lensless focusing at an unparalleled resolution by complex wavefront shaping. This paves the way toward high-resolution imaging exceeding the capabilities of imaging with multi-core single-mode optical fibers. We analyze the beam waist and power in the focal spot on the fiber output using different types of fibers and different wavefront shaping approaches. We show that the complex wavefront shaping technique, together with a properly designed multimode photonic crystal fiber, enables us to create a tightly focused spot on the desired position on the fiber output facet with a subwavelength beam waist.

Two-photon imaging through a multimode fiber

In this work we demonstrate 3D imaging using two-photon excitation through a 20 cm long multimode optical fiber (MMF) of 350 µm diameter. The imaging principle is similar to single photon fluorescence through a MMF, except that a focused femtosecond pulse is delivered and scanned over the sample. In our approach, focusing and scanning through the fiber is accomplished by digital phase conjugation using mode selection by time gating with an ultra-fast reference pulse. The excited two-photon emission is collected through the same fiber. We demonstrate depth sectioning by scanning the focused pulse in a 3D volume over a sample consisting of fluorescent beads suspended in a polymer. The achieved resolution is 1 µm laterally and 15 µm axially. Scanning is performed over an 80x80 µm field of view. To our knowledge, this is the first demonstration of high-resolution three-dimensional imaging using two-photon fluorescence through a multimode fiber.

Light control in a multicore fiber using the memory effect

Endoscopic imaging through a multicore fiber (MCF) is widely used but is affected by pixelated images, which limits its resolution to a few micrometers. This is due to the spacing between the cores in the MCF, which is large enough to avoid core-to-core light coupling. Wavefront shaping techniques have been shown to focus light to a resolution finer than the inter core spacing, however a long calibration procedure is needed. Moreover the calibration depends on the optical fiber conformation. Here, we show a calibration method using only one digital hologram. The method is based on digital phase conjugation and the memory effect of the MCF to focus and scan a spot. In addition, we show how simple patterns can be projected using the same multicore fiber.