Spectral control of broadband light through random media by wavefront shaping

Controlling the transmission of broadband light through scattering media using a digital micromirror device

Wavefront shaping has emerged as a valuable technique in complex photonics, wherein the various eigenmodes of the disordered medium are selectively excited to control the overall transmission through the medium. The process utilizes active optical devices such as liquid crystal-based spatial light modulators (LC-SLM), deformable mirrors (DM), and digital micromirror devices (DMD). Among these, the latter is preferred for imaging through dynamic scattering media such as living biological tissues due to their high-speed refresh rate and increased resolution. This study employs a genetic algorithm along with binary amplitude modulation generated by a digital micromirror device to spatially and spectrally control the large spectral bandwidth through a scattering medium. We illustrate spatial single-point focusing of broadband light, multipoint focusing of broadband light, and programmable spectral filtering of the same through disordered samples.

Efficient Enhancement of Second Harmonic Generation via Noninvasive Modulation

Second harmonic generation has been widely applied in various fields. High second harmonic intensity can facilitate optical imaging, signal sensing, and detection. Thus, enhancing the intensity of the second harmonic is a significant work. However, changing the external character of crystal or increasing the pump light intensity to improve the intensity of the second harmonic is not always advisable in some applications, such as bioimaging, biopsies, etc. Here, we implemented a noninvasive method that constructs a specific spatial distribution field via a scattering medium to realize a high enhancement of second harmonic intensity. We studied that different scattering mediums exerted the influence on the optimal enhancement effect of second harmonic. It was found that choosing an appropriate scattering medium can greatly enhance the intensity of the second harmonic. The results can offer a helpful value for second harmonic applications such as bioimaging, sensing, and optical frequency conversion.

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.

Wavefront Shaping Concepts for Application in Optical Coherence Tomography-A Review

Optical coherence tomography (OCT) enables three-dimensional imaging with resolution on the micrometer scale. The technique relies on the time-of-flight gated detection of light scattered from a sample and has received enormous interest in applications as versatile as non-destructive testing, metrology and non-invasive medical diagnostics. However, in strongly scattering media such as biological tissue, the penetration depth and imaging resolution are limited. Combining OCT imaging with wavefront shaping approaches significantly leverages the capabilities of the technique by controlling the scattered light field through manipulation of the field incident on the sample. This article reviews the main concepts developed so far in the field and discusses the latest results achieved with a focus on signal enhancement and imaging.

Disordered Optics: Exploiting Multiple Light Scattering and Wavefront Shaping for Nonconventional Optical Elements

Advances in diverse areas such as inspection, imaging, manufacturing, telecommunications, and information processing have been stimulated by novel optical devices. Conventional material ingredients for these devices are typically made of homogeneous refractive or diffractive materials and require sophisticated design and fabrication, which results in practical limitations related to their form and functional figures of merit. To overcome such limitations, recent developments in the application of disordered materials as novel optical elements have indicated great potential in enabling functionalities that go beyond their conventional counterparts, while the materials exhibit potential advantages with respect to reduced form factors. Combined with wavefront shaping, disordered materials enable dynamic transitions between multiple functionalities in a single active optical device. Recent progress in this field is summarized to gain insight into the physical principles behind disordered optics with regard to their advantages in various applications as well as their limitations compared to conventional optics.

Controlling light in complex media beyond the acoustic diffraction-limit using the acousto-optic transmission matrix

Studying the internal structure of complex samples with light is an important task but a difficult challenge due to light scattering. While the complex optical distortions induced by scattering can be effectively undone if the medium’s scattering-matrix is known, this matrix generally cannot be retrieved without the presence of an invasive detector or guide-star at the target points of interest. To overcome this limitation, the current state-of-the-art approaches utilize focused ultrasound for generating acousto-optic guide-stars, in a variety of different techniques. Here, we introduce the acousto-optic transmission matrix (AOTM), which is an ultrasonically-encoded, spatially-resolved, optical scattering-matrix. The AOTM provides both a generalized framework to describe any acousto-optic based technique, and a tool for light control and focusing beyond the acoustic diffraction-limit inside complex samples. We experimentally demonstrate complex light control using the AOTM singular vectors, and utilize the AOTM framework to analyze the resolution limitation of acousto-optic guided focusing approaches.

Various techniques combine light and ultrasound to study the inside of strongly scattering samples, beyond the reach of purely optical imaging. Here, Katz et al. introduce the acousto-optic transmission matrix framework that allows to control and focus light beyond the acoustic diffraction limit.

Simulated annealing optimization in wavefront shaping controlled transmission

In this research, we present results of simulated annealing (SA), a heuristic optimization algorithm, for focusing light through a turbid medium. Performance of the algorithm on phase and amplitude modulations has been evaluated. A number of tips to tune the optimization parameters are provided. The effect of measurement noise on the performance of the SA algorithm is explored. Additionally, SA performance is compared with continuous sequential and briefly with other optimization algorithms.

Generation of focal pattern with controllable polarization and intensity for laser beam passing through a multi-mode fiber

Similar to coherent light passing through a scattering medium, the propagation of coherent light through a multi-mode fiber (MMF) will result in a random speckle field. For a non-polarization maintaining MMF, the randomization can be observed not only in the intensity distribution, but also in the polarization state. In this paper, we propose a new technique known as phase combination to control the optical field for the light passing through the MMF. We show that, based on this new technique, the random speckle pattern can be modulated into an intensity distribution of two bright focal spots with mutually perpendicular polarization by only one polarizer. In particular, the intensity distribution of these two focal spots can be quantitatively controlled. This technique may find applications in medical imaging, nonlinear optics and optical communication etc.

Mapping the energy density of shaped waves in scattering media onto a complete set of diffusion modes

We study the energy density of shaped waves inside a quasi-1D disordered waveguide. We find that the spatial energy density of optimally shaped waves, when expanded in the complete set of eigenfunctions of the diffusion equation, is well described by considering only a few of the lowest eigenfunctions. Taking into account only the fundamental eigenfunction, the total internal energy inside the sample is underestimated by only 2%. The spatial distribution of the shaped energy density is very similar to the fundamental eigenfunction, up to a cosine distance of about 0.01. We obtain the energy density of transmission eigenchannels inside the sample by numerical simulation of the scattering matrix. Computing the transmission-averaged energy density over all transmission channels yields the ensemble averaged energy density of shaped waves. From the averaged energy density, we reconstruct its spatial distribution using the eigenfunctions of the diffusion equation. The results of our study have exciting applications in controlled biomedical imaging, efficient light harvesting in solar cells, enhanced energy conversion in solid-state lighting, and low threshold random lasers.

Spatiotemporal Coherent Control of Light through a Multiple Scattering Medium with the Multispectral Transmission Matrix

We report the broadband characterization of the propagation of light through a multiple scattering medium by means of its multispectral transmission matrix. Using a single spatial light modulator, our approach enables the full control of both the spatial and spectral properties of an ultrashort pulse transmitted through the medium. We demonstrate spatiotemporal focusing of the pulse at any arbitrary position and time with any desired spectral shape. Our approach opens new perspectives for fundamental studies of light-matter interaction in disordered media, and has potential applications in sensing, coherent control, and imaging.

Broadband Coherent Enhancement of Transmission and Absorption in Disordered Media

Spatial modulation of the incident wave front has become a powerful method for controlling the diffusive transport of light in disordered media; however, such interference-based control is intrinsically sensitive to frequency detuning. Here, we show analytically and numerically that certain wave fronts can exhibit strongly enhanced total transmission or absorption across bandwidths that are orders of magnitude broader than the spectral correlation width of the speckles. Such broadband enhancement is possible due to long-range correlations in coherent diffusion, which cause the spectral degrees of freedom to scale as the square root of the bandwidth rather than the bandwidth itself.

Deterministic control of broadband light through a multiply scattering medium via the multispectral transmission matrix

We present a method to measure the spectrally-resolved transmission matrix of a multiply scattering medium, thus allowing for the deterministic spatiospectral control of a broadband light source by means of wavefront shaping. As a demonstration, we show how the medium can be used to selectively focus one or many spectral components of a femtosecond pulse, and how it can be turned into a controllable dispersive optical element to spatially separate different spectral components to arbitrary positions.

Microgenetic optimization algorithm for optimal wavefront shaping

One of the main limitations of utilizing optimal wavefront shaping in imaging and authentication applications is the slow speed of the optimization algorithms currently being used. To address this problem we develop a microgenetic optimization algorithm (μGA) for optimal wavefront shaping. We test the abilities of the μGA and make comparisons to previous algorithms (iterative and simple-genetic) by using each algorithm to optimize transmission through an opaque medium. From our experiments we find that the μGA is faster than both the iterative and simple-genetic algorithms and that both genetic algorithms are more resistant to noise and sample decoherence than the iterative algorithm.

Scanning-free imaging through a single fiber by random spatio-spectral encoding

We present an approach for 2D imaging through a single fiber without the need for scanners. A random scattering medium placed next to the distal end of the fiber is used to encode the collected light from every imaged pixel with a different random spectral signature. We demonstrate imaging of externally illuminated 2D objects from a single measured spectrum at the fiber's proximal end. The technique is insensitive to fiber bending, an advantage for endoscopic applications.

Superpixel-based spatial amplitude and phase modulation using a digital micromirror device

We present a superpixel method for full spatial phase and amplitude control of a light beam using a digital micromirror device (DMD) combined with a spatial filter. We combine square regions of nearby micromirrors into superpixels by low pass filtering in a Fourier plane of the DMD. At each superpixel we are able to independently modulate the phase and the amplitude of light, while retaining a high resolution and the very high speed of a DMD. The method achieves a measured fidelity F = 0.98 for a target field with fully independent phase and amplitude at a resolution of 8 × 8 pixels per diffraction limited spot. For the LG10 orbital angular momentum mode the calculated fidelity is F = 0.99993, using 768 × 768 DMD pixels. The superpixel method reduces the errors when compared to the state of the art Lee holography method for these test fields by 50% and 18%, with a comparable light efficiency of around 5%. Our control software is publicly available.

Coherent control of total transmission of light through disordered media

We demonstrate order of magnitude coherent control of total transmission of light through random media by shaping the wave front of the input light. To understand how the finite illumination area on a wide slab affects the maximum values of total transmission, we develop a model based on random matrix theory that reveals the role of long-range correlations. Its predictions are confirmed by numerical simulations and provide physical insight into the experimental results.

Direct imaging of fluorescent structures behind turbid layers

We present a method to directly image fluorescent structures inside turbid media. This is based on wave-front shaping to optimize the scattered light onto a single fluorescent particle, as the optical memory effect for a scanning image of the surroundings of this particle. We show that iterating the optimization leads to the focusing on a single particle whose surroundings are subsequently scanned. In combination with a parabolic phase pattern, this method can be extended to a three dimensional imaging method inside turbid media.

Digital optical phase conjugation for delivering two-dimensional images through turbid media

Optical transmission through complex media such as biological tissue is fundamentally limited by multiple light scattering. Precise control of the optical wavefield potentially holds the key to advancing a broad range of light-based techniques and applications for imaging or optical delivery. We present a simple and robust digital optical phase conjugation (DOPC) implementation for suppressing multiple light scattering. Utilizing wavefront shaping via a spatial light modulator (SLM), we demonstrate its turbidity-suppression capability by reconstructing the image of a complex two-dimensional wide-field target through a highly scattering medium. Employing an interferometer with a Sagnac-like ring design, we successfully overcome the challenging alignment and wavefront-matching constraints in DOPC, reflecting the requirement that the forward- and reverse-propagation paths through the turbid medium be identical. By measuring the output response to digital distortion of the SLM write pattern, we validate the sub-wavelength sensitivity of the system.

Focusing polychromatic light through strongly scattering media

We demonstrate feedback-optimized focusing of spatially coherent polychromatic light after transmission through strongly scattering media, and describe the relationship between optimized focus intensity and initial far-field speckle contrast. Optimization is performed using a MEMS spatial light modulator with camera-based or spectrometer-based feedback. We observe that the spectral bandwidth of the optimized focus depends on characteristics of the feedback signal. We interpret this dependence as a modification in the number of independent frequency components, or spectral correlations, transmitted by the sample, and introduce a simple model for polychromatic focus enhancement that is corroborated by experiment with calibrated samples.

Image restoration through thin turbid layers by correlation with a known object

A method to recover the image of an object behind thin turbid layers is developed by wavefront shaping technique. The optimized wavefront is generated by modulating the scattering light of a known object with a spatial light modulator. A Pearson Correlation Coefficient is introduced as a cost function for the optimization. A beam scanning method based on optical memory effect is proposed to further enlarge the Field-of-View (FOV). The experimental results show good fidelity and large FOV of the recovered image.

Complex wavefront shaping for optimal depth-selective focusing in optical coherence tomography

We report on an approach to exploit multiple light scattering by shaping the incident wavefront in optical coherence tomography (OCT). Most of the reflected signal from biological tissue consists of multiply scattered light, which is regarded as noise in OCT. A digital mirror device (DMD) is utilized to shape the incident wavefront such that the maximal energy is focused at a specific depth in a highly scattering sample using a coherence-gated reflectance signal as feedback. The proof-of-concept experiment demonstrates that this approach enhances depth-selective focusing in the presence of optical inhomogeneity, and thus extends the penetration depth in spectral domain-OCT (SD-OCT).

Optimal control of light propagation through multiple-scattering media in the presence of noise

We study the control of coherent light propagation through multiple-scattering media in the presence of measurement noise. In our experiments, we use a two-step optimization procedure to find the optimal incident wavefront that generates a bright focal spot behind the medium. We conclude that the control of coherent light propagation through a multiple-scattering medium is only determined by the number of photoelectrons detected per optimized segment. The prediction of our model agrees well with the experimental results. Our results offer opportunities for imaging applications through scattering media such as biological tissue in the shot noise limit.

Polarization control of multiply scattered light through random media by wavefront shaping

We show that the polarization state of coherent light propagating through an optically thick multiple scattering medium can be controlled by wavefront shaping, that is, by controlling only the spatial phase of the incoming field with a spatial light modulator. Any polarization state of light at any spatial position behind the scattering medium can be attained with this technique. Thus, transforming the random medium to an arbitrary optical polarization component becomes possible.