Changhyeong Yoon

Transmission matrix of a scattering medium and its applications in biophotonics

A conventional lens has well-defined transfer function with which we can form an image of a target object. On the contrary, scattering media such as biological tissues, multimode optical fibers and layers of disordered nanoparticles have highly complex transfer function, which makes them impractical for the general imaging purpose. In recent studies, we presented a method of experimentally recording the transmission matrix of such media, which is a measure of the transfer function. In this review paper, we introduce two major applications of the transmission matrix: enhancing light energy delivery and imaging through scattering media. For the former, we identified the eigenchannels of the transmission matrix with large eigenvalues and then coupled light to those channels in order to enhance light energy delivery through the media. For the latter, we solved matrix inversion problem to reconstruct an object image from the distorted image by the scattering media. We showed the enlargement of the numerical aperture of imaging systems with the use of scattering media and demonstrated endoscopic imaging through a single multimode optical fiber working in both reflectance and fluorescence modes. Our approach will pave the way of using scattering media as unique optical elements for various biophotonics applications.

Optical Imaging With the Use of a Scattering Lens

“Turbidity” caused by multiple light scattering distorts the propagation of waves, and thus undermines optical imaging. For example, translucent biological tissues exhibiting optical turbidity have posed limitations on the imaging depth and energy transmission. Here, we introduce a novel method called turbid lens imaging (TLI) that records a transmission matrix of a scattering medium charactering the input-output response of the medium. The knowledge of this transmission matrix allows one to find an incident wave out of the distorted transmitted wave. Therefore, it converts the highly complex medium into a useful imaging optics. We demonstrate that the image distortion by a scattering medium can be eliminated by the use of the transmission matrix and a clean object image can be retrieved as a result. We extend TLI for imaging through a multimode optical fiber, which is also a scattering medium, and demonstrate an endoscopic imaging by using a single multimode optical fiber itself as a lens. In addition, we show that TLI removes the pixelation artifact in using an image fiber bundle and improve spatial resolution. Our method of making use of multiple light scattering will lay a foundation for advance optical bioimaging methods.

Disorder-mediated enhancement of fiber numerical aperture

The numerical aperture (NA) of a multimode optical fiber sets the limit of the information transport capacity along the spatial degree of freedom. In this Letter, we report that the application of a highly disordered medium can overcome the capacity limit set by the fiber NA. Specifically, we coated the input surface of a multimode fiber with a disordered medium made of ZnO nanoparticles and transported a wide-field image through the fiber with a spatial resolution beyond the diffraction limit given by the fiber NA. This was made possible because multiple scatterings induced by the disordered medium physically increased the NA of the entire system. Our study will lead to enhancing the spatial resolution of fiber-based endoscopic imaging and also improving the information transport capacity in optical communications.

Synthetic aperture microscopy for high resolution imaging through a turbid medium

We report on synthetic aperture microscopy through a highly turbid medium. We first recorded a transmission matrix for the turbid medium with an angular basis of 20,000 complex images covering 0.6 NA. This effectively converts the medium into a lens of the same NA. Distorted images of a target object are then taken at 500 different angles of illumination covering 0.6 NA. For each of the distorted images, the original object image is reconstructed from the transmission matrix by the recently developed turbid lens imaging (TLI) technique. All 500 reconstructed images are synthesized to enhance the NA to 1.2 and thereby generate an object image with twice the enhanced spatial resolution of the individual images. Our method of applying aperture synthesis for TLI makes it possible to enhance the resolving power without increasing the number of transmission matrix elements. This relieves the demand for data acquisition and processing that has impeded the practicality of TLI.

Speckle suppression via sparse representation for wide-field imaging through turbid media

Speckle suppression is one of the most important tasks in the image transmission through turbid media. Insufficient speckle suppression requires an additional procedure such as temporal ensemble averaging over multiple exposures. In this paper, we consider the image recovery process based on the so-called transmission matrix (TM) of turbid media for the image transmission through the media. We show that the speckle left unremoved in the TM-based image recovery can be suppressed effectively via sparse representation (SR). SR is a relatively new signal reconstruction framework which works well even for ill-conditioned problems. This is the first study to show the benefit of using the SR as compared to the phase conjugation (PC) a de facto standard method to date for TM-based imaging through turbid media including a live cell through tissue slice.

Relation between transmission eigenchannels and single-channel optimizing modes in a disordered medium

The wave transport through disordered media, although a random process, has some universal physical properties. One of these properties that has been investigated in this report is the relation between transmission eigenchannels and the so-called single-channel optimizing mode, which maximizes the intensity of the transmitted wave at a single specific output channel. Since single-channel optimizing modes have higher transmittance than the uncontrolled waves, it has been predicted before that transmission eigenchannels with higher transmittance preferentially contribute to the single-channel optimizing modes in proportion to the square of eigenvalues. In this Letter, we report the experimental validation of this prediction by measuring cross-correlation between the single-channel optimizing modes and the transmission eigenchannels.

Collective pulsatile expansion and swirls in proliferating tumor tissue

Understanding the dynamics of expanding biological tissues is essential to a wide range of phenomena in morphogenesis, wound healing and tumor proliferation. Increasing evidence suggests that many of the relevant phenomena originate from complex collective dynamics, inherently nonlinear, of constituent cells that are physically active. Here, we investigate thin disk layers of proliferating, cohesive, monoclonal tumor cells and report the discovery of macroscopic, periodic, soliton-like mechanical waves with which cells are collectively ratcheting, as in the traveling-wave chemotaxis of dictyostelium discodium amoeba cells. The relevant length-scale of the waves is remarkably large (~1 mm), compared to the thickness of a mono-layer tissue (). During the tissue expansion, the waves are found to repeat several times with a quite well defined period of approximately 4 h. Our analyses suggest that the waves are initiated by the leading edge that actively pulls the tissue in the outward direction, while the cells within the bulk tissue do not seem to generate a strong self-propulsion. Subsequently, we demonstrate that a simple mathematical model chain of nonlinear springs that are constantly pulled in the outward direction at the leading edge recapitulates the observed phenomena well. As the areal cell density becomes too high, the tissue expansion stalls and the periodic traveling waves yield to multiple swirling vortices. Cancer cells are known to possess a broad spectrum of migration mechanisms. Yet, our finding has established a new unusual mode of tumor tissue expansion, and it may be equally applicable for many different expanding thin layers of cell tissues.

Experimental measurement of the number of modes for a multimode optical fiber.

For a multimode optical fiber, the number of modes (N(m)) can be calculated by analytic theory when the fiber is straight, twist-free, and strain-free. In practice, however, the fiber is subject to distortions that modify its mode characteristics. In this Letter, we present an experimental method to interrogate the mode properties of a multimode optical fiber. We experimentally measured the transmission matrix of a multimode optical fiber and performed singular value decomposition. We proved, both theoretically and experimentally, that the rank of the transmission matrix is equal to N(m). We expect that the suggested method will contribute to the fields of the biomedical optics and optical communications where optical fiber is widely used.

Preferential coupling of an incident wave to reflection eigenchannels of disordered media

Light waves incident to a highly scattering medium are incapable of penetrating deep into the medium due to the multiple scattering process. This poses a fundamental limitation to optically imaging, sensing, and manipulating targets embedded in opaque scattering layers such as biological tissues. One strategy for mitigating the shallow wave penetration is to exploit eigenchannels with anomalously high transmittance existing in any scattering medium. However, finding such eigenchannels has been a challenging task due to the complexity of disordered media. Moreover, it is even more difficult to identify those eigenchannels from the practically relevant reflection geometry of measurements. In this Letter, we present an iterative wavefront control method that either minimizes or maximizes the total intensity of the reflected waves. We proved that this process led to the preferential coupling of incident wave to either low or high-reflection eigenchannels, and observed either enhanced or reduced wave transmission as a consequence. Since our approach is free from prior characterization measurements such as the recording of transmission matrix, and also able to keep up with sample perturbation, it is readily applicable to in vivo applications. Enhancing light penetration will help improving the working depth of optical sensing and treatment techniques.

Exploring anti-reflection modes in disordered media

Sensing and manipulating targets hidden under scattering media are universal problems that take place in applications ranging from deep-tissue optical imaging to laser surgery. A major issue in these applications is the shallow light penetration caused by multiple scattering that reflects most of incident light. Although advances have been made to eliminate image distortion by a scattering medium, dealing with the light reflection has remained unchallenged. Here we present a method to minimize reflected intensity by finding and coupling light into the anti-reflection modes of a scattering medium. In doing so, we achieved more than a factor of 3 increase in light penetration. Our method of controlling reflected waves makes it readily applicable to in vivo applications in which detector sensors can only be positioned at the same side of illumination and will therefore lay the foundation of advancing the working depth of many existing optical imaging and treatment technologies.