Transmission matrix of a scattering medium and its applications in biophotonics

Abstract

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.

Ultrathin endoscopes based on multicore fibers and adaptive optics: a status review and perspectives

“…This can be formalized with the transmission matrix formulation. [24][25][26] This means that spatial information-perhaps counter-intuitively-is not lost during propagation through the waveguide and that the spatial information (in other words, the image of the object) can be recovered, e.g., by point-scanning imaging, which is sketched in Fig. 1(d), but other wave front shaping methods, computational methods, or a combination of the two can also be used.…”

Focusing light inside scattering media with magnetic-particle-guided wavefront shaping

“…These techniques control the optical field on a target plane inside a scattering medium by shaping the optical field on an input plane outside the medium. The relationship between the input plane and target plane can be described by a transmission matrix, which characterizes the propagation of light through the scattering medium [7,8]. …”

Focusing light through scattering media by transmission matrix inversion

“…However, because of the refractive index inhomogeneity, light is scattered when propagating through scattering media. To focus light through such turbid media, researchers have developed a number of wavefront shaping techniques, including feedback-based methods [9,10], optical phase conjugation [11][12][13][14] and transmission matrix methods [15][16][17][18]. Feedback-based methods employ a spatial light modulator (SLM) to continuously shape the wavefront of the incident light while monitoring the feedback signal from a guidestar which is proportional to the light intensity at a target location.…”