The information age in optics: Measuring the transmission matrix

Tracing multiple scattering trajectories for deep optical imaging in scattering media

Multiple light scattering hampers imaging objects in complex scattering media. Approaches used in real practices mainly aim to filter out multiple scattering obscuring the ballistic waves that travel straight through the scattering medium. Here, we propose a method that makes the deterministic use of multiple scattering for microscopic imaging of an object embedded deep within scattering media. The proposed method finds a stack of multiple complex phase plates that generate similar light trajectories as the original scattering medium. By implementing the inverse scattering using the identified phase plates, our method rectifies multiple scattering and amplifies ballistic waves by almost 600 times. This leads to a significant increase in imaging depth-more than three times the scattering mean free path-as well as the correction of image distortions. Our study marks an important milestone in solving the long-standing high-order inverse scattering problems.

Reference-less wavefront shaping in a Hopfield-like rough intensity landscape

This study introduces a new digital-micromirror based binary-phase wavefront shaping technique, which allows the measurement of the full coupling matrix of a disordered medium without a reference and enables to focusing transmitted light. The coupling matrix takes on a bi-dyadic structure, similar to a Hopfield memory matrix containing two memory patterns. Sequential wavefront optimization in this configuration often stalls due to a rough intensity landscape, resulting in a non-optimal state. To overcome this issue, we propose the Complete Couplings Mapping method, which consistently reaches the theoretically expected maximum intensity.

Time-averaged image projection through a multimode fiber

Many disciplines, ranging from lithography to opto-genetics, require high-fidelity image projection. However, not all optical systems can display all types of images with equal ease. Therefore, the image projection quality is dependent on the type of image. In some circumstances, this can lead to a catastrophic loss of intensity or image quality. For complex optical systems, it may not be known in advance which types of images pose a problem. Here we show a new method called Time-Averaged image Projection (TAP), allowing us to mitigate these limitations by taking the entire image projection system into account despite its complexity and building the desired intensity distribution up from multiple illumination patterns. Using a complex optical setup, consisting of a wavefront shaper and a multimode optical fiber illuminated by coherent light, we succeeded to suppress any speckle-related background. Further, we can display independent images at multiple distances simultaneously, and alter the effective sharpness depth through the algorithm. Our results demonstrate that TAP can significantly enhance the image projection quality in multiple ways. We anticipate that our results will greatly complement any application in which the response to light irradiation is relatively slow (one microsecond with current technology) and where high-fidelity spatial distribution of optical power is required.

Single-shot coherent power-spectrum imaging of objects hidden by opaque scattering media

We report coherent imaging of objects behind opaque scattering media with only one piece of the power spectrum pattern. We solve the unique solution and improve algorithm speed for the inverse problem. Based on the proposed scattering-disturbance model, with only one piece of the Fourier transform power spectrum pattern under coherent illumination, we successfully reconstruct clear images of the objects fully hidden by an opaque diffuser. The experimental results demonstrate the feasibility of the reconstruction method and the scattering-disturbance model. Our method makes it possible to carry out snapshot coherent imaging of the objects obscured by scattering media, which extends the methodology of x-ray crystallography to visible-light scattering imaging for underwater and living biomedical imaging.

Simulation and experimental verification for imaging of gray-scale objects through scattering layers

We analyze the imaging of gray-scale objects through highly scattering layers. The theoretical investigation with numerical simulations shows that the contrast of the speckle autocorrelations varies regularly with the change of the gray scale of the object. Therefore, gray information is well contained in the autocorrelations of the speckle patterns, and gray-scale objects are able to be exacted from these autocorrelations via speckle correlation technology. Combined with phase retrieval via the generalized approximate message passing algorithm, recovery of the objects is realized and accurate gray-scale reconstruction is demonstrated via numerical simulations. Experiment results further demonstrate the good performance of the scheme in the imaging of gray-scale objects through scattering layers. Particularly, this work will be beneficial for applications of imaging through turbid media in biomedical and biophotonics imaging.

Statistics and control of waves in disordered media

Fundamental concepts in the quasi-one-dimensional geometry of disordered wires and random waveguides in which ideas of scaling and the transmission matrix were first introduced are reviewed. We discuss the use of the transmission matrix to describe the scaling, fluctuations, delay time, density of states, and control of waves propagating through and within disordered systems. Microwave measurements, random matrix theory calculations, and computer simulations are employed to study the statistics of transmission and focusing in single samples and the scaling of the probability distribution of transmission and transmittance in random ensembles. Finally, we explore the disposition of the energy density of transmission eigenchannels inside random media.

Filtering random matrices: the effect of incomplete channel control in multiple scattering

We present an analytic random matrix theory for the effect of incomplete channel control on the measured statistical properties of the scattering matrix of a disordered multiple-scattering medium. When the fraction of the controlled input channels, m1, and output channels, m2, is decreased from unity, the density of the transmission eigenvalues is shown to evolve from the bimodal distribution describing coherent diffusion, to the distribution characteristic of uncorrelated Gaussian random matrices, with a rapid loss of access to the open eigenchannels. The loss of correlation is also reflected in an increase in the information capacity per channel of the medium. Our results have strong implications for optical and microwave experiments on diffusive scattering media.

Transmission eigenvalues and the bare conductance in the crossover to Anderson localization

We measure the field transmission matrix t for microwave radiation propagating through random waveguides in the crossover to Anderson localization. From these measurements, we determine the dimensionless conductance g and the individual eigenvalues τ(n) of the transmission matrix tt(†) whose sum equals g. In diffusive samples, the highest eigenvalue, τ(1), is close to unity corresponding to a transmission of nearly 100%, while for localized waves, the average of τ(1), is nearly equal to g. We find that the spacing between average values of lnτ(n) is constant and demonstrate that when surface interactions are taken into account it is equal to the inverse of the bare conductance.