Seeing through multimode fibers with real-valued intensity transmission matrices

Abstract

Image transmission through multimode optical fibers has been an area of immense interests driven by the demand for miniature endoscopes in biomedicine and higher speed and capacity in telecommunications. Conventionally, a complex-valued transmission matrix is obtained experimentally to link the input and output light fields of a multimode fiber for image retrieval, which complicates the experimental setup and increases the computational complexity. Here, we report a simple and high-speed method for image retrieval based on our demonstration of a pseudo-linearity between the input and output light intensity distributions of multimode fibers. We studied the impact of several key parameters to image retrieval, including image pixel count, fiber core diameter and numerical aperture. We further demonstrated with experiments and numerical simulations that a wide variety of input binary and gray scale images could be faithfully retrieved from the corresponding output speckle patterns. Thus, it promises to be useful for highly miniaturized endoscopy in biomedicine and spatial-mode-division multiplexing in telecommunications.

Focusing light through multimode fibres using a digital micromirror device: a comparison study of non-holographic approaches

“…The relationship between the input and output light intensity distributions of a disordered medium such as a MMF can be approximated by a RVITM, which indicates the contribution of each micromirror to the light intensity at the target output position. In previous studies, we demonstrated that binary and grayscale images that were projected into a MMF could be faithfully retrieved using a RVITM [ 24 ], and high-speed photoacoustic-guided WS through an optical diffuser with a total runtime of 300 ms [ 25 ]. Several WS methods based on similar principles were also reported [ 22 , 23 , 34 ].…”

“…As a high-speed alternative, DMDs have been studied intensively for WS [ 2 , 11 , 20 – 24 ] in the last few years as they possess a much higher frame rate (23 kHz). A DMD comprises a large array of micromirrors; each micromirror can be independently switched between two statuses (‘ON’ and ‘OFF’) and hence provides binary amplitude modulations.…”

“…Another method calculates the conditional probability of switching ‘ON’ each micromirror for causing light focusing at the target position, and produces an optimal DMD pattern by setting a threshold to switch ‘ON’ micromirrors with higher probabilities [ 21 ]. In our previous works [ 24 , 25 ], we developed a high-speed method that characterises the light intensity changes through a disordered medium as a RVITM, based on which an optimal DMD pattern can be determined for light focusing through an optical diffuser [ 25 ].…”

High-speed photoacoustic-guided wavefront shaping for focusing light in scattering media

“…In our previous work, we reported that a real-valued intensity transmission matrix (RVITM) can be used to approximately connect the input and output light intensities of a disordered medium (e.g., multimode optical fiber), and with which input binary and gray scale images can be retrieved from measured intensities of the output speckles [ 23 ]. In this study, we further demonstrate that the RVITM can also be used for focusing light through scattering media as it encodes both the phase and amplitude information of a corresponding complex-valued transmission matrix (TM).…”

“…As such, is linearly proportional to and thus maximizing the amplitude of is equivalent to focusing light at the transducer focus. With the approximate relationship between the intensities of the input and output light field through a scattering medium that can be connected by an RVITM [ 23 ], and can be approximately connected by a row of the elements, , that correspond to light transport from all the DMD input positions to the target location (US transducer focus) as As owing to the Hadamard matrix properties, we have where we define , which connects the light intensities from all the input positions to the PA signal amplitude at the target location. So, a positive value means that the corresponding micromirror contributes positively to the optical intensity.…”