Multiple light scattering is considered as the major limitation for deep imaging and focusing in turbid media. In this paper, we present an innovative method to overcome this limitation and enhance the delivery of light energy ultra-deep into turbid media with significant improvement in focusing. Our method is based on a wide-field reflection matrix optical coherence tomography (RM-OCT). The time-reversal decomposition of the RM is calibrated with the Tikhonov regularization parameter in order to get more accurate reversal results deep inside the scattering sample. We propose a concept named model energy matrix, which provides a direct mapping of light energy distribution inside the scattering sample. To the best of our knowledge, it is the first time that a method to measure and quantify the distribution of beam intensity inside a scattering sample is demonstrated. By employing the inversion of RM to find the matched wavefront and shaping with a phase-only spatial light modulator, we succeeded in both focusing a beam deep (~9.6 times of scattering mean free path, SMFP) inside the sample and increasing the delivery of light energy by an order of magnitude at an ultra-deep (~14.4 SMFP) position. This technique provides a powerful tool to understand the propagation of photon in a scattering medium and opens a new way to focus light inside biological tissues. 

/pdf/enhance-the-delivery-of-light-energy-ultra-deep-into-turbid-2qwrhll5.pdf

Enhance the delivery of light energy ultra-deep into turbid medium by controlling multiple scattering photons to travel in open channels

We developed an accelerated Genetic Algorithm (GA) system based on the cooperation of a field-programmable gate array (FPGA) and the optimized parameters that enables fast light focusing through scattering media. Starting at the searching space, which influences the convergence of the optimization algorithms, we manipulated the mutation rate that defines the number of mutated pixels on the spatial light modulator to accelerate the GA process. We found that the enhanced decay ratio of the mutation rate leads to a much faster convergence of the GA. A convergence-efficiency function was defined to gauge the tradeoff between the processing time and the enhancement of the focal spot. This function allowed us to adopt the shorter iteration number of the GA that still achieves applicable light focusing. Furthermore, the accelerated GA configuration was programmed in FPGA to boost processing speed at the hardware level. It shows the ability to focus light through scattering media within a few seconds, 150 times faster than the PC-based GA. The processing cycle could be further promoted to a millisecond-level with the advanced FPGA processor chips. This study makes the evolution-based optimization approach adaptable in dynamic scattering media, showing the capability to tackle wavefront shaping in biological material. 

Speedy light focusing through scattering media by a cooperatively FPGA-parameterized genetic algorithm

/pdf/enhance-the-delivery-of-light-energy-ultra-deep-into-turbid-3fkn470b.pdf

We develop an accelerated Genetic Algorithm (GA) system constructed by the cooperation of field-programmable gate array (FPGA) and optimized parameters of the GA. We found the enhanced decay of mutation rate makes convergence of the GA much faster, enabling the parameter-induced acceleration of the GA. Furthermore, the accelerated configuration of the GA is programmed in FPGA to boost processing speed at the hardware level without external computation devices. This system has ability to focus light through scattering medium within 4 seconds with robust noise resistance and stable repetition performance, which could be further reduced to millisecond level with advanced board configuration. This study solves the long-term limitation of the GA, it promotes the applications of the GA in dynamic scattering mediums, with the capability to tackle wavefront shaping in biological material.

High-Speed Light Focusing through Scattering Medium by Cooperatively Accelerated Genetic Algorithm

Reflection matrix optical coherence tomography (RM-OCT) has recently emerged as a solution to address the limited imaging depth in conventional optical coherence tomography (OCT). The RM-OCT image relies on the reflection matrix reconstruction technique, assuming distinct thresholds between multiply scattered and singly scattered photons. By setting this threshold, the optical field information composed of singly scattered photons is reconstructed. However, a significant challenge arises when imaging strong reflection regions, where the singly scattered photons from strong reflections contribute equally to those from the target, causing the imaging target to be submerged in strong reflection backgrounds. This study proposes a novel noise reduction technique based on robust principal component analysis (RPCA), applied for the first time in RM-OCT image. In Monte Carlo experiments, images were successfully decomposed into a low-rank matrix representing background noise and a sparse matrix representing the imaging target. Further experiments demonstrated a significant increase of 7.79 dB in the signal-to-noise ratio of the target image, greatly enhancing imaging quality and accuracy. Biological tissue imaging experiments confirmed the unique advantage of this method, which not only reduces background noise but also highlights imaging target details. 

Denoise method for Reflection Matrix Optical Coherence Tomography

We develop a new type of high-speed wavefront determination method with single feedback measurement to focus light through a 15.2 scattering mean free path in ∼113 ms. Our method is based on a heterodyne-detection phase sensitivity interferometer. First, the matrix which describes the light propagation process in the sample is measured by single input and output optical fields’ analysis. Then, by using a spatial light modulator to reshape the incident light with a matched wavefront, a focused beam is observed behind the sample. The proposed high-speed light focusing method will open new spot scanning mode toward deeper imaging through highly scattering biological tissues.

/pdf/high-speed-wavefront-determination-method-based-on-single-in-2y3404tcy1.pdf

High-speed wavefront determination method based on single in-and-out electric field analysis to focus light through highly scattering medium

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High-speed wavefront determination method based on single in-and-out electric field analysis to focus light through highly scattering medium