Optical focusing and imaging through or inside scattering media, such multimode fiber and biological tissues, has significant impact in biomedicine yet considered challenging due to strong scattering nature of light. In the past decade, promising progress has been made in the field, largely benefiting from the invention of iterative optical wavefront shaping, with which deep-tissue high-resolution optical focusing and hence imaging becomes possible. Most of reported iterative algorithms can overcome small perturbations on the noise level but fail to effectively adapt beyond the noise level, e.g. sudden strong perturbations. Re-optimizations are usually needed for significant decorrelation to the medium since these algorithms heavily rely on the optimization performance in the previous iterations. Such ineffectiveness is probably due to the absence of a metric that can gauge the deviation of the instant wavefront from the optimum compensation based on the concurrently measured optical focusing. In this study, a square rule of binary-amplitude modulation, directly relating the measured focusing performance with the error in the optimized wavefront, is theoretically proved and experimentally validated. With this simple rule, it is feasible to quantify how many pixels on the spatial light modulator incorrectly modulate the wavefront for the instant status of the medium or the whole system. As an example of application, we propose a novel algorithm, dynamic mutation algorithm (DMA), which has high adaptability against perturbations by probing how far the optimization has gone toward the theoretically optimal performance. The diminished focus of scattered light can be effectively recovered when perturbations to the medium cause significant drop of the focusing performance, which no existing algorithms can achieve due to their inherent strong dependence on previous optimizations. With further improvement, the square rule and the new algorithm may boost or inspire many applications, such as high-resolution optical imaging and stimulation, in instable or dynamic scattering environments.

No abstract

Iterative wavefront shaping is a powerful tool to overcome optical scattering and enable focusing of diffusive light, which has exciting potentials in many applications that desire localized light delivery at depths in tissue-like complex media. Unsatisfactory performance and efficiency, however, have been a long-standing problem, and the large discrepancy between theoretical and experimental results has hindered the wide applications of the technology. Currently, most algorithms guiding the iterative search of optimum phase compensation rely heavily on randomness to achieve solution diversity. It is similar to black-box optimization in which the mechanism of how a good solution is arrived at is unclear. The lack of clear guidance on the new solution generation process considerably affects the efficiency of optimization. Therefore, we propose a probability-based iterative algorithm combining genetic algorithm (GA) and ant colony optimization (ACO), in which the new solutions can be generated based on a probability map. Thanks to the clearer guidance provided by the probability map and the reduced involvement of randomness, we are able to obtain optimization results with optimal efficiency for single and multiple focuses behind scattering media. Besides, with the proposed algorithm, we also demonstrate higher adaptability in an unstable scattering environment and more spatially uniform optical focusing in the field of view. This study advances the state-of-the-art in the practice of iterative wavefront shaping. More importantly, the significant improvement in optimization efficiency and adaptability, if further engineered, can potentially inspire or open up wide applications that desire localized and enhanced optical delivery in situ.

Focused and controllable optical delivery beyond the optical diffusion limit in biological tissue has been desired for long yet considered challenging. Digital optical phase conjugation (DOPC) has been proven promising to tackle this challenge. Its broad applications, however, have been hindered by the system’s complexity and rigorous requirements, such as the optical beam quality, the pixel match between the wavefront sensor and wavefront modulator, as well as the flatness of the modulator’s active region. In this paper, we present a plain yet reliable DOPC setup with an embedded four-phase, non-iterative approach that can rapidly compensate for the wavefront modulator’s surface curvature, together with a non-phase-shifting in-line holography method for optical phase conjugation in the absence of an electro-optic modulator (EOM). In experiment, with the proposed setup the peak-to-background ratio (PBR) of optical focusing through a standard ground glass in experiment can be improved from 460 up to 23,000, while the full width at half maximum (FWHM) of the focal spot can be reduced from 50 down to 10 μm. The focusing efficiency, as measured by the value of PBR, reaches nearly 56.5% of the theoretical value. Such a plain yet efficient implementation, if further engineered, may potentially boost DOPC suitable for broader applications.