The inhomogeneous distribution of refractive index in media leads to multiple scattering, which has hindered the advancement of various optical technologies, particularly in the field of biomedical imaging [1,2]. Therefore, overcoming light scattering has always been a hot research point. Since wavefront shaping was first experimentally demonstrated to achieve light transmission through scattering media and focusing by Vellekoop and Mosk in 2007 [3], its rapid development has not only injected new vitality into the field of optics but has also given rise to numerous innovative applications, including laser radar and remote sensing [4], super-resolution imaging [5], endoscopic technology [6], cryptography [7], phototherapy [8] and optogenetics [9], among others.

The three key methods involved in wavefront shaping include transmission matrix (TM) measurement [[10], [11], [12], [13], [14], [15]], feedback based iterative optimization [[22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32]] and optical phase conjugation (OPC) [[16], [17], [18], [19]]. In practical applications, TM measurement provides detailed and quantitative information about the transmission of light through scattering media. However, this method requires significant time and resources, and are sensitive to environmental fluctuations. OPC enables rapid optical focusing, yet it confronts challenges such as energy loss, sensitivity to noise, and the complexity of experimental setups. In contrast, the iterative optimization wavefront shaping method is more flexible in practical applications, as it can achieve control over light using simpler settings. However, this method faces challenges related to longer consumption time and sensitivity to parameters.

Many iterative optimization algorithms have shown positive focusing effects, such as the continuous sequential algorithm (CSA) [20,21], particle swarm optimization algorithm (PSO) [[22], [23], [24]], simulated annealing algorithm (SAA) [25,26], genetic algorithm (GA) [[27], [28], [29], [30]], etc. In recent years, researchers have been committed to improving and enhancing algorithm overall performance to adapt to various applications, including the noise resistance performance [31], focusing efficiency [32], parameter adjustment strategy [33] and the development of hybrid algorithms in combination with deep learning [34]. However, these methods demonstrate excellent performance in achieving effective optical focusing and noise resistance, but they still face significant challenges when confronted with sudden strong disturbances. This is particularly evident in algorithms such as genetic algorithms, which heavily depend on previous iterations and a large number of random masks to initialize. The experience gained from past iterations is highly correlated to the previous state of the medium, making the optimization only applicable to subtle instabilities such as environmental noise [27]. When the scattering medium is subjected to disturbances that are stronger than the noise level, possibly caused by sudden changes in the external environment or instability come from the scattering medium, the optical focus produced by the algorithm optimization may weaken or even disappear. This means that when facing complex environments or sudden change in situations, the algorithm may not be able to effectively find the global optimal solution, thus limiting its applicability in practical problems. Also, when applying wavefront shaping imaging, the field of view is constrained by the optical ME [35,36]. ME refers to that when the illumination angle is tilted within a certain range, the produced random speckle patterns on the camera are highly correlated and shift-invariant [37,38]. The effective angular field of view range is given by its half width at half maximum (HWHM) angle, ΔθFOV≈λ∕πL, where λ is the wavelength of the light, and L is the effective thickness of a scattering medium [39]. After generating a single focus behind a scattering layer, it is possible for image to raster scan the generated focus through tilting the impinging wavefront toward the scattering layer, which exploits the optical ME. However, the focus after scanning the scattering medium using the ME has a limited scanning area, which is approximately 250 μm × 250 μm [40]. In addition, an obvious inherent drawback of using ME imaging is the non-uniform distribution of intensity, where the central intensity of the image is larger and the edge intensity is smaller. Several advanced methods have been proposed to overcome the limitations of ME and expand the field of view of imaging. One method consists in separating the speckle patterns emitted by a fluorescent object under variable unknown random illumination, using matrix factorization and a novel fingerprint-based reconstruction covering a field of view up to three times the optical ME range [41]. However, this method is only applicable to static scattering media. Another method utilizes spatial-temporal encoded patterns to recover targets beyond the ME range [42]. Nevertheless, the intensity spectrum obtained by this method is susceptible to noise. Additionally, a method utilizes point-spread-function (PSF) estimations and correlations to recover images of a whole object or multiple objects beyond the ME range [43]. But this method requires assuming that objects beyond the ME range behind the scattering medium are individually illuminated and scanned. Therefore, effectively suppressing noise while expanding the imaging field of view remains a pressing issue that needs to be addressed.

Over the years, researchers have devoted significant efforts to single-point focusing through wavefront shaping, with relatively less emphasis on multi-point focusing. Unlike the grating scanning imaging of single point focusing, multi-point focusing can directly image, so in some practical applications, it is more meaningful. However, multi-point focusing not only requires attention to the intensity of the focal points but also demands ensuring their uniformity. While the currently known multi-point light focusing methods are capable of achieving focus on multiple target points, they suffer from a limitation in that they only consider the enhancement factor (EF) of multiple focal points, without effectively controlling uniformity [44]. Some studies have linked the EF with the standard deviation of focus through a fixed weighting coefficient to achieve uniformly intense multi-point focusing; however, these methods sacrifice the EF for uniformity control [45]. In reality, multi-point focusing constitutes a multi-objective optimization problem, where it is possible to enhance the uniformity of multiple focal points while improving EF. Multi-objective genetic algorithm [46] and its variant [47] perform well in multi-point focusing, especially in enhancing factors and uniformity, but they cannot adapt to the influence of strong disturbances. In addition, the expansion of the focusing field often accompanies an increase in noise impact [48,49], making it more challenging to achieve uniform multi-point simultaneous focusing.

To address the above issues, this paper proposes a N-BA that combines adaptive mutation rates. By calculating the error rate of the current solution in real-time, the mutation rate during the iterative process is adjusted to improve the algorithm’s noise resistance and robustness. In this work, we experimental demonstrate that the algorithm can achieve large-field multi-point uniform focusing even after a sudden strong disturbance causes a decrease in focusing performance. This method has the potential to promote the application of multi-point optical focusing in the biomedical field.