Spatial correlation-based quadratic cost function for wavefront shaping through scattering media

The feedback-based wavefront shaping emerges as a promising method for deep tissue microscopy, energy control in bio-incubation, and re-configurable structural illuminations. The cost function plays a crucial role in the feedback-based wavefront optimization for focusing light through scattering media. However, popularly used cost functions, such as intensity ( $\eta$ ) and peak-to-background ratio (PBR) struggle to achieve precise intensity control and uniformity across the focus spot.

We have proposed an ${\ell }_2$ -norm-based quadratic cost function (QCF) for establishing both intensity and position correlations between image pixels, which helps to advance the focusing light through scattering media, such as biological tissue and ground glass diffusers.

The proposed cost function has been integrated into the genetic algorithm, establishing pixel-to-pixel correlations that enable precise and controlled contrast optimization, while maintaining uniformity across the focus spot and effectively suppressing the background intensity.

We have conducted both simulations and experiments using the proposed QCF, comparing its performance with the commonly used $\eta$ and PBR-based cost functions. The results evidently indicate that the QCF achieves superior performance in terms of precise intensity control, uniformity, and background intensity suppression. By contrast, both the $\eta$ and PBR cost functions exhibit uncontrolled intensity gain compared with the proposed QCF.

The proposed QCF is most suitable for applications requiring precise intensity control at the focus spot, better uniformity, and effective background intensity suppression. This method holds significant promise for applications where intensity control is critical, such as photolithography, photothermal treatments, dosimetry, and energy modulation within and outside bio-incubation systems.