Wavefront shaping is a well-known method of restoring a focus deep within scattering media by manipulating the incident light. However, the achievable focus enhancement depends on and is limited by the optical and geometrical properties of the medium. These properties contribute to the number of linearly independent transmission channels for light propagating through the turbid medium. Correlations occur when the number of incident waves coupled into the scattering medium exceeds this finite number of transmission channels. This paper investigates the wavefront shaping of such correlated electric fields. The influence of the observed correlations persists even though the average electric field distribution at positions in the focal plane follows a circular complex Gaussian. We show that correlations of the transmitted electric fields reduce the achievable intensity enhancement, even deep in the turbid medium. The investigations are carried out using a Monte Carlo algorithm. It is based on the speckle statistics of independent waves and introduces correlations of neighbouring electric fields via a Cholesky decomposition of the covariance matrix. Additional investigations include scenarios where the electric fields are not completely randomized, such as for ballistic or insufficiently scattered light. Significant contributions from such little-scattered light are observed to reduce the intensity enhancement further. Data from simulations solving Maxwell’s equations are compared with the results obtained from the Monte Carlo simulations for validation throughout this paper.

Volumetric scattering prevents imaging modalities in biomedical optics from imaging deep inside tissue. The optimization of the incident wavefront has the potential to improve these imaging modalities. To investigate the optimization and light propagation of such beams inside scattering media rigorously, full-vectorial simulations based on solutions of Maxwell’s equations are necessary. In this publication, we present a versatile two-step beam synthesis method to efficiently simulate the scanning and phase optimization of a focused beam inside a static scattering medium. We present four different approaches to the phase optimization of the energy density and the absolute value of the Poynting vector. We find that these quantities have two regions with different, almost exponential decays over depth for a non-optimized beam. Optimization by conjugating the phase of the projected electric field in various directions at the focus shows an improvement below a certain penetration depth. Seeking global solutions to the optimization problems reveals an even better enhancement in the energy density and the absolute value of the Poynting vector in the focus. For Poynting vector optimization, the differences between the presented optimization approaches are more significant than for the energy density. With the presented method, it is possible to efficiently simulate different imaging methods improved by wavefront shaping to investigate their possible penetration depths.

Manipulating the wavefront of coherent light incident on scattering media to enhance the imaging depth, sensitivity, and resolution is a common technique in biomedical applications. Local phase variations cause changes in the interference and can be used to create a focus inside or behind a scattering medium. We use wavefront shaping (WFS) to force constructive interference at an arbitrary location. The amount of light transmitted into a given region strongly depends on the scattering and absorption characteristics. These are described by their respective coefficients ${\mu }_s$ and ${\mu }_a$ and the scattering phase function. Controlling the scattering and absorption coefficients, we study the behavior of wavefront shaping and the achievable intensity enhancement behind volume scattering media with well-defined optical properties. The phantoms designed in this publication are made of epoxy resin. Into these epoxy matrices, specific amounts of scattering and absorbing particles, such as titanium dioxide pigments and molecular dyes, are mixed. The mixture obtained is filled into 3D-printed frames of various thicknesses. After a precise fabrication procedure, an integrating sphere-based setup characterizes the phantoms experimentally. It detects the total hemispherical transmission and reflection. Further theoretical characterization is performed with a newly developed hybrid $P_N$ method. This method senses the flux of light into a particular angular range at the lower boundary of a slab. The calculations are performed without suffering from ringing and fulfill the exact boundary conditions there. A decoupled two-path detection system allows for fast optimization as well as sensitive detection. The measurements yield results that agree well with the theoretically expected behavior.

Coherent backscattering is an interference phenomenon that occurs in the backwards direction of the incident illumination. It arises from photons traveling the same path in opposite directions within a scattering medium. Accurately determining the background signal for normalization can be challenging in such measurements. This study investigates the use of a spatial light modulator to control spatial coherence, effectively switching the interference on and off. This approach enables independent, absolute measurements of both the signal and background across the full angular detection range without modifying the experimental setup. We demonstrate this method experimentally, highlighting the importance of accurate background determination in coherent backscattering measurements using a Fourier-based setup. Additionally, we demonstrate that measurements normalized to the correct background closely match Monte Carlo simulations of the coherent backscattering signal.

Delivering energy deep into turbid media is essential for applications like biomedical imaging, medical treatment, and material processing. We applied wavefront shaping to enhance light penetration by manipulating the phase of incident light. Using feedback-based phase optimization and numerical solutions of Maxwell’s equations, we present an approach that significantly and non-invasively increases the energy density deep inside complex scattering media by minimizing the reflected light, without prior knowledge of the media. In simulations of media with a transport mean free path as low as 43.36μm, we achieved a 2.5-fold enhancement of the energy density at a depth of about 200μm. Light transport through this simulated medium is equivalent to propagation through approximately 4mm of biological tissue with optical properties typically found in the red or infrared wavelength range. By switching between minimized and maximized reflection, the energy density can be modulated by up to a factor of 12 deep inside the scattering medium, while the energy density at shallow depths remains fairly unchanged.