[Paper Review] Focusing of light by random scattering

Ivo M. Vellekoop, Allard P. Mosk|arXiv (Cornell University)|Apr 10, 2006

Random lasers and scattering media2 references3 citations

TL;DR

This paper demonstrates that coherent light can be focused through strongly scattering media—such as white paint or biological tissue—by shaping the incident wavefront using feedback control. By iteratively optimizing the phase of individual wavefront segments, the researchers achieve a focal spot 1,000 times brighter than the diffuse background, effectively reversing the random scattering process through inverse wave diffusion.

ABSTRACT

Random scattering of light is what makes materials such as white paint, clouds and biological tissue opaque. We show that although light propagating in these media is diffuse, a high degree of control is possible as phase information is not irreversibly lost. Opaque objects such as eggshell or white paint focus coherent light as sharply as a lens when illuminated with a wavefront that inverts the wave diffusion. We demonstrate the construction of such wavefronts using feedback, achieving a focus that is 1000 times brighter than the diffusely transmitted light. Our results are explained quantitatively by a universal relation based on statistical optics.

Motivation & Objective

• To overcome the fundamental limitation of random scattering in opaque materials, which prevents precise light delivery and imaging.
• To investigate whether coherent light can be focused through strongly scattering media despite the absence of ballistic transmission.
• To develop a method for achieving high-intensity, diffraction-limited focusing in scattering media using adaptive wavefront shaping.
• To demonstrate the universality and robustness of this method across diverse scattering materials, including biological tissues and inorganic pigments.

Proposed method

• The incident wavefront is divided into 3,228 spatially independent segments using a reflective spatial light modulator (SLM) operating in phase-only mode.
• A feedback loop adjusts the phase of each segment individually, using the intensity at the target focus as the optimization metric.
• The optimization process involves scanning the phase of each segment over 0–2π in ten steps, fitting a sinusoid to the measured intensities to determine the optimal phase.
• A two-step iterative algorithm is employed: a coarse pre-optimization with 12 segments is followed by a full optimization using the pre-optimized field as a reference.
• The system stabilizes for 100 ms after each phase adjustment to ensure measurement accuracy.
• The transmitted light is detected via a CCD camera in the back focal plane of a microscope objective, with intensity integrated over an area smaller than a typical speckle.

Experimental results

Research questions

• RQ1 Can coherent light be focused through a strongly scattering medium with a degree of control comparable to that of a lens?
• RQ2 Is it possible to achieve high-intensity focal spots in scattering media without relying on ballistic or unscattered light components?
• RQ3 To what extent is the wavefront shaping method robust and universally applicable across different scattering materials?
• RQ4 What is the maximum intensity enhancement achievable through inverse wave diffusion in a disordered medium?
• RQ5 Can multiple foci or simple images be formed simultaneously through optimized wavefront shaping in scattering media?

Key findings

• A single focal spot was achieved that was 1,000 times brighter than the average intensity of the diffuse speckle pattern before optimization.
• The focal spot was diffraction-limited, with a full width at half maximum (FWHM) of approximately 1.2 μm, indicating high spatial resolution.
• Multiple foci (e.g., a pentagon-shaped pattern) were successfully formed simultaneously by optimizing the target intensity distribution across multiple points.
• The optimal wavefront showed no correlation between adjacent segments, confirming that the light had undergone hundreds of scattering events and that no ballistic transmission contributed to the focus.
• The transport mean free path in the TiO₂ sample was measured as 0.55 ± 0.10 μm at 632.8 nm, confirming the highly scattering nature of the medium.
• The method was successfully applied to biological samples including eggshell, flower petals, and a primary tooth, demonstrating its broad applicability beyond synthetic materials.