Optimal control of light propagation through multiple-scattering media in the presence of noise

Abstract

We study the control of coherent light propagation through multiple-scattering media in the presence of measurement noise. In our experiments, we use a two-step optimization procedure to find the optimal incident wavefront that generates a bright focal spot behind the medium. We conclude that the control of coherent light propagation through a multiple-scattering medium is only determined by the number of photoelectrons detected per optimized segment. The prediction of our model agrees well with the experimental results. Our results offer opportunities for imaging applications through scattering media such as biological tissue in the shot noise limit.

Keywords: (030.6600) Statistical optics; (110.7050) Turbid media; (290.4210) Multiple scattering.

Fig. 1

The experimental setup for wavefront shaping. Laser light reflected by the SLM is focused on a white ZnO sample. The light transmitted through the sample is detected by a CCD camera. Abbreviations used, SLM: Spatial light modulator, PBS: polarizing beam splitter, λ/2: half-wave plate, CCD:charge coupled device, 20×: 20× beam expander.

Fig. 2

Cartoon showing the effect of the noise on phase estimation. The target intensity I ₀ is shown versus the phase Δθ. The modulation signal S and the background B at the target position are shown during the phase modulation Δθ of a single segment. The standard deviation of the noise is represented by σ, and the standard deviation of the phase is represented by δθ. Yellow dots represent the measurements used to construct the quadratures.

Fig. 3

Cartoon shows the phase map on the SLM after the pre-optimization (a), and after the second optimization (c). The focal spot at the target position after a pre-optimization (b), and after the second optimization (d).

Fig. 4

Three contributions to the normalized noise to signal ratio versus the pre-enhancement factor at a fixed photon budget. The black curve shows the total noise to signal ratio. The dashed green curve represents the noise to signal ratio when there is only shot noise, the dashed blue curve the noise to signal ratio when there is only camera readout noise, and the dashed red curve the noise to signal ratio when there is only laser excess noise.

Fig. 5

The final enhancement versus the pre-enhancement. The black dots show the experimental data. The red curve shows the enhancement according to Eq. (8) without adjustable parameters. The area between dashed red lines expresses the uncertainty region of the enhancement factor due to intensity drift at the target position during optimization.