Friday, April 30, 2010

Paper watch: Sharper focus by random scattering

The paper at Nature Photonics: "Exploiting disorder for perfect focusing" (subscription required).

The paper is also summarized here. I extract some paragraphs:

In the field of optics, three different approaches have recently been demonstrated that focus monochromatic waves in a strongly scattering medium. The first is an elegant and versatile method that is based on the use of spatial light modulators, which allow the phase of an optical field to be controlled over thousands of pixels (64 × 64 square segments in the experiment) through a learning feedback algorithm. As a lens focuses a beam of light through a strongly scattering medium onto a CCD camera, the spatial light modulator shapes the wavefront of the light that impinges on the lens. The algorithm then adjusts the relative phases of the segments so that the transmitted light interferes constructively at a given focal point. Maximizing the intensity at the focal spot, the feedback process turns into a matched filter of the wave transfer function, and therefore the shaped wavefront is practically identical to the one given by the time-reversal solution — a wavefield phase conjugation for a monochromatic wave. The second approach is based on the measurement of the transmission matrix of the scattering medium with light modulators. A third approach uses optical phase conjugation through nonlinear optics, in which a transmitted light field is forced to retrace its trajectory through a strongly scattering material in order to reconstruct the source.

Implementing the wavefront correction method using the spatial light modulators and feedback algorithm mentioned above, Vellekoop and colleagues now clearly demonstrate how the width of the focus is reduced in the presence of a random scattering layer. They carry out the experiment at a wavelength of 632.8 nm, and use a single 6.45 μm × 6.45 μm CCD pixel as a target. A lens with a diameter D1 of 2.1 mm and a focal length of 200 mm is used. In a clean environment, the lens has a diffraction-limited spot size of 76 μm at full-width half-maximum. A disordered medium made of a 6 μm layer of opaque white airbrush paint is placed after the lens.

To analyse the effect, the researchers place the random layer at different distances f2 from the CCD camera and apply the wavefront correction to the spatial light modulator to shape the wavefront of the light transmitted through the lens. They observe a decrease in the width of the focus spot as the opaque layer is moved closer to the CCD camera. At distances of 25 mm or smaller, the focus spot becomes smaller than a single camera pixel. More specifically, the width of the spot is approximately one-tenth of the diffraction limit of the lens in a clean environment [...]. The team show both experimentally and theoretically that it is the scattering medium, rather than the lens or the quality of the reconstruction process, that determines the width of the focus — a surprising property of scattered light that agrees with primary observations in ultrasound experiments. More quantitatively, they demonstrate that the new focus is always an Airy disc with a full-width half-maximum determined by an effective numerical aperture f2/D2, where f2 and D2 are the distance and diameter of the illuminated area of the scattering layer, respectively. In essence, the whole illuminated area of the scattering medium behaves as a coherent focusing lens.

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