Overcoming the Diffraction Limit Using Multiple Light Scattering in a Highly Disordered Medium

We report that disordered media made of randomly distributed nanoparticles can be used to overcome the diffraction limit of a conventional imaging system. By developing a method to extract the original image information from the multiple scattering induced by the turbid media, we dramatically increase a numerical aperture of the imaging system. As a result, the resolution is enhanced by more than 5 times over the diffraction limit, and the field of view is extended over the physical area of the camera. Our technique lays the foundation to use a turbid medium as a far-field superlens.

Figure 1

Experimental schematics. (a) Conventional imaging with an objective ($L_O$) and a tube ($L_T$) lenses. ${\theta }_{\max }$ is the maximum angle that the object lens can accept. (b) Scattered wave whose angle ${\theta }_T$ exceeding ${\theta }_{\max }$ can be captured after inserting a disordered medium. (c) The scattered waves reach the camera sensor through multiple scattering process (solid red lines), although the object is shifted away from the conventional field of view (gray area).

Figure 2

Schematics of TLI. (a) Recording of the transmission matrix for a disordered medium. The incident angle of a plane wave, $({\theta }_x,{\theta }_y)$, from a He-Ne laser ($\lambda =633\mathrm{nm}$) is scanned, and the transmitted wave is recorded at each incident angle. (b) The recorded transmission images constituting a transmission matrix. Only amplitude images are shown here, although conjugate phase images are recorded at the same time. (c) Recording of an object image following the configuration of Fig. 1b. (d) The distorted image of an object, a resolution target pattern. (e) Angular spectrum of the object acquired by projection operation (see the text). Only amplitude components are shown here, although the phase information is also crucial (see 13). Scale bar: $0.5\mu {\mathrm{m}}^{-1}$. (f) The resolution target image taken prior to inserting the ZnO layer. Scale bar: $10\mu \mathrm{m}$. (g) The target image reconstructed from the angular spectrum in (e).

Figure 3

TLI overcomes the diffraction limit. (a) A conventional imaging by a high N.A. objective lens (1.0 N.A.) and (b) by a low N.A. objective lens (0.15 N.A.), respectively. The fine pitches indicated by red arrows are not visible in (b). Scale bar: $10\mu \mathrm{m}$. (c) A distorted image of the object taken by a low N.A. objective lens after inserting ZnO layers ($T=6\%$). (d) Object image recovered from the distorted image in (c) by TLI. Fine pitches are visible even if the image is taken by a 0.15 N.A. objective lens. (e) Angular spectra from the finest lines [red box in (a)] taken by high N.A. (blue curve) and low N.A. (green curve) objective lenses, respectively. The peak indicated by an orange arrow is conjugate to the periodicity of the structure. (f) The angular spectra acquired from the distorted image for turbid media of high turbidity ($T=6\%$, red curve) and low turbidity ($T=70\%$, black curve), respectively. (g) Normalized signal to noise ratio defined in the text is plotted for various turbid media.

Figure 4

Field of view enlargement by TLI. (a) A target object without turbidity and (b) with turbidity. Only the solid red box is a recording area. Scale bar: $10\mu \mathrm{m}$. (c)–(e) Reconstructed images under various turbidities of $T=100\%$ [(c), no turbidity], $T=20\%$ (d), and $T=6\%$ (e). (f) The extended field of view versus the spot broadening for various turbidities. The extended field of view is estimated to the extent that the contrast of structure drops by one half. The HWHM of the transmitted image of a spot ($5\mu \mathrm{m}$ in diameter) through a disordered medium is used to determine the spot broadening. Representative broadened spot images are shown at the bottom of the figure. From left, $T=100\%$, 20%, and 6%, respectively. Scale bar: $10\mu \mathrm{m}$. Data points correspond to the transmission of $T=100\%$, 70%, 50%, 30%, 20%, 10%, and 6%, reading, respectively, from the left.