Signal reconstruction from a scanning near-field optical microscopy, lock-in non-linear filtering and tomography.

Objectives
We want to retrieve physical properties of the complex interaction pattern between light, nanostructures and probe from experimental data obtained with near-field optical microscopes. This problem is known as the reconstruction of near-field signal.

Methods
Development of algorithms in order to reconstruct and recover the optical signal near-field and use of linear and non-linear strategies in order to explore the space of the solutions.

Results and prospects

Scanning Near-field Optical Microscopies suffer from the low signal to noise ratio, due to the smallness of the diffracting probe used to get images. Therefore a lock-in amplifier is commonly used to perform homodyne detection. The detected signals are therefore the Fourier harmonics of the signal along a vertical vibration of the probe and depend drastically on the vibration amplitude. All the the Fourier harmonics contain contribution of the ``near-field'' and the ``far-field'' that are mixed in the near-field zone (i.e. at very short distance). Therefore, physical interpretation of contrast in high harmonics records may be questionable.

From the lock-in data, we reconstruct the near-field intensity diffracted by the probe-end in the case of approach curves. Such a reconstructed optical signal can strongly differ from the detected signal. Thanks to the reconstruction which gives a tomography-like 3D map of the detected signal, the vertical decay lengths can be measured directly, from only one lateral scan. Such a reconstruction of the optical signal in near-field zone permits to study the influence of the lock-in amplifier and the probe vibration on the measurement of the decay lengths of evanescent waves.