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The precision of proportion estimation with binary filtering of a Raman spectrum mixture is analyzed when the number of binary filters is equal to the number of present species and when the measurements are corrupted with Poisson photon noise. It is shown that the Cramer-Rao bound provides a useful methodology to analyze the performance of such an approach, in particular when the binary filters are orthogonal. It is demonstrated that a simple linear mean square error estimation method is efficient (i.e., has a variance equal to the Cramer-Rao bound). Evolutions of the Cramer-Rao bound are analyzed when the measuring times are optimized or when the considered proportion for binary filter synthesis is not optimized. Two strategies for the appropriate choice of this considered proportion are also analyzed for the binary filter synthesis.

Second-harmonic generation microscopy can provide estimation of some local molecule distribution properties. However, in order not to get erroneous conclusions, it is important to detect measurements with insufficient precision. Such a detection technique is developed considering an approximation of the ultimate precision provided by the Cramer-Rao bound. This method is characterized and a simple approximation of its detection and false alarm probabilities is developed.

We develop a full vectorial theoretical investigation of the chemical interface detection in conventional coherent anti-Stokes Raman scattering (CARS) microscopy. In Part I, we focus on the detection of axial interfaces (i.e., parallel to the optical axis) following a recent experimental demonstration of the concept [Phys. Rev. Lett. 104, 213905 (2010)]. By revisiting the Young's double slit experiment, we show that background-free microscopy and spectroscopy is achievable through the angular analysis of the CARS far-field radiation pattern. This differential CARS in k space (Dk-CARS) technique is interesting for fast detection of interfaces between molecularly different media. It may be adapted to other coherent and resonant scattering processes.

We address the general problem of detecting chemical interfaces arbitrarily oriented in space in coherent anti-Stokes Raman scattering (CARS) microscopy. Such a task is accomplished by using a beam reversal scheme, as recently demonstrated experimentally [J. Biomed. Opt. 16, 086006 (2011)]. We develop a full vectorial theoretical analysis of the situation and show that transverse chemical interfaces are readily highlighted without special care in the CARS signal detection. In addition, a finer analysis reveals that adequate angular analysis of the CARS far-field radiation pattern enables the detection of axial interfaces. Background-free CARS microscopy and spectroscopy are thus achievable through the combined application of excitation beam reversal and angular analysis of the CARS far-field radiation pattern. This differential CARS (D-CARS) technique is relevant for fast detection of interfaces between molecularly different media.

A perturbation theory based on a single-scattering approximation is developed from the rigorous differential theory of diffraction in cylindrical coordinates. It results in analytical formulas in the inverse space for the field amplitudes providing results that are in quantitative agreement with the results of the rigorous method, in both the near- and far-field regions, when a proper correction to the incident field inside the aperture is made by using the renormalized Born approximation. When working in reflection by a screen having permittivity high in modulus, the method proposes an equivalence with the simple model consisting of the emission by a single magnetic dipole excited inside the pierced layer, emission that is then transferred back into the cladding following the Fresnel's coefficients of transmission from the layer into the cladding. The theory predicts a directivity of the radiation pattern that increases for smaller values of modulus of permittivity, both for dielectrics and metals, thus independently of the possibility of plasmon surface wave excitation along the interface. The theory can take into account such surface wave resonances, as well as the waveguide supported by a dielectric slab, but cannot implicitly recognize the modes carried out by the cylindrical waveguide corresponding to the aperture. This fact limits its domain of validity when used in transmission, although the far- and near-field maps can be reconstructed sufficiently well within a multiplicative factor corresponding to the enhanced transmission due to the excitation of these modes.

A peak of the detected fluorescence rate per molecule has recently been observed in experiments of fluorescence correlation spectroscopy carried out on subwavelength apertures in metallic screens, a phenomenon that appears at a diameter-to-wavelength ratio below the fundamental mode cutoff. Although the origin of the resonant transmission through a subwavelength aperture has been well explained in terms of excitation of plasmon surface modes on the aperture ridge, the origin of the maximum that occurs at a radius-to-wavelength ratio smaller than 1/4 was not clear. Using a rigorous electromagnetic theory of light diffraction in cylindrical geometry, we show that it is linked to the appearance of the fundamental mode propagating inside the aperture. We obtain good agreement between the theoretical and the experimental results.

We present a detailed electromagnetic analysis for the radiation of an electric source located inside grating structures. Our analysis is based on the differential method and uses the scattering-matrix algorithm. We show that gratings that exhibit periodic modulations along two spatial directions (crossed gratings) enable one to couple out the totality of the light emitted by the source into the guided modes of the structure. This property is investigated through the computation of the far-field radiation patterns for crossed gratings with various etching depths. One key result is the possibility to confine the emitted light in a direction about the sample normal, a property that is of interest in the context of spontaneous emission control by microcavity structures.