Optimal trade-off filters for compressed Raman classification and spectrum reconstruction.

Compressed Raman spectroscopy is a promising technique for fast chemical analysis. In particular, classification between species with known spectra can be performed with measures acquired through a few binary filters. Moreover, it is possible to reconstruct spectra by using enough filters. As classification and reconstruction are competing, designing filters allowing one to perform both tasks is challenging. To tackle this problem, we propose to build optimal trade-off filters, i.e., filters so that there exist no filters achieving better performance in both classification and reconstruction. With this approach, users get an overview of reachable performance and can choose the trade-off most fitting their application.

Compressed Raman method combining classification and estimation of spectra with optimized binary filters.

Compressed Raman methods allow classification between known chemical species with only a few measurements through binary filters. We propose a methodology for binary filter optimization, in which filters are modified at each pixel so that classification can still be achieved pixel by pixel with a few measurements acquired in parallel, while retaining the ability to reconstruct a full spectrum when combining measurements from several pixels. This approach is robust to intensity variations between pixels. It relies on a generalized Bhattacharyya bound and on the Cramér-Rao bound to tailor filters with optimized performance.

Biomass measurements of single neurites in vitro using optical wavefront microscopy.

Quantitative phase microscopies (QPMs) enable label-free, non-invasive observation of living cells in culture, for arbitrarily long periods of time. One of the main benefits of QPMs compared with fluorescence microscopy is the possibility to measure the dry mass of individual cells or organelles. While QPM dry mass measurements on neural cells have been reported this last decade, dry mass measurements on their neurites has been very little addressed. Because neurites are tenuous objects, they are difficult to precisely characterize and segment using most QPMs. In this article, we use cross-grating wavefront microscopy (CGM), a high-resolution wavefront imaging technique, to measure the dry mass of individual neurites of primary neurons in vitro. CGM is based on the simple association of a cross-grating positioned in front of a camera, and can detect wavefront distortions smaller than a hydrogen atom (∼0.1 nm). In this article, an algorithm for dry-mass measurement of neurites from CGM images is detailed and provided. With objects as small as neurites, we highlight the importance of dealing with the diffraction rings for proper image segmentation and accurate biomass measurements. The high precision of the measurements we obtain using CGM and this semi-manual algorithm enabled us to detect periodic oscillations of neurites never observed before, demonstrating the sufficient degree of accuracy of CGM to capture the cell dynamics at the single neurite level, with a typical precision of 2%, i.e., 0.08 pg in most cases, down to a few fg for the smallest objects.

Van Cittert-Zernike theorem and symmetry properties of the normalized cross-spectral density matrix.

The van Cittert-Zernike theorem is formulated for the normalized cross-spectral density matrix of fields emitted by spatially incoherent sources. This formulation shows that sources with homogeneous polarization characteristics at second-order lead in the far field to normalized cross-spectral density matrices that possess high-symmetry properties. These symmetry properties are lost with polarization inhomogeneities of the source. These results are illustrated with ring-shaped sources.

Isotropic bicomponent partially polarized and partially coherent light.

The degree of coherence of scalar light remains constant when the fields are modified by the same random linear transformation, which can be represented by the multiplication by a random complex number. This shows that the coherence properties of scalar light at order two are not modified with the increase of disorder of each field that results from these transformations. We analyze the generalization of this property to partially polarized light. We determine the class of fields that can possess this property for any couple of points in a space-frequency or space-time domain after modification with deterministic Jones transformations. We show that the second-order coherence properties of this class of light can be generated experimentally with two uncorrelated totally polarized sources that have the same scalar coherence properties.

Two-point Stokes parameters: interpretation and properties.

Whereas the classic Stokes parameters are measures of intensity, the recently introduced two-point Stokes parameters characterize spatial coherence. It is shown that in analogy to the Stokes parameters, the two-point parameters have a physical interpretation as sums and differences of (scalar) cross-spectral density functions of specific electric-field components. A measurement scheme and several physical consequences of the two-point parameters are discussed.

Separation technique of a mixing of two uncorrelated and perfectly polarized lights with different coherence and polarization properties.

The sum of two uncorrelated and totally polarized lights with different coherence and polarization properties usually results in a partially polarized light. It is shown in this paper that the initial totally polarized lights can be recovered from the mixed partially polarized light. The proposed technique is based on coherence analysis and does not require the knowledge of the polarization states or the coherence properties of the initial perfectly polarized beams as long as these properties are different for the two waves. Some practical optical implementations of this technique are discussed on different illustrative applications.

Visibility interference fringes optimization on a single beam in the case of partially polarized and partially coherent light.

We analyze the optimal visibility one can obtain in interference experiments with partially polarized light when one acts on only one of the two interfering beams. This is a practical situation that can appear when one does not want to modify or attenuate one of the beams, such as in homodyne detection. It is shown that the optimal configuration usually does not correspond to light with the same degrees of polarization for the two interfering beams. We also demonstrate that a simple interpretation can be obtained with the recently introduced normalized mutual coherence matrix.

Linear relations of partially polarized and coherent electromagnetic fields.

We show that having a Wolf degree of coherence of unit modulus or having intrinsic degrees of coherence of unit modulus imply different relations between the electric fields of the light. The mean square meaning of such relations is discussed. On the one hand, we demonstrate that if the intrinsic degrees of coherence are equal to 1, then there is a linear relation between the electrical fields. On the other hand, we show that a Wolf degree of coherence of unit modulus corresponds to a stronger property that implies that the fields have to be proportional.

Coherence polarization filtering and relation with intrinsic degrees of coherence.

It is demonstrated for stationary fields that when the polarization state of the electric field can be modified arbitrarily the maximal value of the modulus of the degree of coherence proposed by Wolf [Phys. Lett. A312, 263 (2003)] is equal to the largest intrinsic degree of coherence. In addition, when the light is a mixing of a coherent light that satisfies the factorization condition in the two spatial variables with a statistically uncorrelated, partially coherent, perfectly polarized light, but with a nonparallel polarization state, we show that the polarization modifications that maximize the modulus of the Wolf degree of coherence lead to a light that also satisfies the factorization condition.