2pi ambiguity-free optical distance measurement with subnanometer precision with a novel phase-crossing low-coherence interferometer

We report a highly accurate phase-based technique for measuring arbitrarily long optical distance with subnanometer precision. The method employs a Michelson interferometer with a pair of harmonically related light sources, one cw and the other low coherence. By slightly detuning (~2 nm) the center wavelength of the low-coherence source between scans of the target sample, we can use the phase relationship between the heterodyne signals of the cw and the low-coherence light to measure the separation between reflecting interfaces with subnanometer precision. As this technique is completely free of 2pi ambiguity, an issue that plagues most phase-based techniques, it can be used to measure arbitrarily long optical distances without loss of precision. We demonstrate one application of this technique, the high-precision determination of the differential refractive index.     

Application of Mie theory to determine the structure of spheroidal scatterers in biological materials

We present here the results of a numerical study on light scattering from nonspherical particles with relevance to detecting precancerous states in epithelial tissues. In previous studies of epithelial cell nuclei, the experimental light scattering data have been analyzed by comparison with Mie theory. However, given the spheroidal shape of many cell nuclei, the validity of this assumption demands a thorough investigation. We investigate this assumption by using the T-matrix method to model light scattered from spheroids with parameters relevant to epithelial cell nuclei. In our previous studies, we have developed a data analysis procedure that extracts the oscillatory component of the angular-scattering distribution for an ensemble of epithelial cell nuclei for comparison with Mie theory. We demonstrate that application of our analysis procedure to the predictions of the T-matrix method for spheroids, oriented such that their axis of symmetry is aligned with the incident light propagation direction, generally yields the spheroid dimension that is transverse to the incident light propagation direction with subwavelength accuracy.     

Origin of large Landau-Placzek ratio in a liquid metallic alloy

Dynamic structure factors for Na(c)K(1-c) liquid metallic alloys and pure components are studied by molecular dynamics simulations. Large values of Landau-Placzek ratio for four compositions of the liquid alloy are analyzed by wave-number dependent contributions from relaxation and propagating processes within the generalized collective modes method. The origin of the large Landau-Placzek ratio for liquid alloys is discussed.     

Generalized ridge regression,least squares with stochastic prior information,and Bayesian estimators

The ridge estimator of the usual linear model is generalized by the introduction of an a priori vector r and an associated positive semidefinite matrix S. It is then shown that the generalized ridge estimator can be justified in two ways: (a) by the minimization of the residual sum of squares subject to a constraint on the length, in the metric S, of the vector of differences between r and the estimated linear model coefficients, (b) by incorporating prior knowledge, r playing the role of the vector of means and S proportional to the precision matrix. Both a Bayesian and an Aitken generalized least squares frameworks are used for the latter. The properties of the new estimator are derived and compared to the ordinary least squares estimator. The new method is illustrated with different assumptions on the form of the S matrix.     

Tissue self-affinity and polarized light scattering in the born approximation: a new model for precancer detection

Light scattered from biological tissues can exhibit an inverse power law spectral component. We develop a model based on the Born approximation and von Karman (self-affine) spatial correlation of submicron tissue refractive index to account for this. The model is applied to light scattering spectra obtained from excised esophagi of normal and carcinogen-treated rats. Power law exponents used to fit dysplastic tissue site spectra are significantly smaller than those from normal sites, indicating that changes in tissue self-affinity can serve as a potential biomarker for precancer.     

Periodic solutions of generalized Liénard equations

In the new theory of generalized functions introduced by one author we study the generalized functions G on open sets of $\text{C}$ⁿ solutions of the equation $\text{?}\text{G = 0}$. These generalized functions—which cannot be distributions except if they are usual holomorphic functions—have many properties of the usual holomorphic functions but they present also serious differences in relation with the analytic continuation.     

Measurement of angular distributions by use of low-coherence interferometry for light-scattering spectroscopy

We present a novel interferometer for measuring angular distributions of backscattered light. The new system exploits a low-coherence source in a modified Michelson interferometer to provide depth resolution, as in optical coherence tomography, but includes an imaging system that permits the angle of the reference field to be varied in the detector plane by simple translation of an optical element. We employ this system to examine the angular distribution of light scattered by polystyrene microspheres. The measured data indicate that size information can be recovered from angular-scattering distributions and that the coherence length of the source influences the applicability of Mie theory.     

Spectral-domain differential interference contrast microscopy

We present a fiber-optic low-coherence imaging technique, termed spectral-domain differential interference contrast microscopy (SD-DIC), for quantitative DIC imaging of both reflective surfaces and transparent biological specimens. SD-DIC combines the common-path nature of a Nomarski DIC interferometer with the high sensitivity of spectral-domain low-coherence interferometry to obtain high-resolution, quantitative measurements of optical pathlength gradients from a single point on the sample. Full-field imaging can be achieved by scanning the sample. A reflected-light SD-DIC system was demonstrated using a USAF resolution target as the phase object. Live cardiomyocytes were also imaged, achieving a resolution of 36 pm for pathlength gradient measurements. The dynamics of cardiomyocyte contraction were recorded with high sensitivity at selected sites on the cells.     

Reproducibility of linear and nonlinear input-output systems

An algebraic setting for the Roman-Rota umbral calculus is introduced. It is shown how many of the umbral calculus results follow simply by introducing a comultiplication map and requiring it to be an algebra map. The same approach is used to construct a q-umbral calculus. Our umbral calculus yields some of Andrews recent results on Eulerian families of polynomials as corollaries. The homogeneous Eulerian families are studied. Operator and functional expansions are also included.