Multi-frequency imaging of perfectly conducting cracks via boundary measurements

Imaging of perfectly conducting crack(s) in a 2-D homogeneous medium using boundary data is studied. Based on the singular structure of the Multi-Static Response (MSR) matrix whose elements are normalized by an adequate test function at several frequencies, an imaging functional is introduced and analyzed. A non-iterative imaging procedure is proposed. Numerical experiments from noisy synthetic data show that acceptable images of single and multiple cracks are obtained.Comment: 4 pages, 3 figure

Precision polarimetry with real-time mitigation of optical-window birefringence

Optical-window birefringence is frequently a major obstacle in experiments measuring changes in the polarization state of light traversing a sample under investigation. It can contribute a signal indistinguishable from that due to the sample and complicate the analysis. Here, we explore a method to measure and compensate for the birefringence of an optical window using the reflection from the last optical surface before the sample. We demonstrate that this arrangement can cancel out false signals due to the optical-window birefringence-induced ellipticity drift to about 1%, for the values of total ellipticity less than 0.25 rad

Semi-blind Sparse Image Reconstruction with Application to MRFM

We propose a solution to the image deconvolution problem where the convolution kernel or point spread function (PSF) is assumed to be only partially known. Small perturbations generated from the model are exploited to produce a few principal components explaining the PSF uncertainty in a high dimensional space. Unlike recent developments on blind deconvolution of natural images, we assume the image is sparse in the pixel basis, a natural sparsity arising in magnetic resonance force microscopy (MRFM). Our approach adopts a Bayesian Metropolis-within-Gibbs sampling framework. The performance of our Bayesian semi-blind algorithm for sparse images is superior to previously proposed semi-blind algorithms such as the alternating minimization (AM) algorithm and blind algorithms developed for natural images. We illustrate our myopic algorithm on real MRFM tobacco virus data.Comment: This work has been submitted to the IEEE Trans. Image Processing for possible publicatio

Development of a computerized analysis for solid propellant combustion instability with turbulence

A multi-dimensional numerical model has been developed for the unsteady state oscillatory combustion of solid propellants subject to acoustic pressure disturbances. Including the gas phase unsteady effects, the assumption of uniform pressure across the flame zone, which has been conventionally used, is relaxed so that a higher frequency response in the long flame of a double-base propellant can be calculated. The formulation is based on a premixed, laminar flame with a one-step overall chemical reaction and the Arrhenius law of decomposition with no condensed phase reaction. In a given geometry, the Galerkin finite element solution shows the strong resonance and damping effect at the lower frequencies, similar to the result of Denison and Baum. Extended studies deal with the higher frequency region where the pressure varies in the flame thickness. The nonlinear system behavior is investigated by carrying out the second order expansion in wave amplitude when the acoustic pressure oscillations are finite in amplitude. Offset in the burning rate shows a negative sign in the whole frequency region considered, and it verifies the experimental results of Price. Finally, the velocity coupling in the two-dimensional model is discussed

Formulation of the information capacity of the optical-mechanical line-scan imaging process

An expression for the information capacity of the optical-mechanical line-scan imaging process is derived which includes the effects of blurring of spatial, photosensor noise, aliasing, and quantization. Both the information capacity for a fixed data density and the information efficiency (the ratio of information capacity to data density) exhibit a distinct single maximum when displayed as a function of sampling rate, and the location of this maximum was determined by the system frequency-response shape, signal-to-noise ratio, and quantization interval

A spectral reflectance estimation technique using multispectral data from the Viking lander camera

A technique is formulated for constructing spectral reflectance curve estimates from multispectral data obtained with the Viking lander camera. The multispectral data are limited to six spectral channels in the wavelength range from 0.4 to 1.1 micrometers and most of these channels exhibit appreciable out-of-band response. The output of each channel is expressed as a linear (integral) function of the (known) solar irradiance, atmospheric transmittance, and camera spectral responsivity and the (unknown) spectral responsivity and the (unknown) spectral reflectance. This produces six equations which are used to determine the coefficients in a representation of the spectral reflectance as a linear combination of known basis functions. Natural cubic spline reflectance estimates are produced for a variety of materials that can be reasonably expected to occur on Mars. In each case the dominant reflectance features are accurately reproduced, but small period features are lost due to the limited number of channels. This technique may be a valuable aid in selecting the number of spectral channels and their responsivity shapes when designing a multispectral imaging system

Observational constraints on a unified dark matter and dark energy model based on generalized Chaplygin gas

We study a generalized version of Chaplygin gas as unified model of dark matter and dark energy. Using realistic theoretical models and the currently available observational data from the age of the universe, the expansion history based on the type Ia supernovae, the matter power spectrum, the cosmic microwave background radiation anisotropy power spectra, and the perturbation growth factor we put the unified model under observational test. As the model has only two free parameters in the flat Friedmann background [$\Lambda$CDM (cold dark matter) model has only one free parameter] we show that the model is already tightly constrained by currently available observations. The only parameter space extremely close to the $\Lambda$CDM model is allowed in this unified model.Comment: 7 pages, 9 figure