Travis E. Oliphant

Accuracy of scatterometer-derived winds using the Cramer-Rao bound

A wind scatterometer makes measurements of the normalized radar-backscatter coefficient /spl sigma//spl deg/ of the ocean surface. To retrieve the wind, a geophysical model function (GMF), which relates /spl sigma//spl deg/ to the near-surface wind, is used. The wind vector can be estimated using maximum-likelihood techniques from several /spl sigma//spl deg/ measurements made at different azimuth angles. The probability density of the measured /spl sigma//spl deg/ is assumed to be Gaussian with a variance that depends on the true /spl sigma//spl deg/ and therefore, depends on the wind through the GMF. With this model for wind estimation, the Cramer-Rao (C-R) bound is derived for wind estimation, and its implications for wind retrieval are discussed. As part of this discussion, the role of geophysical modeling error is considered and shown to play a significant role in the performance of near-surface wind estimates. The C-R bound is illustrated using parameters from the ERS AMI, NSCAT, and Sea Winds scatterometers.

Noncontact scanning impedance imaging in an aqueous solution

We present a method for imaging based on noncontact electrical impedance measurements and mechanical scanning. Measurement results are shown for an initial system based on this concept. An impedance probe design is presented, applicable to the test system. Line-scan data plots of high impedance contrast structures show a good fit to a theoretical physical model. Image resolutions on the order of 100μm are indicated for the initial system. Two-dimensional impedance images of biological tissue generated by this technique are shown.

Estimation techniques for GMSK using linear detectors in satellite communications

This paper describes data-aided signal level and noise variance estimators for Gaussian minimum shift keying (GMSK) when the observations are limited to the output of a filter matched to the first pulse-amplitude modulation (PAM) pulse in the equivalent PAM representation. The estimators are based on the maximum likelihood (ML) principle and assume burst-mode transmission with known timing and a block of L0 known bits. While it is well known that ML estimators are asymptotically unbiased and efficient, the analysis quantifies the rate at which the estimators approach these asymptotic properties. It is shown that the carrier phase, amplitude, and noise variance estimators are unbiased and can achieve their corresponding Cramer-Rao bounds with modest combinations of signal-to-noise ratio and observation length. The estimates are used to estimate the signal-to-noise ratio. It is shown that the mean squared error performance of the ratio increases with signal-to-noise ratio while the mean squared error performance of the ratio in decibels decreases with signal-to-noise ratio. Simulation results are provided to confirm the accuracy of the analytic results.

Simple Linear Models of Scanning Impedance Imaging for Fast Reconstruction of Relative Conductivity of Biological Samples

Scanning impedance imaging (SII) uses a noncontacting electrical probe held at a known voltage and scanned over a thin sample on a ground plane in a conductive medium to obtain images of current. The current image is related in a nonlinear way to the conductivity of the sample. This paper develops the theory behind SII showing how the measured current relates to the desired conductivity. Also included is the development of a simplified, linear model that is effective in explaining many of the experimental results. Good agreement of the linear model with step-response data over an insulator is shown. The linear model shows that the current is a blurred version of the conductivity. Simple deblurring methods can, therefore, be applied to obtain relative conductivity images from the raw current data. Raw SII data from a flower-petal and a leaf sample are shown as well as relative conductivity images deblurred using the linear model

Resolution scaling in noncontact scanning impedance imaging

Noncontact scanning impedance imaging has been presented as a method to provide high resolution, high contrast images for a variety of material systems. This technique combines electrical impedance measurements with very high resolution scanning. This article reports on efforts to scale this technique down to the very important single micron range and reveals measurements for both thick and thin samples with a measured minimum resolution below 30 μm. A design for a shielded impedance probe applicable to this process is outlined and probes of several different sizes were made and tested. Fabrication of these impedance probes is explained and a testing methodology to characterize the probes’ imaging capability is outlined. Measured results are reported and compared to a predictive model based on image blurring. Two-dimensional impedance images of objects have also been made indicating good image contrast and high resolution. Based on measured data and the model, scaling down to submicron resolution dimensio...

General fractional derivative viscoelastic models applied to vibration elastography

In this work we derive general fractional-derivative-based viscoelastic models built from one, two, or three basic elements called viscoelastic springs. The basic viscoelastic spring used has a stress-strain relationship where stress is the fractional derivative of the strain. Fractional derivative models extend traditional Maxwell and Kelvin-Voigt viscoelastic models to allow for fractional powers of frequency in the Fourier domain. Combining these basic viscoelastic elements in series and in parallel results in increasingly complex models for the modulus as a function of frequency. We show how these models can be applied in the frequency domain to shear modulus data acquired using vibration elastography. Shear modulus data for curve fitting in the frequency domain were acquired using 10% and 15% bovine-gel mixtures (with added graphite particles) that were vibrated at 200 to 600 Hz in 100 Hz steps. The vibrations were detected using a 3.5 MHz ultrasound transducer. Shear modulus data for the same materials were also acquired using the dynamic mechanical analyzer (DMA 2980 from TA Instruments, Inc.) in a frequency range from 10Hz to 200Hz. Weighted least-squares fitting was used to determine the model parameters for two and three-element models applicable to viscoelastic solids. The results show that a two-element parallel combination of viscoelastic springs (the Kelvin-Voigt fractional derivative model) can somewhat explain the modulus data, though perhaps a three-element model generalizing the standard linear solid is more accurate over a wider frequency range.

Non-contact Scanning Electrical Impedance Imaging

We are interested in applying electrical impedance imaging to a single cell because it has potential to reveal both cell anatomy and cell function. Unfortunately, classic impedance imaging techniques are not applicable to this small scale measurement due to their low resolution. In this paper, a different method of impedance imaging is developed based on a non-contact scanning system. In this system, the imaging sample is immersed in an aqueous solution allowing for the use of various probe designs. Among those designs, we discuss a novel shield-probe design that has the advantage of better signal-to-noise ratio with higher resolution compared to other probes. Images showing the magnitude of current for each scanned point were obtained using this configuration. A low-frequency linear physical model helps to relate the current to the conductivity at each point. Line-scan data of high impedance contrast structures can be shown to be a good fit to this model. The first two-dimensional impedance image of biological tissues generated by this technique is shown with resolution on the order of 100 μm. The image reveals details not present in the optical image.

Development of a statistical method for eliminating improbable wind aliases in scatterometer wind retrieval

Wind velocities over the ocean can be estimated using measurements from spaceborne scatterometers by inverting the geophysical model function (GMF) which relates normalized backscatter to wind velocity. Current estimation procedures employ maximum-likelihood techniques. Unfortunately, there are several local maxima of the maximum-likelihood function. As a result, several (2-6) wind estimates are returned as possible solutions at each wind vector cell. An ambiguity-removal step is required to determine a wind field. In this paper, we develop a statistical test to distinguish among the maxima of a maximum likelihood equation, and apply it to wind estimation. An upper bound is derived on the probability of error if a lower likelihood wind estimate is discarded. This bound is used to eliminate improbable wind solutions. Using this procedure we show that for most ERS-1 wind vector cells the number of wind estimates can be reduced to two. This reduces the complexity of the ambiguity-removal step while at the same time increasing the confidence in the entire retrieved wind field.

Fast Nonlinear Image Reconstruction for Scanning Impedance Imaging

Scanning (electrical) impedance imaging (SII) is a novel high-resolution imaging modality that has the potential of imaging the electrical properties of thin biological tissues. In this paper, we apply the reciprocity principle to the modeling of the SII system and develop a fast nonlinear inverse method for image reconstruction. The method is fast because it uses convolution to eliminate the requirement of a numerical solver for the 3-D electrostatic field in the SII system. Numerical results show that our approach can accurately reveal the exact conductivity distribution from the measured current map for different 2-D simulation phantoms. Experiments were also performed using our SII system for a piece of butterfly wing and breast cancer cells. Two-dimensional current images were measured and corresponding quantitative conductivity images were restored using our approach. The reconstructed images are quantitative and reveal details not present in the measured images.

A fast linear reconstruction method for scanning impedance imaging.

Scanning electrical impedance imaging (SII) has been developed and implemented as a novel high resolution imaging modality with the potential of imaging the electrical properties of biological tissues. In this paper, a fast linear model is derived and applied to the impedance image reconstruction of scanning impedance imaging. With the help of both the deblurring concept and the reciprocity principle, this new approach leads to a calibrated approximation of the exact impedance distribution rather than a relative one from the original simplified linear method. Additionally, the method shows much less computational cost than the more straightforward nonlinear inverse method based on the forward model. The kernel function of this new approach is described and compared to the kernel of the simplified linear method. Two-dimensional impedance images of a flower petal and cancer cells are reconstructed using this method. The images reveal details not present in the measured images