Spectral Uncertainty Research Articles

Uncertainty Bounds for Spectral Estimation

The purpose of this paper is to study metrics suitable for assessing uncertainty of power spectra when these are based on finite second-order statistics. The family of power spectra which is consistent with a given range of values for the estimated statistics represents the uncertainty set about the “true” power spectrum. Our aim is to quantify the size of this uncertainty set using suitable notions of distance, and in particular, to compute the diameter of the set since this represents an upper bound on the distance between any choice of a nominal element in the set and the “true” power spectrum. Since the uncertainty set may contain power spectra with lines and discontinuities, it is natural to quantify distances in the weak topology-the topology defined by continuity of moments. We provide examples of such weakly continuous metrics and focus on particular metrics for which we can explicitly quantify spectral uncertainty. We then consider certain high resolution techniques which utilize filter-banks for preprocessing, and compute worst case a priori uncertainty bounds solely on the basis of the filter dynamics. This allows the a priori tuning of the filter-banks for improved resolution over selected frequency bands.

Reflectance conversion methods for the VIS/NIR imaging spectrometer aboard the Chang'E-3 lunar rover: based on ground validation experiment data

The second phase of the Chang'E Program (also named Chang'E-3) has the goal to land and perform in-situ detection on the lunar surface. A VIS/NIR imaging spectrometer (VNIS) will be carried on the Chang'E-3 lunar rover to detect the distribution of lunar minerals and resources. VNIS is the first mission in history to perform in-situ spectral measurement on the surface of the Moon, the reflectance data of which are fundamental for interpretation of lunar composition, whose quality would greatly affect the accuracy of lunar element and mineral determination. Until now, in-situ detection by imaging spectrometers was only performed by rovers on Mars. We firstly review reflectance conversion methods for rovers on Mars (Viking landers, Pathfinder and Mars Exploration rovers, etc). Secondly, we discuss whether these conversion methods used on Mars can be applied to lunar in-situ detection. We also applied data from a laboratory bidirectional reflectance distribution function (BRDF) using simulated lunar soil to test the availability of this method. Finally, we modify reflectance conversion methods used on Mars by considering differences between environments on the Moon and Mars and apply the methods to experimental data obtained from the ground validation of VNIS. These results were obtained by comparing reflectance data from the VNIS measured in the laboratory with those from a standard spectrometer obtained at the same time and under the same observing conditions. The shape and amplitude of the spectrum fits well, and the spectral uncertainty parameters for most samples are within 8%, except for the ilmenite sample which has a low albedo. In conclusion, our reflectance conversion method is suitable for lunar in-situ detection.

Intersatellite calibration of NOAA HIRS CO2 channels for climate studies

AbstractThe 30 years of observations from the High‐Resolution Infrared Radiation Sounder (HIRS) longwave CO2 channels aboard the NOAA series of satellites are being used to detect climatological changes of cloud. However, the intersatellite radiance discrepancies in the channels need to be removed for the development of a consistent cloud series using HIRS data. By analyzing the intersatellite radiance comparisons at simultaneous‐nadir‐overpass locations for HIRS longwave CO2 channels onboard the NOAA and MetOp series of satellites, this study optimizes the spectral response functions (SRF) for each HIRS to generate a more consistent long‐term set of observations. Intersatellite radiance biases as large as 5% are found for these channels; the spectral differences and spectral uncertainties are shown to be the main causes. To estimate the radiance change for a specific channel due to SRF difference and uncertainty, a linear model is developed to correlate the radiance change for the channel being analyzed with the spectral radiances in the eight selected HIRS channels. The hyperspectral measurements from the Infrared Atmospheric Sounding Interferometer on the MetOp satellite are used to simulate HIRS observations and estimate the parameters of the linear models. The linear models are applied to the NOAA and MetOp HIRS data at simultaneous‐nadir‐overpass locations to estimate the intersatellite radiance differences due to the SRF differences and uncertainties. The intersatellite mean radiance biases are minimized toward zero with residual maximum uncertainty less than 1% after the SRF differences and uncertainties are mitigated. Using the MetOp Infrared Atmospheric Sounding Interferometer as a reference, the optimized SRFs for every NOAA HIRS are found by effectively minimizing the root‐mean‐square values of the intersatellite radiance differences. The optimized shifts of the SRF can be as large as 3 cm−1.

PROSPECTS FOR USING COHERENT ELASTIC NEUTRINO-NUCLEUS SCATTERING TO MEASURE THE NUCLEAR NEUTRON FORM FACTOR

We review the prospects of using coherent elastic neutrino-nucleus scattering (CENNS) to measure the nuclear neutron form factor. The merits and limitations of several potential neutrino sources are discussed. The effects of detector shape uncertainty and detector size on a measurement of the neutron RMS radius are also considered. We find that the detector spectral shape uncertainty is the important limiting factor on a measurement of the neutron RMS radius. In order to measure the neutron RMS radius to 5%, the spectral shape uncertainty of the detector needs to be known to 1% or better.

Spectral uncertainty and similarity effects in informational masking identically related to the Simpson-Fitter metric of target-masker separation

Evidence is provided suggesting a primary dependence of informational masking (IM) on the stochastic separation of target and masker given by Simpson-Fitter’s da [Lutfi et al. J. Acoust. Soc. Am. 132, EL109-113 (2012)]. The stimuli were synthesized impact sounds of plates played in sequence as masker-target-masker triads. Their spectra varied independently and at random on each presentation as would correspond to changes in plate size. In the 2IFC procedure the listener’s task was to choose the larger-sized target. The effect of spectral uncertainty regarding the masker was examined by measuring d’ performance for different values of the variance in masker size. The effect of spectral similarity of target and masker was examined by measuring performance for different values of the mean difference between target and masker size. The functions relating d’ to da in both cases were identical and of similar slope across listeners. Identical functions were also obtained, though with shallower slopes, when listeners judged the target hit with greater impact force. The results are considered in terms of their implications for the development of a model of IM that emphasizes the statistical properties of signals over loosely defined concepts of target-masker similarity and masker uncertainty.

Spatial uncertainty and proximity effects in informational masking identically related to the Simpson–Fitter metric of target-masker separation

Further evidence is provided suggesting a primary dependence of informational masking (IM) on the stochastic separation of target and masker given by Simpson-Fitter’s da [Lutfi et al. J. Acoust. Soc. Am. 132, EL109-113 (2012)]. The stimuli were brief bursts of Gaussian noise or words played in sequence as masker-target-masker triads. The apparent position of bursts (words), from left to right, was varied independently and at random on each presentation using KEMAR HTRFs. In the 2IFC procedure, the listener’s task was to choose the target positioned further to the right. The effect on performance of spatial uncertainty regarding the masker was examined by manipulating the position variance of the masker. The effect on performance of spatial proximity of target to masker was examined by manipulating the position mean difference between target and masker. In both cases, the data were well described by a single linear function relating d’ performance to da; intercepts differed across listeners, but slopes were similar. Comparable results presented at this meeting for the effects of spectral uncertainty and similarity of target and masker suggest that the statistical properties of signals may be a more significant determinant of IM than their specific acoustic properties.

Uncertainty analysis of cross-calibration for HJ-1 CCD camera

Radiometric calibration of sensor is the basis of quantitative remote sensing, and uncertainty analysis is critical to ensure the accuracy of cross-calibration. Therefore, firstly, cross-calibration formulas were improved by redefining calibration coefficient and spectral band matching factor. In these formulas, cci was redefined as the calibration coefficient of normalized apparent reflectance, and spectral band matching factor as the ratio of normalized apparent reflectance. Secondly, based on the contrast of ideal and actual conditions in cross-calibration, 8 sources of cross-calibration uncertainty were proposed: calibration uncertainty of standard sensor; pixel matching uncertainty; spectral band matching factor uncertainty caused by site altitude setting error, atmospheric parameters setting error, surface spectrum source, surface bidirectional reflectance characteristic, and error of atmospheric radiative transfer model; and uncertainty caused by other factors which were not considered. Finally, the contribution of each uncertainty was further analyzed and discussed for the HJ-1 CCD camera. The results provide many valuable references for evaluating the feasibility of alternative cross-calibration measurements.

Assessment of Spectral, Misregistration, and Spatial Uncertainties Inherent in the Cross-Calibration Study

Cross-calibration of satellite sensors permits the quantitative comparison of measurements obtained from different Earth Observing (EO) systems. Cross-calibration studies usually use simultaneous or near-simultaneous observations from several spaceborne sensors to develop band-by-band relationships through regression analysis. The investigation described in this paper focuses on evaluation of the uncertainties inherent in the cross-calibration process, including contributions due to different spectral responses, spectral resolution, spectral filter shift, geometric misregistrations, and spatial resolutions. The hyperspectral data from the Environmental Satellite SCanning Imaging Absorption SpectroMeter for Atmospheric CartograpHY and the EO-1 Hyperion, along with the relative spectral responses (RSRs) from the Landsat 7 Enhanced Thematic Mapper (TM) Plus and the Terra Moderate Resolution Imaging Spectroradiometer sensors, were used for the spectral uncertainty study. The data from Landsat 5 TM over five representative land cover types (desert, rangeland, grassland, deciduous forest, and coniferous forest) were used for the geometric misregistrations and spatial-resolution study. The spectral resolution uncertainty was found to be within 0.25%, spectral filter shift within 2.5%, geometric misregistrations within 0.35%, and spatial-resolution effects within 0.1% for the Libya 4 site. The one-sigma uncertainties presented in this paper are uncorrelated, and therefore, the uncertainties can be summed orthogonally. Furthermore, an overall total uncertainty was developed. In general, the results suggested that the spectral uncertainty is more dominant compared to other uncertainties presented in this paper. Therefore, the effect of the sensor RSR differences needs to be quantified and compensated to avoid large uncertainties in cross-calibration results.

Kinetics of H atom attack on unsaturated hydrocarbons using spectral uncertainty propagation and minimization techniques

Unsaturated hydrocarbons are an important component of hydrocarbon fuels and intermediates in their oxidation. Under rich conditions, H atom attack is one of the principal pathways of the decomposition of these unsaturated compounds. Consequently, it is critical to understand the H atom attack mechanisms as part of chemical model development. Previous studies have examined the kinetics of H atom attack on various unsaturated hydrocarbons in single pulse shock-tubes. These studies have noted that there are multiple pathways by which H atom attack can proceed, so it is straightforward to measure relative rates but absolute rates are more difficult to estimate. In addition, there is a confounding influence from secondary chemistry. A multiparameter optimization and uncertainty minimization technique is used to constrain a chemical model for the oxidation of H2/CO/C1–C4 hydrocarbons against a range of measurements of the H atom attack process on toluene, trimethylbenzene (TMB), propyne, and propene. The recommended rate constant expressions, with 2σ uncertainties, are as follows:k(CH4+H↔CH3+H2)=108.81±0.21s-1cm3mol-1K1.6T1.6exp(-5400±500K/T)k(C2H2+CH3↔p-C3H4+H)=1011.17±0.18s-1cm3mol-1K0.6T0.6exp(-7200±400K/T)k(p-C3H4+H↔a-C3H4+H)=1018.20±0.21s-1cm3mol-1KT-1exp(-6100±500K/T)k(C3H6+H↔C2H4+CH3)=1024.80±0.20s-1cm3mol-1K3T-3exp(-7400±700K/T)k(C3H6+H↔a-C3H5+H2)=105.14±0.19s-1cm3mol-1K-2.5T2.5exp(-1300±200K/T)k(C6H5CH3+H↔C6H6+CH3)=106.23±0.19s-1cm3mol-1K-2.2T2.2exp(-2000±400K/T)k(C6H5CH3+H↔C6H5CH2+H2)=1014.17±0.25s-1cm3mol-1exp(-4500±500K/T)k(TMB+H↔m-xylene+CH3)=1014.07±0.18s-1cm3mol-1exp(-3900±400K/T)k(TMB+H↔(CH3)2)=1014.52±0.25s-1cm3mol-1exp(-4300±600K/T)In addition, we quantify the effect of secondary chemistry on these rate estimates and the contribution to their uncertainty. Furthermore, we demonstrate how the detailed measurements constrain the model’s predictions of global properties such as ignition delay time in propene oxidation.

Strong duality in robust semi-definite linear programming under data uncertainty

This article develops the deterministic approach to duality for semi-definite linear programming problems in the face of data uncertainty. We establish strong duality between the robust counterpart of an uncertain semi-definite linear programming model problem and the optimistic counterpart of its uncertain dual. We prove that strong duality between the deterministic counterparts holds under a characteristic cone condition. We also show that the characteristic cone condition is also necessary for the validity of strong duality for every linear objective function of the original model problem. In addition, we derive that a robust Slater condition alone ensures strong duality for uncertain semi-definite linear programs under spectral norm uncertainty and show, in this case, that the optimistic counterpart is also computationally tractable.

Assessing the Influence of Fourier Analysis Parameters on Short-Time Modal Parameter Extraction

It is sometimes necessary to determine the manner in which materials and structures deteriorate with respect to time when subjected to sustained random dynamic loads. In such cases a system’s fatigue characteristics can be obtained by continuously monitoring its modal parameters. This allows for any structural deterioration, often manifested as a loss in stiffness, to be detected. Many common structural integrity assessment techniques make use of Fourier analysis for modal parameter extraction. For continual modal parameter extraction, the Fourier transform requires that a compromise be made between the accuracy of the estimates and how frequently they can be obtained. The limitations brought forth by this compromise can be significantly reduced by selecting suitable values for the analysis parameters, mainly subrecord length and number of averages. Further improvements may also be possible by making use of spectral enhancement techniques, specifically overlapped averaging and zero padding. This paper uses the statistical analysis of results obtained from numerous physical and numerical experiments to evaluate the influence of the analysis parameters and spectral enhancement techniques on modal estimates obtained from limited data sets. This evaluation will assist analysts in selecting the most suitable inputs for parameter extraction purposes. The results presented in this paper show that when using the Fourier transform to extract modal characteristics, any variation in the parameters used for analysis can have a significant influence on the extraction of natural frequency estimates from systems subjected to random excitation. It was found that for records containing up to 10% noise, subrecord length; hence spectral resolution, has a more pronounced influence on the accuracy of modal estimates than the level of spectral averaging; therefore spectral uncertainty. It was also found that while zero padding may not increase the actual spectral resolution, it does allow for improved natural frequency estimates with the introduction of interpolated estimates at the nondescribed frequencies. Finally, it was found that for modal parameter extraction purposes (in this case natural frequency), increased amounts of overlapped averaging can significantly reduce the variance of the estimates obtained. This is particularly useful as it allows for increased precision without compromising temporal resolution.

Tristimulus colorimeter calibration matrix uncertainties

Measurement uncertainties are propagated through the matrix calibration of a tristimulus colorimeter. It is shown that reference spectral uncertainties and the colorimeter signal uncertainties during calibration are simply scaled and combined in an applied measurement. Modeling shows that transforming x, y chromaticity and Y luminance can lead to lower chromaticity uncertainties than transforming X, Y, Z tristimulus signals themselves. Accuracy depends on the set of colours used for calibration, especially for measurements of displays. Uncertainties can be large and dominate errors due to accuracy of spectral matching to the CIE colour-matching functions. This is particularly true if commision international de L'Eclariage (CIE) Lab values are to be derived. © 2012 Wiley Periodicals, Inc. Col Res Appl, 38, 251–258, 2013

Discrete-Time, Robust Wiener Filtering with Non-Parametric Spectral Uncertainty

In this paper, a discrete-time, robust Wiener filtering problem is approached along the lines pursued in [4] for the continuous-time case. The robust, multivariate filtering problem considered here involves non-parametric spectral uncertainty defined by the so-called spectral band and generalized-variance constraints. The approach in question centers on computing upper and lower bounds on the minimum worst-case performance achieved with causal filters, together with filters which attain such bounds, on the basis of semi-definite linear programming problems (SDLP, for short). Upper bounds are obained from a Lagrangean duality formulation. Relying on finitedimensional, linearly-parametrized classes of dynamic multipliers and filter transfer functions, the computation of progressively tighter upper bounds together with causal filters which achieve them is reduced to solving SDLPs. Analogously, on the basis of the min-max theorem and relying on similar classes of rational power spectral densities, the computation of lower bounds together with the corresponding filters is also shown to be equivalent to solving SDLPs. Combining these results, causal filters can be obtained whose worst-case, least squares performance can be certified to be close to the optimal one, as illustrated in a simple numerical example.

Flat Crystal x-ray Spectrometer for Quantitative Spectral Measurement in the 2–5 keV Region

A technique of flat crystal x-ray spectrometer for quantitative spectral measurement is described. For the flat crystal spectrograph geometry, the quantitative reduction of relating the CCD counts back to the photon flux from the x-ray source is established. The absolute calibrations of the integral diffraction coefficients of the crystal and the CCD sensitivity make it possible to measure absolute photons flux within the energy range of 2000–5000 eV. The uncertainty analysis of the calibrations is carried out to obtain the energy resolved uncertainties of crystal and CCD. Thus, the experimental spectra with spectral resolved intensity uncertainties are available. Then, a performing experiment of laser-produced Ti plasma is carried out and the absolute x-ray spectra with intensity uncertainty less than 8.5% are obtained. The technique is promising for absolute spectral measurement of high temperature plasmas in a kilo-electron-volt region.

Robust duality for generalized convex programming problems under data uncertainty

In this paper we present a robust duality theory for generalized convex programming problems in the face of data uncertainty within the framework of robust optimization. We establish robust strong duality for an uncertain nonlinear programming primal problem and its uncertain Lagrangian dual by showing strong duality between the deterministic counterparts: robust counterpart of the primal model and the optimistic counterpart of its dual problem. A robust strong duality theorem is given whenever the Lagrangian function is convex. We provide classes of uncertain non-convex programming problems for which robust strong duality holds under a constraint qualification. In particular, we show that robust strong duality is guaranteed for non-convex quadratic programming problems with a single quadratic constraint with the spectral norm uncertainty under a generalized Slater condition. Numerical examples are given to illustrate the nature of robust duality for uncertain nonlinear programming problems. We further show that robust duality continues to hold under a weakened convexity condition.

Single mode emission and non-stochastic laser system based on disordered point-sized structures: toward a tuneable random laser

As an advantage, random lasers may be elaborated from a large variety of materials and do not require any cavity oscillators that usually necessitate complicated and expensive fabrication techniques. Since the feedback process of those non-conventional laser systems is provided by light interference in a disordered medium, spectral and temporal uncertainties are usually considered as an intrinsic part of their optical proprieties. We investigated random laser action under two photon absorption experiments through an auto-organized InGaN/GaN quantum-disks ensemble. Thanks to our experimental approach, we evidence random lasing based on a gain medium constituted by point-sized structures. In such context, a stabilised and individual emission mode is observed as for conventional semiconductor lasers. By controlling the emission energy of these nanostructures, a tuneable and stable random laser may be built. Moreover, our findings suggest that disordered medium should play an important role in the conception of low cost quantum dot and up conversion laser systems.

Fundamental Quantum Limit to Waveform Estimation

We derive a quantum Cramér-Rao bound (QCRB) on the error of estimating a time-changing signal. The QCRB provides a fundamental limit to the performance of general quantum sensors, such as gravitational-wave detectors, force sensors, and atomic magnetometers. We apply the QCRB to the problem of force estimation via continuous monitoring of the position of a harmonic oscillator, in which case the QCRB takes the form of a spectral uncertainty principle. The bound on the force-estimation error can be achieved by implementing quantum noise cancellation in the experimental setup and applying smoothing to the observations.

Optimization of Near-Infrared Spectroscopic Process Monitoring at Low Signal-to-Noise Ratio

An approach for the optimization of near-infrared (NIR) spectroscopic process monitoring at low signal-to-noise ratio is presented. It compromises the combined adjustment of different measurement variables and data pretreatments considering the prediction error, economic aspects of the application, and process constraints. The integration time, light intensity, and number of averaged spectra were varied; their mutual influence on the prediction error of partial least squares (PLS) models (i.e., root-mean-square error of cross-validation (RMSECV)) was evaluated in the laboratory. At low signal levels, the spectral uncertainty had a strong impact on the prediction error. It leveled off with increasing values of all three parameters and was finally dominated by other sources of uncertainty. The experimental findings could be characterized and explained by a mathematical equation, which was deduced from theoretical principles. The knowledge about the interaction of the measurement variables allowed their combined adjustment resulting in a reduced impact of spectral uncertainty on the prediction error (i.e., root-mean-square error of prediction (RMSEP)) without additional costs or process modifications. Moreover, a convenient procedure to compensate the stray light caused by strongly absorbing windows was developed. The whole approach was successfully applied to a challenging process, namely, the NIR inline monitoring of the liquid content of two model substances in a rotating suspension dryer.

A multi-resolution time domain technique for monitoring fatigue progression in elements subjected to random loads

Materials and structures subjected to random loading can deteriorate in a complex fashion. A technique for monitoring the manner in which this decay occurs can be useful, not in the least, for comparative analysis. One method for monitoring structural deterioration is to continually track variations in the system’s modal parameters. Modal parameters are often extracted using the system’s frequency response function, obtained using the Fourier transform. However, for continual parameter extraction, the Fourier transform requires that a compromise be made between the spectral accuracy of the estimates and how frequently they can be obtained. This compromise significantly limits the potential of Fourier transform based techniques as continuous structural integrity assessment tools. The technique presented herein applies the Hilbert transform to the system’s instantaneous impulse response function, captured using the coefficients of an adaptive finite-impulse-response filter, in order to continually monitor shifts in the system’s natural frequency. This approach allows for the properties of systems to be evaluated at regular intervals without compromising spectral uncertainty. Numerous damage scenarios were performed (using both physical and numerical systems) in order to test the sensitivity of the technique as well as its ability to converge with changes in system characteristics.

Portable PVS-02 spectrometer for transfer of the spectral radiance scale in the 0.4–2.5 μm range

We describe selection of an optical layout and calculation of the spectral sensitivity and measurement uncertainty in a portable spectrometer. The spectrometer is used for transfer of the brightness scale in the 0.4–2.5 μm range from one brightness reference standard to another.