The accurate spectral characterization of high-resolution spectrometers is required for correctly computing, interpreting, and comparing radiance and reflectance spectra acquired at different times or by different instruments. In this paper, we describe an algorithm for the spectral characterization of field spectrometer data using sharp atmospheric or solar absorption features present in the measured data. The algorithm retrieves systematic shifts in channel position and actual full width at half-maximum (FWHM) of the instrument by comparing data acquired during standard field spectroscopy measurement operations with a reference irradiance spectrum modeled with the MODTRAN4 radiative transfer code. Measurements from four different field spectrometers with spectral resolutions ranging from 0.05 to 3.5nm are processed and the results validated against laboratory calibration. An accurate retrieval of channel position and FWHM has been achieved, with an average error smaller than the instrument spectral sampling interval.
Abstract. The study of nonlinear vibrations/oscillations in mechanical and electronic systems has always been an important research area. While important progress in the development of mathematical chaos theory has been made for finite dimensional second order nonlinear ODEs arising from nonlinear springs and electronic circuits, the state of understanding of chaotic vibrations for analogous infinite dimensional systems is still very incomplete.The 1-dimensional vibrating string satisfying wtt − wxx = 0 on the unit interval x ∈ (0, 1) is an infinite dimensional harmonic oscillator. Consider the boundary conditions: at the left end x = 0, the string is fixed, while at the right end x = 1, a nonlinear boundary condition wx = αwt − βw 3 t , α, β > 0, takes effect. This nonlinear boundary condition behaves like a van der Pol oscillator, causing the total energy to rise and fall within certain bounds regularly or irregularly. We formulate the problem into an equivalent first order hyperbolic system, and use the method of characteristics to derive a nonlinear reflection relation caused by the nonlinear boundary condition. Since the solution of the first order hyperbolic system depends completely on this nonlinear relation and its iterates, the problem is reduced to a discrete iteration problem of the type u n+1 = F (un), where F is the nonlinear reflection relation. We say that the PDE system is chaotic if the mapping F is chaotic as an interval map. Algebraic, asymptotic and numerical techniques are developed to tackle the cubic nonlinearities. We then define a rotation number, following J.P. Keener [11], and obtain denseness of orbits and periodic points by either directly constructing a shift sequence or by applying results of M.I. Malkin [17] to determine the chaotic regime of α for the nonlinear reflection relation F , thereby rigorously proving chaos. Nonchaotic cases for other values of α are also classified. Such cases correspond to limit cycles in nonlinear second order ODEs. Numerical simulations of chaotic and nonchaotic vibrations are illustrated by computer graphics.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.