Nonlinear measurements in complex physical systems - Lim, May Tan (2003)
We investigate different aspects of measurements and nonlinearity in complex physical systems. This study includes (1) modeling the emergence of hysteresis ( a nonlinear phenomenon) as a collective behavior, (2) analyzing the nonlienar properties of two-color and two-photon excitation confocal fluorescence microscopy in the presence of confocality breakdown, (3) taking advantage of nonlinear behavior in making noise-aided measurements of a very weak (normally undetectable) signal, and (4) enhancing a low-resolution Raman signal using the simplex projection which is a nonlinear recovery method. In the first part, we model the emergence of hysteresis as a collective behavior in a lattice network of individuality non-hysteretic agents with continuous responses. The network exhibits rich behavior including power law variations, chaos and system saturation. Our model is used to described the hysteresis and high-frequency fluctuations in the oxygen isotope variation (δˡ⁸O) data of ice (Greenland Ice Core Project) that exhibit the Younger Dryas cold event. Next, we evaluate the point spread function (PSF) of the two-color excitation (2CE) microscope when the confocality condition is not strictly by the two focused excitation beams which are separated by an angle Ɵ. Spatio-temporal simultaneity for the two excitation beams is essential in 2CE (λ₁≠ λ₂). Aberration-free misalignment of the geometrical foci and primary spherical aberration are considered. The deterioration of the fluorescence PSF together with the Linfoot's criteria of fidelity, structural content and correlation quality are used in comparing the different 2CE PSF behavior with that of the two-photon excitation (2PE) fluorescence (λ₁≠ λ₂) under the same misalignment or abberation settings. Our calculations reveal that 2CE imaging is more resilient to the ill-effects of misalignment and spherical aberration than the two-beam 2PE, with the Ɵ = π /2-configuration providing clearest advantage. the prospect of aberration-correction in the two-beam 2CE microscope is also discussed. Then, we demonstrate an efficient noise dithering procedure for measuring the power spectrum of a weak spectral doublet with a Fourier-transform spectrometer in which the subthreshold interferogram is measured by a 1-bit analog-to-digital converter without oversampling. In the absence of noise, no information is obatined regarding the doublet spectrum because the modulation term s(x) of its interferogram is below the instrumental detection limit B. Our experiements show that, even for short observation times, the reasonant frequencies of s(x) could be located with high accuracy over a wide range of <f> and β values. Signal-to-noise ratios as high as 50 are also gained for the revocered power spectra. Finally, we demonstrate the enhancement of low-resolution spontaneous Raman spectra by simplex projection wihich extrapolates the high-frequency components that are lost when the entrance slit width ω of the grating spectrometer is widened to increase the optical throughput. On the weak Raman spectrum CCl₄, the combination of simplex projection and linear deconvolution succeeded in enhancing a low-resolution Raman spectrum (ω = 150 μm) to obtain information that are available in raw spectra measured at ω = 75 μm. Such a recovery performance is superior to what could be achieved via linear deconvolution alone.
Research project funded by the University through the Office of the Vice-Chancellor for Research and Development (OVCRD).
Vita.
"March 2003."
Thesis (Ph.D. Physics)--University of the Philippines Diliman.
Keywords: Nonlinear systems; System theory; Hysteresis -- Mathematical models; Fluorescence microscopy; Raman spectroscopy; Noise -- Measurement