Mathematical functions for the representation of chromatographic peaks.

At present, optical coherence tomography systems have a limited imaging depth or axial scan range, making diagnosis of large diameter arterial vessels and hollow organs difficult. Adaptive ranging is a feedback technique where image data is utilized to adjust the coherence gate offset and range. In this paper, we demonstrate an adaptive optical coherence tomography system with a 7.0 mm range. By matching the imaging depth to the approximately 1.5 mm penetration depth in tissue, a 3 dB sensitivity improvement over conventional imaging systems with a 3.0 mm imaging depth was realized.

/pdf/adaptive-ranging-for-optical-coherence-tomography-3g0ra6krho.pdf

Adaptive ranging for optical coherence tomography

1. Introduction 2. Fundamentals of Fourier Analysis 3. Fourier Analysis in Systems Theory 4. Fourier Transforms in Probability, Random Variables and Stochastic Processes 5. The Sampling Theory 6. Generalizations of the Sampling Theorem 7. Noise and Error Effects 8. Multidimensional Signal Analysis 9. Time-Frequency Representations 10. Signal Recovery 11. Signal and Image Synthesis: Alternating Projections Onto Convex Sets 12. Mathematical Morphology and Fourier Analysis on Time Sales 13. Applications 14. Appendices 15. Reference

/pdf/handbook-of-fourier-analysis-its-applications-3p9g17xkvz.pdf

Handbook of Fourier Analysis & Its Applications

Preface.Acknowledgments.1. Introduction.2. Your Personal "OPUS Workstation".3. OPUS Basics.4. Basic Principles of Vibrational Spectroscopy.5. Fourier Transform Technique.6. Files.7. Edit.8. View.9. Window.10. Manipulating.11. Evaluating.12. Display.13. Print.Bibliography.Index.

/pdf/ir-and-raman-spectroscopy-fundamental-processing-4iq9styqeb.pdf

IR and Raman spectroscopy : fundamental processing

We present a miniaturized Fourier transform spectrometer implemented on a silicon optical bench platform. Both optical and opto-mechanical components of a Michelson interferometer, including a silicon beam splitter, micromirrors, MEMS actuators, and fiber U-grooves, are simultaneously fabricated by micromachining of the device layer of a silicon-on-insulator wafer. Our specialized bulk micromachining process combines the flexible definition capability of deep reactive ion etching with the good surface quality provided by anisotropic KOH wet etching. This integrated Fourier transform spectrometer has a measured spectral resolution of approximately 45 nm near 1500 nm wavelength.

Micromachined Fourier transform spectrometer on silicon optical bench platform

I MATHEMATICAL FUNDAMENTALS: Basic Definitions General Properties of Fourier Transforms Discrete Fourier Transforms Fast Fourier Transforms Laplace and Other Integral Transforms II SPECTRAL APPLICATIONS: Fourier Transform Spectroscopy Fourier Transform Nuclear Magnetic Resonance (NMR) Spectrometry FT Ion Cyclotron Resonance Mass Spectrometry Diffraction and Fourier Transform Uncertainty Principle Signal Processing Fourier Self-Deconvolution Linear Prediction.

Fourier Transforms in Spectroscopy

In this work we introduce a new method for testing spectral line shape models and optimizing the parameters in any parametric model. Given some general parametric line shape and a piece of a spectrum, the method finds the optimal values for the parameters and gives a number which tells how well the spectrum under consideration is explained by that model. The number of spectral lines under analysis may be more than one, and their exact locations need not be known. This characteristic follows from the property that the method does not need the information about line positions and amplitudes at all. Thus, in the absence of a singlet line, a set of overlapping lines can also be analyzed. The analysis is carried out in the signal domain by utilizing linear prediction. Application examples of the method to a molecular spectrum measured in gas phase are given. The results suggest that the Voigt line shape, despite its common use, is not a correct model in molecular spectroscopy. Its limitations become evident when one is trying to enhance the resolution by linear prediction, which requires detailed knowledge of the line shape. Instead a stochastic model, which is also tested, turns out to be rather promising.

New Method for Spectral Line Shape Fitting and Critique on the Voigt Line Shape Model

The carousel interferometer is a new type of an interferometer, which has been invented at the University of Turku. It consists of a beamsplitter and five plane mirrors. Four of the mirrors are mounted on a carousel, which rotates back and forth. We have modified the interferometer for use in the Fourier-transform ultraviolet (FT-UV) spectroscopy. Test measurement with plasma radiation gives favourable results. The most important property, which makes the carousel interferometer suitable for UV measurements, is its good stability in modulation.

Jari Partanen

Papers

Fourier Transforms in Spectroscopy

New Method for Spectral Line Shape Fitting and Critique on the Voigt Line Shape Model

The Use of Carousel Interferometer in Fourier-Transform Ultraviolet Spectroscopy

High Resolution IR Spectroscopy (Gas Phase) Instrumentation

Fast Fourier Transform (FFT)