WŁAŚCIWOŚCI CZĘSTOTLIWOŚCIOWE POCHODNYCH TYPU NORRIS GAP I ICH ZASTOSOWANIE DO ANALIZY WIDM GAZÓW

The article deals with an analysis of the properties of Norris gap derivatives. It discusses issues related to determining information from optical spectra measured with spectrometers. Impulse responses of differentiating filters were introduced using both Norris and Savitzky-Golay methods. The amplitude-frequency responses of the first and second order Norris differentiating filters were compared. The length impact of both segment and gaps on the frequency characteristics of filters was compared. The processing of exemplary gas spectra using the discussed technique was subsequently presented. The effect of first and second order derivatives on the spectra of carbon monoxide rotational lines for low resolution measurements is investigated. The Norris method of derivatives are very simple to implement and the calculation of their parameters does not require the use of advanced numerical methods.Artykuł przedstawia analizę właściwości pochodnych według metody Norrisa. Omówiono w nim zagadnienia związane z wyznaczaniem informacji z widm optycznych mierzonych spektrometrami. Przedstawiono odpowiedzi impulsowe filtrów różniczkujących zarówno metodą Norrisa jak też Savitzky-Golay. Porównano odpowiedzi amplitudowo-częstotliwościowe filtrów różniczkujących Norrisa pierwszego i drugiego rzędu. Porównano wpływ zarówno długości segmentów jak i rozstępu (luk) na charakterystyki częstotliwościowe filtrów. Kolejno zaprezentowano przetwarzanie przykładowych widm gazu z wykorzystaniem omawianej techniki. Przedstawiono także wpływ pochodnych pierwszego i drugiego rzędu na widma linii rotacyjnych tlenku węgla dla pomiarów o małej rozdzielczości. Metoda pochodnych według Norrisa jest bardzo prosta w implementacji a obliczanie jej parametrów nie wymaga stosowania zaawanasowanych metod numerycznych

Single- and Double-Comb Tilted Fibre Bragg Grating Refractive Index Demodulation Methods with Fourier Transform Pre-Processing

The development of fibre optic sensors for measuring the refractive index is related to the creation of new periodic structures and demodulation algorithms for the measured spectrum. Recently, we proposed a double-comb Tilted fibre Bragg grating (DCTFBG) structure. In this article, we analyse such a structure for measuring the refractive index in comparison to a single classical structure. Increasing the number of modes causes a significant change in the Fourier spectrum of optical spectra. For the purpose of data pre-processing, we propose the Fourier Transform as a filtering method in the frequency domain. Then, we analyse separately the band-filtered optical spectra for several frequency ranges. For quantitative analysis, we use algorithms that use quantitative changes in the transmission, i.e., the method of the envelope and the length of the spectrum contour. We propose the use of the Hilbert transform as the envelope method. The second type of algorithms used are methods determining the shift of spectrum features along the wavelength axis. The method of determining the centre of gravity of the area bounded by the envelope and the maximum of the second derivative of the smoothed cumulative spectrum contour length is proposed here. Using the developed methods, the measurement resolution was achieved at the level of 2 × 10−5 refractive index unit

Open-Path FTIR Spectral Radiation Intensity Of Hot Combustion Gases – Measurement And Interpretation

Spectral remote sensing is a very popular method in atmospheric monitoring. The paper presents an approach that involves mid-infrared spectral measurements of combustion processes. The dominant feature in this spectral range is CO2 radiation, which is used to determine the maximum temperature of nonluminous flames. Efforts are also made to determine the temperature profile of hot CO2, but they are limited to the laboratory conditions. The paper presents an analysis of the radiation spectrum of a non-uniform-temperature gas environment using a radiative transfer equation. Particularly important are the presented experimental measurements of various stages of the combustion process. They allow for a qualitative description of the physical phenomena involved in the process and therefore permit diagnostics. The next step is determination of a non-uniform-temperature profile based on the spectral radiation intensity with the 8 m optical path length

A novel method of elimination of light polarization cross sensitivity on tilted fiber Bragg grating bending sensor

The article shows the possibility of using TFBG gratings to measure the radius of curvature of fiber bending in conditions of variable polarization of the introduced light. Most of the modern, stable light sources generate light with a high degree of polarization. Due to the spatial asymmetry, the direction of the light polarization plane affects the spectral parameters of individual modes. For this reason, in the measurement systems using TFBGs presented so far it becomes necessary to determine and control the state of light polarization directly in front of the periodic structure. The article presents the determined spectral parameters of the cladding modes which allow bending measurements regardless of the direction of polarization of the introduced light. Thanks to this, the measuring system can be constructed without providing control of the introduced light polarization angle, which makes its construction simpler. When using TFBGs with an angle of 2°, the accuracy of determining the bending radius in the range from 15 mm to 30 mm when changing the angle of the plane of polarization in the full range is 0.318 mm in the case of changes in the transmission coefficient. For changes in the wavelength of the selected cladding mode, the accuracy is 0.3203 mm, with the input light polarization being changed in the range from 0° (P type) to 90° (S type)

New Parameters Extracted from Tilted Fiber Bragg Grating Spectra for the Determination of the Refractive Index and Cut-Off Wavelength

Tilted fiber Bragg grating (TFBG) is a very popular fiber optic element that is used as a sensor for various physical quantities. The calculation of the refractive index of a substance surrounding the TFBG is based on its spectrum demodulation, which consists of determining a certain parameter that is correlated with the sought quantity. The most commonly used parameter is the area created by the maxima and minima of the cladding mode resonances. In this article, we propose a new group of methods, which are based on calculating the parameters related to the spectrum differences between the local average values in the range of occurrence of the cladding modes. The basic parameter used in this group of methods is the mean absolute deviation from the local mean, which is characterized by the best linearity among the considered group of methods. The calculated parameters, in their cumulative form, can also be used to determine the cut-off wavelength, which can also indirectly indicate the refractive index value. The proposed approaches were compared, in terms of measurement resolution, to the most commonly used methods, such as the cladding modes’ envelope area and the spectral contour lengths

Numerical and Experimental Analysis of Matched Filter Interrogation of FBG Sensors with Large Side Lobes

This article presents the effect of fiber Bragg gratings side lobes on interrogation systems consisting of sensor and matched filters. The conducted research shows that high-value side lobe structures applied as sensors and/or filters are characterized by some interesting properties. The paper presents both numerical analysis and experimental verification of the fiber Bragg gratings (FBG) interrogation systems with matched filters for gratings containing high side lobes. Numerical modeling of Bragg structures was performed for two different cases: uniform and inverse apodization. Modification of apodization can change the side lobe reflectance level even above levels found in uniform structures. This is a case not described in the literature, especially in terms of possible applications. Transfer characteristics, i.e., the relationship between power intensity as a function of wavelength shift, were determined. A collection of gratings with spectra corresponding to those analyzed in numerical experiments were fabricated. Next, the transfer characteristics of the interrogation systems containing real FBG were determined. The properties of the proposed systems are described. It has been shown that a significant level of sidebands, which is often the subject of many drawbacks in filtering or telecommunications systems, can be an advantage. It has been demonstrated that a high level of side lobes can be used to increase the measurement range of the FBG sensor interrogation systems. It has been determined numerically and confirmed experimentally that from the point of view of the design of sensor interrogation systems, it is beneficial to combine specific pairs of gratings: one with a spectrum characterized by a low side lobe level and a second one in which the spectrum has very high side lobes

Methods of Projecting Mode Amplitude Changes on the Wavelength Axis in Order to Determine the Bending Radius on the Basis of TFBG Grating Spectra

Tilted fibre Bragg grating (TFBG) are used as sensors to determine many quantities such as refractive index, temperature, stress, rotation and bending. The TFBG spectrum contains a lot of information and various algorithms are used for its analysis. However, most of these algorithms are dedicated to the analysis of spectral changes under the influence of the refractive index. The most popular algorithm used for this purpose is to calculate the area occupied by cladding modes. Among the remaining algorithms, there are those that use the determination of the cut-off wavelength as a surrounding refractive index (SRI) indicator. Projection on the wavelength axis can also be used to calculate the bending radius of the fibre. However, this is a more difficult task than with SRI, because the mode decay in bending is not so easy to catch. In this article, we propose a multi-step algorithm that allows to determine the impact of bending on mode leakage. At the same time, the place on the wavelength from the side of the Bragg mode and the ghost mode is determined, which represents the cladding mode radiated from the cladding under the influence of bending. The developed algorithm consists of the following operations carried out on the transmission spectrum: Fourier filtering, calculation of the cumulative value of the spectral length, low-pass filtering of the cumulative curve or its corresponding polynomial approximation, determination of the first and second derivative of the approximated curve, and projection of the second derivative of the curve on the wavelength axis. The shift of the wavelength determined in this way indirectly indicates the bending radius of the optical fibre. Based on multiple measurements, we prove that the presented algorithm provides better results when determining the bending radius compared to other algorithms adopted for this purpose and proposed for SRI measurements. Additionally, we analyse the method of determining the shift of a fragment of the spectrum using the phase of the discrete Fourier transform