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Apodyzowane siatki Bragga o stałym okresie jako przetworniki odkształceń impulsowych. Analiza numeryczna

Sikora A.

Pomiary Automatyka Kontrola

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2010

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R. 56, nr 12

1436-1438

PL

Artykuł dotyczy analizy wpływu długości apodyzowanych siatek równomiernych na dokładność przetwarzania odkształceń impulsowych o kształcie połowy sinusoidy. Nowością jest wykonanie tej analizy z jednoczesnym porównaniem wpływu wybranych profili apodyzacyjnych siatki równomiernej na dokładność tego przetwarzania. Przedstawiono wyniki obliczeń wybranych miar błędów dynamicznych. Na ich podstawie można stwierdzić, że wpływ profili apodyzacyjnych (w modelowanym zakresie) jest widoczny dla błędów czasu narastania i amplitudy, dla błędu średniokwadratowego jest nieznaczny.

EN

The fibre Bragg gratings (FBG) are used in measurements as optical transducers which can also be used in high-frequency strain measurements [1, 2]. In such applications the output signal is distorted mainly due to the grating length [3, 4]. In order to select the proper grating length, the rise-time error (RTE, Fig. 2, Eq. 3), the amplitude error of the frequency change (AFCE, Fig. 2, Eq. 4) and the mean square error (MSE, Fig. 3, Eq. 5) were calculated. The calculations were carried out in several steps. In order to model the reflected grating power, the transfer matrix description [5] was used when taking into account the individual changes of parameters of each section of the grating (Eq. 1) [6]. The effective central fre-quency was assumed to be the grating output signal (Eq. 2)[7]. The dynamic errors were calculated [8] for a half sinusoidal (Eq. 8) impulsive strain waveform, and different apodization functions (raised-cosine profile Eq. 6, sinc Eq. 7) (Fig. 1) [9]. The results can be summarized in a conclusion: the calculated errors allow selecting the proper length of the fibre grating if the errors are established, and the waveform of the pulse is identified. The influence of the apodization function is observable for the RTE and AFCE, while for the MSE it is insignifi-cant.

2

Influence of the length of a uniform fiber Bragg grating on the accuracy of measuring an impulsive strain

Kaczmarek Z., Sikora A.

Optica Applicata

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2008

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Vol. 38, nr 2

305-314

EN

The influence of the length of a uniform, unapodized and apodized fiber Bragg grating on the accuracy of converting an impulsive strain is discussed. Using the transfer matrix description of the grating, derived from the coupled mode theory, the reflectivity spectrum changes of the grating are calculated, which are caused by the strain pulses propagating along it. On the basis of the introduced effective central frequency of the grating, the rise-time error (RTE) and the amplitude error of the frequency change (AFCE) were calculated as a function of the ratio of the strain pulse leading front width to the grating length. These errors were calculated for different waveforms of the strain pulses. Charts presenting results of the calculations allow to select the proper length of the uniform fiber grating, when the converting error is established, and the waveform of the pulse is identified.

3

The reconstruction of waveforms of impulsive strain occurring in an elastic bar by means of deconvolution in the frequency domain

Kaczmarek Z., Detka M.

Metrology and Measurement Systems

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2007

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Vol. 14, nr 2

257-268

EN

The paper presents a method of reconstruction of impulsive strain waveforms based on deconvolution in the frequency domain and the spectral transmittance of the bar, which was determined experimentally and given in an analytic form. A regularization of the deconvolution is obtained by means of limiting the frequency band of the inversion filter. In this method the one-point or the two-point measurement of strain waves in an elastic bar can be utilized.