“…One can thus estimate the jump probability by Eqs. (16) and (21). The probability escalates rapidly if σ p is large and/or the range is not centered at φ 0 ; we will illustrate this situation in more detail in Section 3.E.2.…”
Section: Cause Of the Jump (Ii): Estimation Noise Of φmentioning
confidence: 96%
“…In some applications, the signal is amplitude-modulated by an envelope stemming from the source spectrum. The envelope can be removed by precalibrating the source spectrum or by an interpolation process [21,22]. In sum, after the removal of the envelope and the DC component, the signal is expressed as…”
Section: A Backgroundmentioning
confidence: 99%
“…Without the knowledge of the fringe order there is an 2π ambiguity in Φ [19]. In order to enable absolute measurement, an improved algorithm estimates the fringe order in the first step by FT or LR and subsequently determines the OPD by tracking one peak [20,21]. This strategy was extended further to utilize the whole spectrum [22].…”
Signal processing for low-finesse fiber-optic Fabry-Perot sensors based on white-light interferometry is investigated. The problem is demonstrated as analogous to the parameter estimation of a noisy, real, discrete harmonic of finite length. The Cramer-Rao bounds for the estimators are given, and three algorithms are evaluated and proven to approach the bounds. A long-standing problem with these types of sensors is the unpredictable jumps in the phase estimation. Emphasis is made on the property and mechanism of the "total phase" estimator in reducing the estimation error, and a varying phase term in the total phase is identified to be responsible for the unwanted demodulation jumps. The theories are verified by simulation and experiment. A solution to reducing the probability of jump is demonstrated.
“…One can thus estimate the jump probability by Eqs. (16) and (21). The probability escalates rapidly if σ p is large and/or the range is not centered at φ 0 ; we will illustrate this situation in more detail in Section 3.E.2.…”
Section: Cause Of the Jump (Ii): Estimation Noise Of φmentioning
confidence: 96%
“…In some applications, the signal is amplitude-modulated by an envelope stemming from the source spectrum. The envelope can be removed by precalibrating the source spectrum or by an interpolation process [21,22]. In sum, after the removal of the envelope and the DC component, the signal is expressed as…”
Section: A Backgroundmentioning
confidence: 99%
“…Without the knowledge of the fringe order there is an 2π ambiguity in Φ [19]. In order to enable absolute measurement, an improved algorithm estimates the fringe order in the first step by FT or LR and subsequently determines the OPD by tracking one peak [20,21]. This strategy was extended further to utilize the whole spectrum [22].…”
Signal processing for low-finesse fiber-optic Fabry-Perot sensors based on white-light interferometry is investigated. The problem is demonstrated as analogous to the parameter estimation of a noisy, real, discrete harmonic of finite length. The Cramer-Rao bounds for the estimators are given, and three algorithms are evaluated and proven to approach the bounds. A long-standing problem with these types of sensors is the unpredictable jumps in the phase estimation. Emphasis is made on the property and mechanism of the "total phase" estimator in reducing the estimation error, and a varying phase term in the total phase is identified to be responsible for the unwanted demodulation jumps. The theories are verified by simulation and experiment. A solution to reducing the probability of jump is demonstrated.
“…[1][2][3][4][5][6][7][8] In a white-light measurement system, light from a low-coherence source, such as a light-emitting diode (LED), a superluminescent LED, or a broadband lamp, is transmitted to a single or multiplexed fiber sensors. A fringe pattern is produced by the light transmitted by or reflected from the sensor and recorded either spectrally by an optical spectrum analyzer (OSA) or temporally by a photodiode in a scanning interferometric system.…”
Section: Introductionmentioning
confidence: 99%
“…The fringe analysis approach most often used for white-light interferometers is the fringe peak tracking method, in which the peak position of a fringe or the fractional sample points between fringes in the interferogram are identified to determine the fringe order and to estimate the OPD of the sensor. [1][2][3][4][5] Although this fringe analysis method has been successfully used in many single interferometric sensor systems, it requires a high signal-tonoise ratio (SNR) to determine the fringe orders correctly and detect the peak positions accurately and cannot be directly applied to multiplexed sensor systems.…”
A novel signal-processing algorithm based on frequency estimation of the spectrogram of single-mode optical fiber Fabry-Perot interferometric sensors under white-light illumination is described. The frequency-estimation approach is based on linear regression of the instantaneous phase of an analytical signal, which can be obtained by preprocessing the original spectrogram with a bandpass filter. This method can be used for a relatively large cavity length without the need for spectrogram normalization to the spectrum of the light source and can be extended directly to a multiplexed sensor system. Experimental results show that the method can yield both absolute measurement with high resolution and a large dynamic range. Performance analysis shows that the method is tolerant of background noise and variations of the source spectrum.
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