## 1 Introduction  
Although fiber optic interferometric sensors offer the possibility of performing measurements with very high sensitivity and resolution [1], they suffer from problems such as complex signal processing techniques, quadrature point stabilization, and uncertainty as to whether an increase or decrease in the value of measurands has occurred. In order to fully utilize the capability of fiber optic sensors, a different sensing principle termed as \"white light interferometer\" or \"white light interferometry (WLI)\" was developed [2]. From the beginning of this research, an all fiber white light interferometry (AFWLI) absolute temperature measurement system as shown in Figure 1 was selected as the application area of the proposed signal processing algorithm. White light interferometry departs from the conventional interferometry in that it uses a broadband light source. SLD in Figure 1 represents a superluminescent diode (SLD) used as a broadband light source and PD1, PD2 denote photodetectors 1 and 2, respectively. In the AFWLI two fiber Fabry-Perot interferometers (FFPI, sensing FFPI and reference FFPI in Figure 1) and a Mach-Zehnder Interferometer as a processing interferometer (scanning interferometer in Figure 1, hereafter termed as MZI), which has two piezoelectric transducers (hereafter termed as PZT) in its two arms, are connected in tandem. The s  
Figure 1: All Fiber White Light Interferometer. interferometer output signals from PD1 (Equation 1 for PD1) and PD2 (Equation 2 for PD2) are given respectively by:  
\[I_{S}(\Phi_{P}) = 1+\frac{1}{2}\exp\Biggl{\{}-\Biggl{[}\frac{\Phi_{P}-\Phi_{S}}{\pi \underline{L}_{C}\,/\,\lambda}\Biggr{]}^{2}\Biggr{\}}\cos(\Phi_{P}-\Phi_{S}) \tag{1}\] \[I_{R}(\Phi_{P}) = 1+\frac{1}{2}\exp\Biggl{\{}-\Biggl{[}\frac{\Phi_{P}-\Phi_{R}}{ \pi\underline{L}_{C}\,/\,\lambda}\Biggr{]}^{2}\Biggr{\}}\cos(\Phi_{P}-\Phi_{R}) \tag{2}\]  
where \(L_{C}\) is the coherence length of light source, \(\Phi_{P}\) is the OPD (Optical Path-length Difference) between two arms of Mach-Zehnder processing interferometer and \(\Phi_{S}\), \(\Phi_{R}\) are the round trip phase shifts for the sensing and reference FFPIs, respectively. In Equation 1 and Equation 2 it is assumed that light source has a Gaussian power spectrum. A constant d.c. voltage \(V_{DC}\) (100\(\sim\)150 volt, Figure 1) is applied to the PZT1 in one arm to coarsely match the OPD of the MZI to that of the sensing FFPI. And an alternating ramp voltage \(V_{SAW}\) (Figure 1) is applied to PZT2 in the other arm to scan the processing interferometer so that OPD \(\Phi_{P}\) between two arms of MZI can be varied over a certain range. This AFWLI for temperature measurement produces two fringe scans, one from the sensing FFPI and another one from the reference FFPI, as shown Figure 2. In AFWLI, the sensing FFPI is exposed to the temperature \(T_{S}\) to be measured and the reference FFPI is protected from environmental disturbances but exposed to the known reference temperature \(T_{R}\). Now, assume that the known temperature of the sensing FFPI and the reference FFPI are \(T_{S}\) and \(T_{R}\), respectively. When the phase \(\Phi_{P}\) of MZI is scanned and exactly matched to that of the sensing FFPI (the reference FFPI), a zero order fringe peak of the sensing FFPI (the reference FFPI) is produced at certain \(\Phi_{P}=\Phi_{P,S}\) (\(\Phi_{P}=\Phi_{P,R}\)), as shown in Figure 2. In Figure 2, \(\Phi_{P,S}\) (\(\Phi_{P,R}\)) denotes the phase of the processing interferometer producing the zero order fringe peak of the sensing FFPI (the reference FFPI). If we can identify the phase difference \(\Phi^{d}=\Phi_{P,S}-\Phi_{P,R}\) (this is possible by the proposed signal processing algorithm which will be shown later in this article) then \(\Phi^{d}\) is mapped to the temperature \(T_{S}\)and absolute temperature  
Figure 2: Output of sensing and reference FFPI from AFWLI. measurement is possible. This problem has been known as \"Time Delay Estimation (TDE) [3] (or Phase Delay Estimation)\".