2.1. First Method: Simulated Tunable Bragg Grating

The first of the two implemented methods described herein is based on simulating a tunable fiber Bragg grating by using a tunable filter and a fiber mirror. This ensemble behaves analogously to an actual fiber Bragg grating by reflecting particular wavelengths of light with comparable bandwidths [18], while presenting the additional advantage of being fully tunable and providing a symmetrical spectrum. The use of the mirror is a requirement for the type of interrogators used in this study, which operate in reflection and not in transmission, but it also adds the benefit of a narrower reflected signal as a consequence of the double pass through the filter. Figure 1 shows the shape and spectral width of the simulated FBG formed by the tunable filter and the fiber mirror used in our setup, as detailed below. A full-width at half-maximum (FWHM) bandwidth of 0.175 nm is achieved, similar to most common Bragg gratings used by the interrogators under calibration. The combination of the tunable filter and the fiber mirror results in a symmetric spectrum, typically Gaussian or Lorentzian. The slope symmetry of the ascending and descending flanks facilitates accurate peak measurement, regardless of the particular methodology implemented by the interrogator [10,15].

Spectrum and band-width of the simulated fiber Bragg grating (FBG) formed by the tunable filter and the fiber mirror.

The simulated FBG is alternately fed with the signal produced by a broadband source, such as a superluminescent diode (SLD) or the spontaneous emission from an Erbium Doped Fiber Amplifier (EDFA), and with the signal produced by the FBG interrogator under test. The switch further prevents any cross-talk between the broadband light source and the optical source of the FBG interrogator under test. In the first case (i.e., with SLD or EDFA illumination), the reflected peak is measured with a calibrated wavelength meter (WM), which acts as the reference to which the interrogator is compared. Furthermore, by performing both measurements under the same conditions, any environmental effects which may affect the simulated Bragg grating are inherently incorporated into both measurements and do not result in deviations of the correction constants. The setup is depicted in Figure 2.

Setup of the first calibration method, based on a simulated fiber Bragg grating.

The wavelength obtained with the FBG interrogator under test (λ_FBGI) and the wavelength measured with the WM (λ_WM) are compared for multiple wavelengths, selected by the tunable filter along the range of measurement of the FBG interrogator. The correction constant of the FBG interrogator at any wavelength (K_λ) is hence calculated as:

The identified components of uncertainty in the determination of K_λ are the WM calibration, the WM accuracy due to the linewidth of the simulated tunable FBG, and the repeatability of the reference, all of them affecting λ_WM, as well as the optical resolution, the display resolution, and the on-off repeatability of the interrogator affecting λ_FBGI. The main sources of uncertainty arise as a consequence of the spectral width of the simulated tunable FBG, which affects the WM accuracy and the repeatability of the reference. For the particular case of a WM based on a Michelson interferometer and a He-Ne reference laser [19,20,21], the attainable wavelength accuracy is influenced by several sources of systematic errors [22]: the uncertainty in the knowledge of the reference laser wavelength, the accuracy of measuring the refractive index of air, the alignment of the reference laser beam and the input laser beam in the Michelson interferometer, diffraction effects along the beam path, and the fringe counting error, which is inversely proportional to the signal bandwidth.

Compared to using calibrated FBGs as wavelength references [15], our method presents the advantage of not being affected by strain and temperature, as the wavelength measured by the interrogator is compared to a reference provided by the wavemeter in the same environmental conditions, instead of a nominal value which may not represent the actual operating conditions of the calibrated FBGs. Although, in principle, a set of athermal calibrated FBGs could be used instead of the proposed simulated FBG, the latter presents the advantage that its peak wavelength can be finely or coarsely tuned to any value within the operating range of the interrogator, and that the shape of the spectrum is symmetrical (see Figure 1) and kept constant throughout the whole range. This means that the component of uncertainty in the determination of λ_WM due to the FBG linewidth, which is one of the main components of uncertainty in the determination of K_λ, is constant, and thus there is no need to characterize the reflection spectra of all of the FBGs to ensure that their spectral characteristics remain unaltered.