4.3        New OLCR set-ups

4.3.2       Measurement principle

Small perturbations (e.g. temperature variations) in both interferometer arms modify the optical path length difference (OPLD) and determine the phase drifts. Typical variations of 2p in the OLCR or laser phase signal are possible in a few seconds. For complex OLCR measurements, these phase drifts have to be either limited by very fast measurements or compensated by another reference laser signal when the measurements are slow. Two main complex OLCR measuring methods has been studied :

-         Dynamic method : moving the mirror at constant speed produces a Doppler frequency used to measure the real part amplitude; the imaginary part is calculated by an Hilbert transformation and subsequently the complex response is obtained [4-2]

-         Static method : for a given mirror position, the OPLD is ramp modulated over a multiple of the interference period producing a quasi sinusoidal signal (Fig. 4-8); a dual-phase lock-in amplifier then directly derives the amplitude and phase signals

Both methods have their own advantages and drawbacks :

-         Dynamic method : the main advantages are the high speed (e.g. 42-m/s with rotating mirror cubes [4-9]) and the small phase drifts; on the other hand, the signal to noise ratio (S/N) is limited by the shot noise of the detectors, the phase reconstruction using the Hilbert transform is not optimal for small signals and a constant mirror speed is needed; moreover, a high precision reference distance and an OPLD resolution that fulfills the Nyquist criteria (under l/2) are required

-         Static method : the main advantages are the high dynamic range (only limited by the fiber Raleigh scattering around -120 dB) and an OPLD resolution that is not limited by the Nyquist criteria as only the phase difference between the laser and the OLCR phases is measured, which is slowly varying with the OPLD; on the other hand the measurement is slow (3 min/mm in our set-up) due to the ramp modulation process at each position (150 Hz maximal frequency for piezoelectric plates) that limits the measurement speed and then requires to compensate the important phase drifts

The static method has been chosen for its high dynamic range that enables the measurement of weak FBGs. Fig. 4-8a shows the interference amplitude for the OPLD, z. The period is given by half the low coherence light source wavelength l/2. For a given mirror position z (stationary condition), the OPLD is ramp modulated at frequency f as seen in Fig. 4-8b. The time dependent signal measured by the detector (Fig. 4-8c) is a piecewise reconstructed sinus function obtained by concatenation of the interference signal over a period. The amplitude a(z) corresponds to the OLCR envelope amplitude and the phase difference b(z) between the ramp excitation and the signal minima gives the OLCR phase. The transition time between two ramps (between dotted and dashed lines) explains induced signal distortions that limit the modulation frequency. The reference laser signal is similar but the amplitude is nearly constant over the measurement range due to the much longer coherence length.

Fig. 4-8 Signal generation for OLCR set-ups with static method