We have already made mention of that at the beginning of the chapter: for the fringes of an interferogram to be visible, the optical path difference between the waves need to be shorter than the coherence length of the source lc which is equal to:
where is the central wavelength and is the spectral width of the source.
Generally laser diodes' coherence lengths are within dozens of centimeters and meters, whereas LED's (Light Emitting Diodes) ones vary from dozens to several hundreds of micrometers. Consequently, by illuminating an interferometer with a low coherence source, it is possible to determine the position for which the optical path difference is null: you have to find the position where the fringes have the best visibility. You can use this technique to resolve the ambiguity related to fringes order (i.e. the real displacement of the fringe system) which is a recurrent problem in interferometry. Then the measure range is widened.
It is possible to measure the optical path difference of an interferometer by using the configuration shown on Figure 12. This assembly is made of a double interferometer, one which is used in sensing and the other which is receiving and which OPD we can control. For a better understanding of the second interferometer's role, let's study the influence of the second interferometer's control OPD on the intensity seen by the detector. If the OPD is near zero, fringes are visible. When the OPD is increased beyond the coherence length of the source, the fringes disappear. If you increase even more its OPD so that it comes closer to the sensing interferometer's OPD, interferences can appear again. These interferences are obtained between the two next waves if their phase difference is smaller than the coherence length of the source:
Wave 1: the wave which takes the longer path in the sensing interferometer and the shorter path in the receiving
Wave 2: the wave which takes the shorter path in the sensing interferometer and the longer path in the receiving
Consequently, the fringe visibility shows a local maximum, as shown on Figure 13, when both measuring and receiving interferometers have equal OPD. When the OPD is defined, you immediately get the measurand.
In practice, there are different ways to make an interferometer's OPD vary. The simplest methods are based on the displacement of a reflector which is put on a motorized linear stage so that you can make the length of the interferometer's arms vary . This method is simple and has a wide range of possible variations, but its drawback is its being in open space. So you have to bring the light out of the fiber to inject it back, so that you create leakages. Furthermore, you need to be extremely precise when positioning the opto-mechanical elements. Nevertheless it is possible to accomplish a length variation without bringing the light out of the fiber: you have to stick the fiber on a piezoelectrical element which dilates or reduces according to the electrical signal you give to it. But this technique has a very limited range of variation.