Interference and fringe pattern demodulation

Illustrations

This paragraph presents an illustration of the phase stepping method. We consider an interferogram with a fringe pattern such as the one represented on figure 13.


   
    Figure 13 : instantaneous interferogram
Figure 13 : instantaneous interferogram [zoom...]

We now apply the phase stepping method with 4 phase steps separated by , generated (for example) with a piezoelectric transducer. Figure 14 shows the 4 shifted interferograms, obtained with phase steps of 0, , and respectively.


   
    Figure 14 : phase shifted interferograms
Figure 14 : phase shifted interferograms [zoom...]

As we have seen previously, the phase can be calculated using the following relation:

Figure 15 shows the results obtained after applying the algorithm to the 4 shifted interferograms.


   
    Figure 15 : wrapped phase estimated using the 4 shifted interferograms
Figure 15 : wrapped phase estimated using the 4 shifted interferograms [zoom...]

The phase is only obtained modulo , thus producing the phase jumps observed on the figure. When we apply a phase unwrapping algorithm, we obtain the result shown on figure 16.


   
    Figure 16 : unwrapped phase
Figure 16 : unwrapped phase [zoom...]

The reader will note that the 0 value of the phase measurement is arbitrary and depends on the starting point of the phase unwrapping algorithm. This level can therefore be adjusted if it is possible to know a point in the phase map where the phase is really equal to 0.

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