Phase stepping

In this case, the phase modulation is a step that we maintain constant during the integration time of the detector [2,4]. We are not imposing a phase ramp as in the previous case but successive phase steps. The instantaneous signal therefore reads:

and the signal integrated by the detector during the time interval Δt, during which   is constant and equal to , can be written as:

Phase stepping is illustrated on figure 8.

The values registered for each phase step are represented on figure 9. The samples follow a sine wave (represented with a dotted line) with the same modulation and phase.

We consider the case where three images are registered with , and ; we obtain the following equation system:

By developing the cosine functions, we obtain :

and since:

we obtain Δφ the phase using an arctangent function:

The amplitude of fringes oscillation can be evaluated by:

and the constant component of the signal reads:

Therefore, we can determine the modulation ratio of the fringe pattern:

This technique is known as "phase stepping".