Is there need of any modulation in the pyramid wavefront sensor?

In the pyramid wavefront sensor some dynamic range is accomplished by modulating the optical signal across the four faces of the pyramid before the dissection and detection of the light. Although this can be realized in different ways, including systems which do not require any moving part, we question and discuss the real needs for such a modulation. In fact, when the closed-loop performance is not perfect, some residual errors on the wavefront sensor are expected and one should take care to allow for enough dynamic range to get a linear response within such a residual range. However, the non-corrected aberrations themselves can be considered as a form of modulation. Higher order uncompensated residuals are equivalent to a modulation for the lower compensated modes. We present a preliminary study showing that this sort of 'natural' modulation could be, at least under certain conditions, enough to reach comparable results with respect to dynamical modulation during correction, hence rising the question of the need of a modulation in the realization of the pyramid wavefront sensor.