Reply to comment on “Phase-shift extraction and wave-front reconstruction in phase-shifting interferometry with arbitrary phase steps”

TLDR: In this article, it was shown that the phase shift procedure is still necessary for correct reconstruction of the object wave field and that the statistical approximation used in our previous Letter [Opt. Lett.28, 1808] is reasonable for most objects, including both smooth and diffusing surfaces.

Abstract: In answer to the questions raised by Ferrari Garbusi [Opt. Lett.29, 1257 (2004)] we indicate that, even if the intensities of the object and reference waves can be measured, the phase-shifting procedure is still necessary for correct reconstruction of the object wave field. We also show that the statistical approximation used in our previous Letter [Opt. Lett.28, 1808 (2003)], sin φox,y=2/π, where φox,y is the phase of a diffraction field and means average over the whole interferogram frame, is reasonable for most objects, including both smooth and diffusing surfaces, and that the method we proposed for phase-shift extraction is correct.