Phase-map measurements by interferometry with sinusoidal phase modulation and four integrating buckets

Phase-shifting interferometry based on the integrating-bucket technique wit h sinusoidal phase modulation is studied theoretically and demonstrated exp erimentally to obtain phase maps from double-beam interferometers. The meth od uses four frames obtained by integration of the time-varying intensity i n an interference pattern during the four quarters of the modulation period . An optimum sinusoidal phase modulation is found to minimize the effect of the additive noise. The absolute accuracy of the phase measurements is dis cussed. Possible applications of the method are demonstrated with two inter ference microscopes with which the phase modulation is achieved by sinusoid al oscillation of a mirror attached to a piezoelectric transducer and by si nusoidal birefringence modulation with a photoelastic modulator. images can be produced in real time at a rate of several hertz. pared with theory. (C ) 2001 Optical Society of America.