Three beams Phase-shifting interferometry by their amplitude variation

A novel phase shifting interferometry method based on the variation of the electric field under the scheme of a three beams interferometer is proposed. One beam contains the object under study, that makes this beam the probe beam; the other two will be consider as the reference beams with a phase difference of pi/2. Due to this, one of the three resulting interference terms will be cancelled and the two remaining will be in quadrature. Applying some trigonometric identities, we show that the resulting interference pattern could become modeled by the interfering of two beams with an additional phase term; we obtain that the tangent function of the additional phase depends on the division of the amplitude of the third field divided by the amplitude of the first, and it is possible to group the sum of the squares of these fields in a square amplitude. To recover the phase by using the phase shifting interferometry techniques it is necessary to keep constant the visibility of the interference pattern, at first sight we can think that this is not possible because the variations of the field amplitude affect the visibility of the patterns. However this problem is solved if the values of the amplitude corresponding to the fields one and three are seen as an ordered pair contained over an arc segment at the first quadrant. We justify the viability of this method by a theoretical analysis and a numerical simulation of the interference of three beams under the conditions mentioned above.