Experimental setup and Theory

A collimated laser beam was launched into an interferometric setup, as shown in fig. 1. The polarizer P₁ was aligned at 45⁰ ensures 50-50 splitting of light from polarizing beam splitter (PBS). The transmitted beam (only p-polarized light) from PBS passed through Quarter Wave Plate Q2 (QWP at 45⁰) converted into right circularly polarized (r.c.p.) light. The r.c.p. beam reflected from mirror M2, became left circularly polarized (l.c.p.) and passed back through Q2. It turned into s-polarized light and reflected completely from PBS. The reflected beam (only s-polarized light) after passing through Q₁, M₁ and back from Q₁ is converted into p-polarized light finally transmitted through PBS. So two orthogonal linearly polarized beams came out at the output of PBS. These orthogonal polarized beams produced fringe free pattern. To obtain the fringes, beams were passed through the third QWP Q₃ and then through the polarizer P and the interference pattern was finally recorded on to CCD.

Fig.1.

Experimental setup for phase shifting interferometry; Q₁, Q₂ and Q₃: quarter wave plates, M₁, M₁: mirrors, P₁, P₂: polarizers, PBS: polarizing beam splitter, CCD: charge coupled device.

For analyzing the effect of the azimuth angle of polarizer (and hence the phase shift) onto the interferograms, Q₁ to Q₃ were aligned at 45⁰ with respect to polarization plane of the incident beam on the respective QWP’s and P₂ was rotated. The resultant intensity at output plane can be shown to be given by^6,7

Where spatial frequency is the angular separation between the two interfering beams which can be controlled by the tilt of mirror M2, M1 being kept for the normal incidence. From above equation, if the analyzer is rotated by θ then 2θ phase difference is introduced between the two interfering beams and there will be corresponding fringe shift in the interference pattern, which is recorded onto CCD. The condition for minima for the nth order fringe from equation (1) is 2θ + μy = (2n # ½)π. If the spatial frequency μ is kept constant then the location of fringe for any particular order will change linearly with respect to the azimuth angle θ. The fringe shift is used to measure the corresponding phase shift as a function of θ which will also vary linearly with θ.

Results

The recorded interference patterns for θ= 0°, 45°, 90°, 135°, 180° on to CCD are shown in the fig.2. (a), (b), (c), (d), (e) respectively. From fig.2, it is clearly observed that 180° rotation of the analyzer gives one fringe shift confirming an additional phase difference of 2π is developed between the two interfering orthogonal beams. The plot of measured phase shift versus the azimuth of analyzer (θ) is shown in fig.3 The plot confirm that the phase shift goes linearly with the azimuth θ of analyzer P₂.

Fig.2.

Interference pattern recorded onto CCD for (a) θ= 0⁰, (b) θ=45⁰, (c) θ= 90⁰, (d)θ=135⁰, (e) θ=180⁰. (b) variation of phase shift as a function of azimuth of output polarizer.

Conclusion

We have experimentally observed the phase shift between the two orthogonal interfering beams using the set-up similar to Michelson interferometer and a quarter wave plate and an analyzer (rotating) at the output of the interferometer. We have recorded the interference pattern on to CCD and measured the fringe shift. The experiment can very well be performed using a photodiode mounted on the translation stage in place of CCD.