Camera influence on the phase-measurement accuracy of a phase-shifting speckle interferometer

In a real phase-shifting interferometer the camera (i.e., a photodetector plus an analog-to-digital converter) cuts off intensities above some saturation level and provides a limited number of digitization steps. Owing to the intensity statistics of speckle fields, this might severely influence the accuracy of the calculated speckle phase. The optimum beam ratio and the modulation of the camera are computed. To calculate the standard deviation of the phase difference, first, we derive a relation that shows that the variances of the two measured phase frames are equal and that they must be added with the decorrelation-dependent variance. To obtain the minimum phase-measurement error of 25.1 mrad, it is found that the mean speckle intensity ought to be adjusted to be 0.058 times the saturation intensity of the camera and that the beam ratio is to be 5.7. The results are confirmed by computer simulation of a two-wavelength speckle interferometer.