Statistical properties of phase-shift algorithms are investigated for the case of additive Gaussian intensity noise. Based on a bivariate normal distribution, a generally valid probability-density function for the random phase error is derived. This new description of the random phase error shows properties that cannot be obtained through Gaussian error propagation. The assumption of a normally distributed phase error is compared with the derived probability-density function. For small signal-to-noise ratios the assumption of a normally distributed phase error is not valid. Additionally, it is shown that some advanced systematic-error-compensating algorithms have a disadvantageous effect on the random phase error.
© 1995 Optical Society of America
Original Manuscript: September 19, 1994
Revised Manuscript: March 15, 1995
Manuscript Accepted: March 29, 1995
Published: September 1, 1995
C. Rathjen, "Statistical properties of phase-shift algorithms," J. Opt. Soc. Am. A 12, 1997-2008 (1995)