A robust spatial phase-stepping ESPI system

A new algorithm is described that uses only two mutually phase-shifted interferograms per deformation state and a mean intensity in order to retrieve the phase signal modulo 2 pi due to displacement. The algorithm was designed for spatial phase-stepping ESPI where the initial phase in the interference term is the phase of speckle that varies randomly over the imaging sensor. An analysis of phase measurement error is presented. System error sources considered here are imperfect phase stepping, variation of modulation depth and intensity noise. The algorithm was implemented into an out-of plane sensitive interferometer for experimental verification. The paper discusses practical advantages, present limitations and possible future enhancements of the system. Obtained experimental results prove that phase measurement uncertainties smaller than 2 pi /15 are feasible.