<title>Reconstruction of a decentered wavefront from several phase-shifted noisy interferograms</title>

Abstract

Abstract A new method to determine unambiguously the phase from several phase-shifted interferograms (intensityfringe patterns) has recently been demonstrated. This method is applied to very noisy interferograms,specifically to the case of four phase-shifted interferograms, to demonstrate the phase determinationprocedure. Key Terms: Noisy interferograms, Fringe analysis, Phase determination, Wavefront reconstruction, Phase shifting interferometry, Phase unwrapping Summary Recently we developed a new method to obtain a phase without performing the phase unwrapping. 1,2 The phase is reconstructed using the line integration ofthe phase gradient. In this manuscript, we apply the algorithm to a series ofnoisy interferograms that were generated from a known phase.The test wavefront has been constructed to include polynomials in x, polynomials in y, and mixed terms todetermine if this noisy and complex wavefront can be reconstructed. It exhibits higher order sphericalaberration, and higher order coma. These aberrations are ofinterest in testing high performance opticalsystems built with off-axis aspherical segments.3