A coordinate-transform technique is proposed that enables the Fourier-transform method to analyze an interferogram that includes a closed-fringe pattern. First, the closed-fringe pattern is converted to an open-fringe pattern by transformation of the Cartesian coordinate system to a polar coordinate system. Then the phase distribution for the open-fringe interferogram is determined by the conventional Fourier-transform method. The phase distribution for the original closed-fringe pattern is obtained by inverse coordinate transformation from the polar coordinate system back to the Cartesian coordinate system. Computer simulation and experiments were performed for a closed-fringe pattern generated by interference of a spherical wave with a reference plane wave, and results are presented that demonstrate the validity of the proposed technique.
© 2001 Optical Society of America
Zongtao Ge, Fumio Kobayashi, Shinichi Matsuda, and Mitsuo Takeda, "Coordinate-Transform Technique for Closed-Fringe Analysis by the Fourier-Transform Method," Appl. Opt. 40, 1649-1657 (2001)