A method based on the fractional Fourier ridges for accurate phase demodulation of a single interferogram withquadratic phase is presented. The interferograms being analyzed may contain circular, elliptic or astigmaticfringes. In signal processing field, such interferograms can be called 2-D chirp-type signals. Since the fractionalFourier transform (FRFT) of a chirp signal is a function under the matched angle that is determined by chirprates of the signal, so the method can be used to match the multiple chirp rates in chirp-type signals with multiplechirp components. In this work, the FRFT of all row (column) signals are firstly calculated, and the ridge ofthe FRFT amplitude of each row (column) signal in FRFT domain is recorded. Repeat the above process foreach angle of a searching range. Then a ridge tracking approach is employed to determine the matched angle,which can be used to calculate the coefficient of the square term of row (column) coordinates. Moreover, underthe matched angle, the ridge of the FRFT amplitude of each row (column) signal all lie on a straight line. Theslope and constant term of the line can be used to calculate the coefficient of the linear term of row (column)coordinates and the coefficient of cross term, respectively. The same procedures are implemented to all column(row) signals to determine the coefficients of the square and liner term of column (row) coordinates. Accordingto the obtained coefficients, the phase of the fringe pattern can be constructed without phase unwrappingoperation. Furthermore, the present procedure is also capable of analysis of interferograms with or withoutcircularly symmetry fringe distribution instead of using complex and time consuming algorithms for recoveringphase from fringe patterns with closed fringes. Finally, the method is tested in simulated and real data.
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