Improved formula of wavefront reconstruction from a radial shearing interferogram

A radial shearing (RS) interferogram obtained by the carrier fringe method is essentially the combination of radial and lateral shearing. The previous phase reconstruction algorithm neglects the effect of lateral shearing on the obtained RS interferogram. A mathematical formula for wavefront reconstruction from an RS interferogram is deduced. If the phase difference of the tested wavefront phase, the RS ratio s, and the laterally sheared amount X₀ in the x direction and y₀ in the y direction, respectively, have been determined, the tested wavefront phase can be precisely reconstructed using this formula. The result of simulation analysis and experiment shows that the formula is correct and more accurate.