In this paper, we present new phase-shifting algorithms (PSAs) that suppress the ripple distortions and spurious pistons in phase-shifting interferometry. These phase errors arise when non-uniform phase-shifting interferograms are processed with PSAs that assume uniform phase shifts. By modeling the non-uniform phase shifts as a polynomial of the unperturbed phase-shift value $\omega_0$ω0, we show that the conditions for eliminating the ripple distortion and the spurious piston are associated with the $m$mth derivative of the PSA's frequency transfer function (FTF). Thus, we propose an approach to design robust algorithms based on the FTF formalism and we present four ready-to-apply PSAs formulas. Finally, our conclusions are supported by computer simulations.

中文翻译：

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抑制相移干涉仪中的波纹失真和伪活塞。

在本文中，我们提出了新的相移算法（PSA），该算法可抑制相移干涉术中的波纹失真和伪活塞。这些相位误差是在假设相移均一的PSA处理不均匀相移干涉图时产生的。通过将非均匀相移建模为不受干扰的相移值$ \ omega_0 $ω0的多项式，我们表明消除脉动失真和伪活塞的条件与PSA的$ m $ mth导数相关频率传递函数（FTF）。因此，我们提出了一种基于FTF形式主义设计鲁棒算法的方法，并提出了四个现成的PSA公式。最后，我们的结论得到了计算机仿真的支持。