通过空间滤波从非线性间隔相移干涉图进行高精度时间干涉测量
High-precision temporal interferometry from nonlinearly-spaced phase-shifted interferograms through spatial-filtering
摘要：
提出了一种适用于随机/系统相移误差影响下的相移干涉测量的高精度时空相位解调算法。标准光学车间中的激光干涉仪受到包括随机相移偏差在内的多种误差源的影响。即使是校准的移相器也不能达到浮点线性精度，这是在多媒体视频投影仪中进行条纹投影轮廓测量时经常得到的。在标准的光学车间中，校准的相移干涉仪仍然在受控的实验室条件下遭受由于振动、湍流和环境波动（温度、压力、湿度、空气成分）引起的非线性。这些随机相位阶跃误差（即使它们很小）增加了相位测量的不确定性。如果波前容差被收紧到高精度光学器件，这是特别重要的。我们表明，这些相位步误差排除了高精度波前测量，因为它的不确定性增加到λ/10左右。我们开发了一个基于光学波前形式主义的解析表达式，表明这些相位阶跃非线性出现作为一个虚假的共轭信号降低所需的波前。去除这种寄生共轭构成了所提出的非线性相移算法（nPSA）的中心目标。使用这种nPSI算法，我们解调实验干涉图受到小振动和移相器的非线性，获得高精度的无杂散，解调波前。我们表明，我们的无伪影，时间-空间正交滤波，实现了一个等效的波前精度从浮点线性相移干涉术。
英文摘要：
We present a high-precision temporal-spatial phase-demodulation algorithm for phase-shifting interferometry (PSI) affected by random/systematic phase-stepping errors. Laser interferometers in standard optical-shops suffer from several error sources including random phase-shift deviations. Even calibrated phase-shifters do not achieve floating-point linear accuracy, as routinely obtained in multimedia video-projectors for fringe-projection profilometry. In standard optical-shops, calibrated phase-shifting interferometers suffer from nonlinearities due to vibrations, turbulence, and environmental fluctuations (temperature, pressure, humidity, air composition) still under controlled laboratory conditions. These random phase-step errors (even if they are small), increases the uncertainty of the phase measurement. This is particularly significant if the wavefront tolerance is tightened to high precision optics. We show that these phase-step errors precludes high-precision wavefront measurements because its uncertainty increases to around lambda/10. We develop an analytical expression based on optical-wavefront formalism showing that these phase-step nonlinearities appear as a spurious conjugate signal degrading the desired wavefront. Removing this spurious conjugate constitutes the central objective of the proposed nonlinear phase-shifting algorithm (nPSA). Using this nPSI algorithm we demodulate experimental interferograms subject to small vibrations and phase-shifter nonlinearities, obtaining a high-precision spurious-free, demodulated wavefront. We show that our artifact-free, temporal-spatial quadrature filtering, accomplishes an equivalent wavefront precision as the one obtained from floating-point linear phase-shifting interferometry.
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