超灵敏双波长相位计量的一般理论：无误差展开和信噪比
General theory for super-sensitive dual-wavelength phase metrology: error-free unwrapping and signal-to-noise ratio
摘要：
从1971年到2012年，双波长光学计量仅使用两个近灵敏条纹的解调低灵敏度相位差。Di等人在2013年首次报道了额外使用相位和的双波长相位计量[28];这是提高光学计量中相位精度的重要一步。然而，这篇论文及其衍生论文没有提供相位差和相位和的信噪比（SNR）的数学分析。两者都没有提供用于无误差地展开相位和的数学分析。本文给出了超灵敏双波长相位计量的一般理论。特别是数学分析和公式的信噪比和无误差的相位展开的双波长计量。首先，我们通过相移算法（PSA）的相位解调两个接近灵敏度的条纹。然后，我们计算它们的相位差和相位和;相位差被假设为非包裹的。然而，相位和是高度包裹的，超灵敏的，并且具有高得多的SNR。空间相位展开的高度不连续的相位总和被排除。然而，正如我们所示，有可能从噪声较大的相位差中无误差地解包噪声相位和。我们将这种超灵敏的相位计量理论应用于轮廓术，使我们能够获得超灵敏的高度测量。据我们所知，本文提出的SNR和无误差解缠的数学分析和公式以前没有报道过。
英文摘要：
From 1971 to 2012 dual-wavelength optical-metrology used only the demodulated low-sensitivity phase-difference of two close-sensitive fringes. Dual-wavelength phase-metrology that additionally uses the phase-sum was first reported by Di et al. in 2013 [28]; this was an important step to increase the phase-accuracy in optical metrology. This and its derived papers however do not offer mathematical analysis for signal-to-noise ratio (SNR) for the phase-difference and phase-sum. Neither provide the mathematical analysis for unwrapping the phase-sum without errors. Here a general theory for super-sensitive two-wavelength phase-metrology is given. In particular mathematical analysis and formulas for SNR and error-free phase-unwrapping for two-wavelength metrology is provided. We start by phase-demodulating two close-sensitivity fringes by phase-shifting algorithms (PSAs). We then calculate their phase-difference and their phase-sum; the phase-difference is assumed non-wrapped. However the phase-sum is highly wrapped, super-sensitive and has much higher SNR. Spatial phase unwrapping for a highly discontinuous phase-sum is precluded. However as we show, it is possible to unwrap the noisy phase-sum from the noisier phase-difference without errors. We apply this super-sensitive phase-metrology theory to profilometry allowing us to obtain super-sensitive height measurements. To the best of our knowledge the mathematical analysis and formulas herein presented for the SNR and error-free unwrapping have not been reported before.
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