The use of phase-shifting interferometry (PSI) in the ultra-low-light region would open the way for important applications, such as imaging of phototoxic substances and sensing of ultrafast phenomena. In the ultra-low-light region, the statistical nature of photons can be a dominant source of noise compared with other noise caused by experimental instruments. Here we theoretically derive the precision limit determined by the statistical nature of photons for simultaneously measuring the transmittance and phase of a sample with PSI. We show that the precision of PSI depends on the phase and transmittance themselves. We also show a trade-off relation between transmittance and phase. Then we compare PSI with sequential optimal measurements in which the transmittance and phase of a sample are separately measured for each corresponding optimal measurement. We also discuss the case where the input number of photons fluctuates with a Poisson distribution and show that the fluctuation affects both the transmittance and phase precision for PSI.

中文翻译：

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使用相移干涉法同时估计相位和透射率的精度限制

在超低光区域使用相移干涉仪 (PSI) 将为重要应用开辟道路，例如光毒性物质的成像和超快现象的传感。在超低光区域，与实验仪器引起的其他噪声相比，光子的统计性质可能是主要的噪声源。在这里，我们从理论上推导出由光子的统计性质决定的精度极限，用于同时测量具有 PSI 的样品的透射率和相位。我们表明 PSI 的精度取决于相位和透射率本身。我们还展示了透射率和相位之间的权衡关系。然后，我们将 PSI 与连续最优测量进行比较，其中针对每个相应的最优测量分别测量样品的透射率和相位。我们还讨论了输入光子数以泊松分布波动的情况，并表明波动会影响 PSI 的透射率和相位精度。