There was a long-standing postulation that the precision of weak-value based metrology using post-selection and spectral analysis is limited by the resolution of spectrometer. Current proposals releasing this limitation require either initially Gaussian spectrum or giving up the weak value amplification approximation, both of which make extra restrictions and increase the difficulty of implementation. However, we find that this compromise is unnecessary. Rather than the spectral resolution, the precision of weak-value based metrology mainly relies on how accurate we know about the initial pointer state. Moreover, the relation between knowledge of the initial pointer state and the error-ratio of output is provided and numerically simulated. Our results suggest that the detection devices of weak-value based metrology can be significantly simplified, thus made it a more convenient technique for real-world applications.

中文翻译：

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光谱分辨率对基于弱值的参数估计的影响

长期存在的假设是，使用后选择和光谱分析的基于弱值的计量精度受光谱仪分辨率的限制。释放此限制的当前建议要求最初是高斯频谱或放弃弱值放大近似值，这两者都带来了额外的限制并增加了实现的难度。但是，我们发现这种折衷是不必要的。基于弱值的度量而不是频谱分辨率，主要取决于我们对初始指针状态的了解程度。此外，提供了初始指针状态的知识与输出的误差比之间的关系并进行了数值模拟。我们的结果表明，基于弱值的度量衡的检测设备可以大大简化，