光干涉测量中功率谱和双谱的检测噪声偏差和方差
Detection noise bias and variance in the power spectrum and bispectrum in optical interferometry
摘要：
长基线光学干涉测量法使用功率谱和双谱结构作为基本观测量。在检测条纹图案时产生的噪声引起功率谱和双谱中的方差和偏差。以前的工作，纠正这些数量的偏差和估计的方差通常包括限制性的假设的采样的干涉图和/或关于泊松和高斯噪声源的相对重要性。到目前为止，很难准确地补偿违反这些假设的数据中的系统性偏差。我们寻求一种形式主义，允许建设的双谱和功率谱的无偏估计，并估计其方差，在限制性较低的条件下，其中包括不均匀采样的数据和测量的噪声源与泊松和高斯统计相结合的影响。我们使用了一种基于噪声分布的矩的方法，推导出公式的偏见时，复杂的条纹振幅来自一组离散的干涉测量的任意线性组合的功率谱和双谱。我们模拟了具有不同光子噪声和读取噪声组合以及具有不同条纹编码方案的干涉图，以说明这些偏差的影响。我们已经推导出公式的无偏估计的功率谱和双谱，它可以与任何线性估计的条纹复振幅。我们已经证明了无偏估计的情况下，微弱的同伴（例如系外行星）使用关闭相位调零检测的重要性。我们已经推导出公式的功率谱的方差，并已显示如何方差的双谱可以计算。
英文摘要：
Long-baseline optical interferometry uses the power spectrum and bispectrum constructs as fundamental observables. Noise arising in the detection of the fringe pattern gives rise to both variance and biases in the power spectrum and bispectrum. Previous work on correcting the biases and estimating the variances for these quantities typically includes restrictive assumptions about the sampling of the interferogram and/or about the relative importance of Poisson and Gaussian noise sources. Until now it has been difficult to accurately compensate for systematic biases in data which violates these assumptions. We seek a formalism to allow the construction of bias-free estimators of the bispectrum and power spectrum, and to estimate their variances, under less restrictive conditions which include both unevenly-sampled data and measurements affected by a combination of noise sources with Poisson and Gaussian statistics. We used a method based on the moments of the noise distributions to derive formulae for the biases introduced to the power spectrum and bispectrum when the complex fringe amplitude is derived from an arbitrary linear combinations of a set of discrete interferogram measurements. We simulated interferograms with different combinations of photon noise and read noise and with different fringe encoding schemes to illustrate the effects of these biases. We have derived formulae for bias-free estimators of the power spectrum and bispectrum which can be used with any linear estimator of the fringe complex amplitude. We have demonstrated the importance of bias-free estimators for the case of the detection of faint companions (for example exoplanets) using closure phase nulling. We have derived formulae for the variance of the power spectrum and have shown how the variance of the bispectrum could be calculated.
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