Phillion D W
Appl Opt. 1997 Nov 1;36(31):8098-115. doi: 10.1364/ao.36.008098.
Two completely independent systematic approaches for designing algorithms are presented. One approach uses recursion rules to generate a new algorithm from an old one, only with an insensitivity to more error sources. The other approach uses a least-squares method to optimize the noise performance of an algorithm while constraining it to a desired set of properties. These properties might include insensitivity to detector nonlinearities as high as a certain power, insensitivity to linearly varying laser power, and insensitivity to some order to the piezoelectric transducer voltage ramp with the wrong slope. A noise figure of merit that is valid for any algorithm is also derived. This is crucial for evaluating algorithms and is what is maximized in the least-squares method. This noise figure of merit is a certain average over the phase because in general the noise sensitivity depends on it. It is valid for both quantization noise and photon noise. The equations that must be satisfied for an algorithm to be insensitive to various error sources are derived. A multivariate Taylor-series expansion in the distortions is used, and the time-varying background and signal amplitudes are expanded in Taylor series in time. Many new algorithms and families of algorithms are derived.
本文提出了两种完全独立的算法设计系统方法。一种方法使用递归规则从旧算法生成新算法，只是对更多误差源不敏感。另一种方法使用最小二乘法在将算法约束为一组期望属性的同时优化其噪声性能。这些属性可能包括对高达特定功率的探测器非线性不敏感、对线性变化的激光功率不敏感以及对具有错误斜率的压电换能器电压斜坡的某一阶不敏感。还推导了对任何算法都有效的噪声品质因数。这对于评估算法至关重要，并且是最小二乘法中最大化的目标。这个噪声品质因数是相位上的某种平均值，因为一般来说噪声灵敏度取决于相位。它对量化噪声和光子噪声都有效。推导了算法对各种误差源不敏感时必须满足的方程。使用了失真的多元泰勒级数展开，并且时变背景和信号幅度在时间上展开为泰勒级数。推导了许多新算法和算法族。
