Fienup J R
Appl Opt. 1997 Nov 10;36(32):8352-7. doi: 10.1364/ao.36.008352.
Expressions are derived for the normalized root-mean-square error of an image relative to a reference image. Different versions of the error metric are invariant to different combinations of effects, including the image's (a) being multiplied by a real or complex-valued constant, (b) having a constant added to its phase, (c) being translated, or (d) being complex conjugated and rotated 180 degrees . Invariance to these effects is particularly important for the phase-retrieval problem. One can also estimate the parameters of those effects. Similarly, two wave fronts can be compared, allowing for arbitrary constant (piston) and linear (tilt) phase terms. One can also include a weighting function. The relation between the error metric and other quality measures is derived.
推导了图像相对于参考图像的归一化均方根误差的表达式。误差度量的不同版本对于不同的效应组合是不变的，这些效应包括：(a) 图像乘以实值或复值常数；(b) 其相位加上一个常数；(c) 图像平移；或 (d) 图像进行复共轭并旋转180度。对于相位恢复问题，对这些效应的不变性尤为重要。还可以估计这些效应的参数。类似地，可以比较两个波前，同时考虑任意常数（活塞）和线性（倾斜）相位项。也可以包含一个加权函数。推导了误差度量与其他质量度量之间的关系。
