The figure shows the behavior of the limit of the localization accuracy of the

*x*_{0} (

*y*_{0}) coordinate of a single-molecule/point-source as a function of defocus distance. Panel A shows the fundamental limit of the 3D localization accuracy

that is given in (●). The fundamental limit of the 2D localization accuracy

that is given in is also shown for reference (—). Panel B shows the limit of the 3D localization accuracy for

*x*_{0} (

*y*_{0}) for a pixelated detector in the absence of noise sources (○), and panel C shows the same in the presence of noise sources (◇). Panels B and C also show the 3D fundamental limit

(●) and the limit of the 3D localization accuracy of

*z*_{0} in the absence of noise sources (○), respectively for reference. In all the plots the photon detection rate is set to be Λ

_{0} = 5000 photons/s, the acquisition time is set to be

*t* = 0.1 s (with

*t*_{0} = 0), the numerical aperture is set to be

*NA* = 1.3, the magnification is set to be

*M* = 100, the wavelength of the detected photons from the single molecule is set to be λ = 520 nm, the pixel array size is set to be 5 × 5, the pixel size is set to be 13

*μm* × 13

*μm*, the mean of the Poisson noise component is set to be

*β*(

*k, t*) = 25 photons/pixel, and the mean and the standard deviation of the Gaussian noise component are set to be

*η*_{k} = 0 and

*σ*_{w,k} = 8

*e*^{−} rms, respectively. The noise statistics are assumed to be the same for all the pixels and the image of the single molecule is assumed to be centered on the pixel array.

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