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. Author manuscript; available in PMC: 2012 Jun 13.
Published in final edited form as: Opt Express. 2009 Dec 21;17(26):24377–24402. doi: 10.1364/OE.17.024377

Fig. 3.

Fig. 3

Dependence of the 3D resolution measure (i.e., the best possible standard deviation for distance estimation) for (a) the SIM-SNG, (b) the SEP-SNG, (c) the SIM-MUM, and (d) the SEP-MUM modality on the distance of separation d and the axial position sz of the imaged point source pair. In (a), (b), (c), and (d), the image of each point source in the pair is assumed to be described by the 3D point spread function of Born and Wolf. Each point source emits photons of wavelength λ = 655 nm, which are detected at a rate of Λ1 = Λ2 = 5000 photons per second. The image acquisition time is set to 1 second per image. The refractive index of the object space medium is set to n = 1.515, and the numerical aperture and the magnification of the objective lens are set to na = 1.4 and M = 100, respectively. A single image consists of a 21×21 array of 13 μm by 13 μm pixels, and the position of the point source pair in the xy-plane is set to sx = sy = 1365 nm, such that its image is centered on the pixel array given the 100-fold magnification. The point source pair is oriented such that it forms a 45° angle with the positive z-axis (ω = 45°) and projects at a 60° angle from the positive x-axis in the xy-plane (φ = 60°). In (c) and (d), the spacing between the two focal planes is set to Δzf = 500 nm. The first focal plane corresponds to the focal plane of the modalities in (a) and (b), and is located at sz = 0 nm with an associated magnification of 100. The second focal plane is located above the first at sz = 500 nm, and its associated magnification is set to M′ = 97.98 (computed using Eq. (12) by assuming a standard tube length of L = 160 mm). The collected photons are assumed to be split 50:50 between the two focal planes. In (a) and (b), the mean of the background noise in each image is assumed to be a constant and is set to β(k) = 80 photons per pixel. In (c) and (d), however, it is set to β(k) = 40 photons per pixel due to the equal splitting of the collected fluorescence. In (a), (b), (c), and (d), the mean and the standard deviation of the readout noise in each image are respectively set to ηk = 0 e− and σk = 8 e− per pixel.