Point-spread sensitivity analysis for computational optical-sectioning microscopy

Experimentally determined point-spread functions (PSF) have been used routinely for reconstructions of three-dimensional (3-D) microscopic objects from optical sections (Agard et al., 1989, Meth. Cell Biol., 30: 353–377; Fay et al., 1986, Opt. Meth. Cell Physiol., 40: 51–63). The microscope's PSF is usually measured by imaging a small fluorescent bead. There is a tradeoff in this measurement: very small beads are dim and bleach rapidly, while larger beads are a poorer approximation to a point source.

We have simulated the effect of the bead's size on the shape of the PSF by convolving a theoretically determined PSF (of a 40 × 1.0 N.A. oil-immersion lens) with spheres of varying diameters. Simulated data were generated with a 3-D phantom and the theoretical PSF, which is defined to be the ‘true’ PSF for the simulation. Reconstructions of the phantom were obtained with each of the theoretical PSFs obtained from the beads using a regularized linear least-squares method (Preza et al., 1992, J. Opt. Soc. Am., 9: 219–228). Results show a significant drop (more than 50%) in the signal-to-noise ratio of the reconstructions for beads with diameter large than 0.22 μm. These results suggest that the bead used in the PSF measurement should have a diameter less than 30% of the diameter of the first dark ring of the infocus two-dimensional (2-D) PSF. This study quantifies the tradeoff between the quality of the reconstructions and the bead size used in the PSF measurement.