Diffraction by a circular aperture as a model for three-dimensional optical microscopy

Abstract

Existing formulations of the three-dimensional (3-D) diffraction pattern of spherical waves that is produced by a circular aperture are reviewed in the context of 3-D serial-sectioning microscopy. A new formulation for off-axis focal points is introduced that has the desirable properties of increased accuracy for larger field angles, invariance to shifts of the focal point about spheres of constant radius when the detection point is on the sphere for both intensity and amplitude fields, and invariance to shifts in three transformed coordinates for intensity fields. Finally, calculated intensity fields for both on-axis and off-axis focal points are included to illustrate the proposal that the classical 3-D diffraction patterns that have been used as analytical models in 3-D serial-sectioning fluorescence microscopy may not be accurate enough for this application.

Ultrahigh-resolution multicolor colocalization of single fluorescent probes

“…Improvements in speed and feedback-loop control of the mechanical and thermal drift of the sample stage will allow the extension of this work to three dimensions. 3D multicolor colocalization also will require a detailed characterization of the volume shape of the PSF, which is very sensitive to the thickness and index of refraction of the coverslip, as well as to the indices of the physiological buffer͞embedding matrix and the immersion oil (39,40).…”

Method of lateral image reconstruction in structured illumination microscopy with super resolution

“…11 Since theoretical model allows the numerical calculation of PSF in various systems and conditions, in this work we modeled the PSF of a conventional microscope by using the scalar di®raction approach. [11][12][13] According to the Kirchho®-Fraunhofer approximation, the near-focus three dimensional (3D) PSF in a wide¯eld imaging system can be written as follows: 11 hðx; y; z; em Þ ¼ FTfP ðk x ; k y ; z; em Þg; ð1Þ where ðx; y; z; em Þ denotes the distance coordinate on the detector plane at the wavelength em of emission light; ðk x ; k y Þ indicates the spatial frequency coordinate on the z-stack planes near the exit pupil (z ¼ 0) of microscope. P ðk x ; k y ; z; em Þ represents the two-dimensional (2D) exit pupil function of the objective (at each defocus z).…”

Blind deconvolution for thin-layered confocal imaging

“…This approach is however handicapped by alignment problems and also the whole process could take a long time. The alternative would be to use an analytical model of the PSF [11,12] that takes into account the acquisition system's physical information as parameters. This information however might not be available or might change during the course of the experiment (for example, due to heating of live samples).…”

“…From (10) and (12), it can be inferred that sites with very high total gradient intensities are more penalized and those with low total gradients are less penalized. This is because it is more likely that high gradients correspond to the case where there is less similarity between the site of interest and their closest neighbors.…”