A novel approach to determining the three-dimensional location of microscopic objects with applications to 3D particle tracking

Abstract

Recent technological advances have rendered widefield fluorescence microscopy as an invaluable tool to image fast dynamics of trafficking events in two dimensions (i.e., in the plane of focus). Three-dimensional trafficking events are studied by sequentially imaging different planes within the specimen by moving the plane of focus with a focusing device. However, these devices are typically slow and hence when the cell is being imaged at one focal plane, important events could be missed at other focal planes. To overcome this limitation, we recently developed a novel imaging technique called multifocal plane microscopy that enables the simultaneous imaging of multiple focal planes within the sample. Here, by using tools of information theory, we present a quantitative evaluation of this technique in the context of 3D particle tracking. We calculate the Fisher information matrix for the problem of determining the 3D location of an object that is imaged on a multifocal plane setup. In this way, we derive a lower bound on the accuracy with which the object can be localized in 3D. We illustrate our results by considering the object of interest to be a single molecule. It is well known that a conventional widefield microscope has poor depth discrimination capability and therefore there exists significant uncertainty in determining the axial location of the object, especially when it is close to the plane of focus. Our results predict that the multifocal plane microscope setup offers improved accuracy in determining the axial location of objects than a conventional widefield microscope.

Super-resolution photon-efficient imaging by nanometric double-helix point spread function localization of emitters (SPINDLE)

“…The fundamental localization precision of a system is determined by the PSF, the number of photons detected, the numerical aperture, and noise; along with other practical parameters such as PSF sampling. This fundamental limit is defined by the Cramer-Rao lower bound (CRB), which is the best achievable precision by any unbiased estimator, estimator CRB σ ≥ [18,22,27]. For transverse shift-invariant and axial shift-variant systems, the CRB associated with localization along each of the three dimensions is a function of the axial position z.…”

Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function

“…In the third (z) dimension, diffraction also limits resolution to Ϸ2n /NA 2 with n the index of refraction, corresponding to a depth of field of Ϸ500 nm in the visible wavelength region with modern microscopes. Improvements in 3D localization beyond this limit are also possible by using astigmatism (10,11), defocusing (12), or simultaneous multiplane viewing (13).…”

A PSF-based approach to Biplane calibration in 3D super-resolution microscopy

“…The PSF model allows one to introduce refractive index mismatch, which results in a non-symmetric PSF pattern (Figure 4). This, in turn, allows us to achieve a relatively high localization accuracy [8]. Calibration results are given in Table 2, demonstrating the accuracy of the proposed approach.…”

“…Motivated by accuracy analysis of particle localization in super-resolution microscopy [5,6,7,8], we use a realistic PSF model of a microscope that takes both defocusing and refractive index mismatch into account. We introduce a calibration procedure that uses a z-stack of fixed particles.…”