Abstract
The combination of two opposing objective lenses in 4Pi fluorescence microscopy significantly improves the axial resolution and increases the collection efficiency. Combining 4Pi microscopy with other super-resolution techniques has resulted in the highest three-dimensional (3D) resolution in fluorescence microscopy to date. It has previously been shown that the performance of 4Pi microscopy is significantly affected by aberrations. However, a comprehensive description of 4Pi microscope aberrations has been missing. In this paper, we introduce an approach to describe aberrations in a 4Pi cavity through a new functional representation. We discuss the focusing properties of 4Pi systems affected by aberrations and discuss the implications for adaptive optics schemes for 4Pi microscopes based on this new insight.
Highlights
The resolution of fluorescence microscopy is largely determined by the extent of the pointspread function (PSF)
In 4Pi microscopy, the laser beam in a confocal laser scanning microscope is divided into two arms that are focused by two opposing objectives into a common spot, creating an interferometric cavity
It is interesting to note that the approach we present here for forming any aberration in 4Pi microscopy based on the Zernike functions, is valid for any other basis that is complete and orthogonal on a single pupil
Summary
The resolution of fluorescence microscopy is largely determined by the extent of the pointspread function (PSF). We introduce a set of basis functions based on Zernike polynomials [13, 14] that express practically relevant physical phenomena such as interference fringe shifts, focal displacements, and distortions such as astigmatism, coma and spherical aberrations Using this new basis, we examine their effects on the 4Pi focal intensity in a polarizationindependent and dependent manner. In single-objective systems, the Zernike polynomials are convenient as the lower order modes tip, tilt and defocus correspond to focal shifts in three dimensions, whereas higher order modes relate to coma, astigmatism, spherical aberration and so on. Any sufficiently smooth real-valued phase function Φ (r ) ∈ 2 defined in the two pupils can be split into two phase functions defined in the upper and lower pupil, respectively These phase functions in turn can be expressed as linear combinations of Zernike modes, which form a complete basis in each individual objective pupil:.
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