Spatio-angular fluorescence microscopy I. Basic theory

Abstract

We introduce the basic elements of a spatio-angular theory of fluorescence microscopy, providing a unified framework for analyzing systems that image single fluorescent dipoles and ensembles of overlapping dipoles that label biological molecules. We model an aplanatic microscope imaging an ensemble of in-focus fluorescent dipoles as a linear Hilbert-space operator, and we show that the operator takes a particularly convenient form when expressed in a basis of complex exponentials and spherical harmonics$-$a form we call the dipole spatio-angular transfer function. We discuss the implications of our analysis for all quantitative fluorescence microscopy studies and lay out a path towards a complete theory.

14 pages, 4 figures

References in corpus (3)

• Efficient Spherical Harmonic Transforms aimed at pseudo-spectral numerical simulations
• Fundamental Limits on Measuring the Rotational Constraint of Single Molecules using Fluorescence Microscopy
• Spatio-angular fluorescence microscopy II. Paraxial 4$f$ imaging

Cited by in corpus (8)

• Super-resolution Imaging of the Fluorescent Dipole Assembly with Polarized Structured Illumination Microscopy
• Birefringent Fourier filtering for single molecule Coordinate and Height super-resolution Imaging with Dithering and Orientation
• Single-molecule orientation localization microscopy II: a performance comparison
• Single-molecule orientation localization microscopy I: fundamental limits
• Quantum limits for precisely estimating the orientation and wobble of dipole emitters
• Spatio-angular fluorescence microscopy II. Paraxial 4$f$ imaging
• Spatio-angular fluorescence microscopy III. Constrained angular diffusion, polarized excitation, and high-NA imaging
• Dipole-Spread Function Engineering for 6D Super-Resolution Microscopy