# Spatio-angular fluorescence microscopy II. Paraxial 4$f$ imaging

## TL;DR

This paper analyzes the spatio-angular properties of a paraxial 4f fluorescence microscope, revealing its ability to record out-of-plane fluorophore orientations and highlighting biases caused by monopole approximations.

## Contribution

It demonstrates the spatio-angular band limit of the system and assesses the impact of monopole approximation on fluorophore concentration estimates.

## Key findings

- Out-of-plane fluorophore orientations are recorded by the system.
- Monopole approximation biases are small with many randomly oriented fluorophores.
- Efficient simulations are enabled by exploiting the band limit.

## Abstract

We investigate the properties of a single-view fluorescence microscope in a 4$f$ geometry when imaging fluorescent dipoles without using the monopole or scalar approximations. We show that this imaging system has a spatio-angular band limit, and we exploit the band limit to perform efficient simulations. Notably, we show that information about the out-of-plane orientation of ensembles of in-focus fluorophores is recorded by paraxial fluorescence microscopes. Additionally, we show that the monopole approximation may cause biased estimates of fluorophore concentrations, but these biases are small when the sample contains either many randomly oriented fluorophores in each resolvable volume or unconstrained rotating fluorophores.