# Inverse Problems of Trapped Objects

## TL;DR

This paper introduces a mathematical method for estimating the movement of transparent particles manipulated by optical or acoustical tweezers, drawing parallels to Cryo-EM imaging techniques, to improve contact-free microscopic imaging.

## Contribution

It presents a novel mathematical framework for motion estimation of particles in optical and acoustical trapping, assuming fixed internal structure, inspired by Cryo-EM orientation estimation.

## Key findings

- Provides a new mathematical formulation for particle motion estimation.
- Shows similarities between trapping particle estimation and Cryo-EM orientation problems.
- Lays groundwork for improved non-invasive microscopic imaging techniques.

## Abstract

Optical and acoustical trapping has been established as a tool for holding and moving microscopic particles suspended in a liquid in a contact-free and non-invasive manner. Opposed to standard microscopic imaging where the probe is fixated, this technique allows imaging in a more natural environment. This paper provides a method for estimating the movement of a transparent particle which is maneuvered by tweezers, assuming that the inner structure of the probe is not subject to local movements. The mathematical formulation of the motion estimation shows some similarities to Cryo-EM single particle imaging, where the recording orientations of the probe need to be estimated.