FOCUS
( Quantum) FISHER INFORMATION
( QUANTUM) FISHER INFORMATION IN LOCALIZATION MICROSCOPY
///////////////////////////////////////////////////////////////////////////////////////////////////
Thomas JUFFMANN 1, 2, *, Stefan NIMMRICHTER 3, Francisco BALZAROTTI 4 and Jonathan DONG 5
1
University of Vienna, Faculty of Physics, VCQ, A-1090 Vienna, Austria
2
University of Vienna, Max Perutz Laboratories, Department of Structural and Computational Biology, A-1030 Vienna, Austria
3
Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Siegen 57068, Germany
4
Research Institute of Molecular Pathology( IMP), Vienna BioCenter( VBC), Campus-Vienna-Biocenter 1, Vienna 1030, Austria
5
Biomedical Imaging Group, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland * thomas. juffmann @ univie. ac. at
https:// doi. org / 10.1051 / photon / 202513158
The precise localization of particles yields structural and dynamical information in applications ranging from fundamental physics to molecular biology. Here, we discuss how the concept of( Quantum) Fisher information can guide the development of localization techniques. Starting from dipole scattering, we discuss imaging based on elastic and inelastic( e. g. fluorescence) scattering and present experimental designs that increase the information obtained per detected photon.
Microscopy and its ability to precisely localize and track single particles has become indispensable in biosciences, material science, and medicine. Most notably, single-molecule localization lies at the heart of many super-resolution fluorescence microscopy techniques, with applications in structural and cellular biology. Recently, elastically scattering particles have also gained attention, as the almost instantaneous scattering rates enable high speed and precision.
The precision in such applications is limited by the finite signal-to-noise ratio in the recorded data. While the signal depends on the properties of the sample and the chosen imaging technique, the noise comprises technical contributions, such as camera read-out noise, and quantum contributions, such as shot noise or backaction noise. The precision of a given technique can often be increased by averaging N consecutive frames. For N independent measurements, this increases the signal-to-noise ratio by √— N, and improves the precision accordingly. However, this is not always possible. A desired temporal resolution or long-term setup stability might preclude longer averaging times. Furthermore, phototoxicity, heating, or camera limitations might preclude the recording at higher light intensity.
It is then crucial to obtain as much information per detected photon as possible. In estimation theory [ 1,2 ], one quantifies this in terms of the Fisher information( FI). It sets the Cramér-Rao bound( CRB) on the achievable estimation precision
58 www. photoniques. com I Photoniques 131