title: Optimal point spread function design for 3D imaging.
abstract: To extract from an image of a single nanoscale object maximum physical information about its position, we propose and demonstrate a framework for pupil-plane modulation for 3D imaging applications requiring precise localization, including single-particle tracking and superresolution microscopy. The method is based on maximizing the information content of the system, by formulating and solving the appropriate optimization problem--finding the pupil-plane phase pattern that would yield a point spread function (PSF) with optimal Fisher information properties. We use our method to generate and experimentally demonstrate two example PSFs: one optimized for 3D localization precision over a 3  μm depth of field, and another with an unprecedented 5  μm depth of field, both designed to perform under physically common conditions of high background signals.
authors.affiliation: Department of Chemistry, Stanford University, 375 North-South Mall, Stanford, California 94305, USA.
authors.forename: Yoav
authors.initials: Y
authors.lastname: Shechtman
authors.affiliation: Department of Chemistry, Stanford University, 375 North-South Mall, Stanford, California 94305, USA.
authors.forename: Steffen J
authors.initials: SJ
authors.lastname: Sahl
authors.affiliation: Department of Chemistry, Stanford University, 375 North-South Mall, Stanford, California 94305, USA and Institute of Computational and Mathematical Engineering, Stanford University, 475 Via Ortega, Stanford, California 94305, USA.
authors.forename: Adam S
authors.initials: AS
authors.lastname: Backer
authors.affiliation: Department of Chemistry, Stanford University, 375 North-South Mall, Stanford, California 94305, USA.
authors.forename: W E
authors.initials: WE
authors.lastname: Moerner
mesh_terms: D021621:Imaging, Three-Dimensional / Q000379:methods*; D053768:Metal Nanoparticles / Q000737:chemistry; D015233:Models, Statistical; D057054:Molecular Imaging / Q000379:methods*; D016012:Poisson Distribution