## Physics & Astronomy ETDs

#### Publication Date

Spring 5-10-2019

#### Abstract

The realization that twisted light beams with helical phasefronts could carry orbital angular momentum (OAM) that is in excess of the photon's spin angular momentum (SAM) has spawned various important applications. One example is the design of novel imaging systems that achieve three-dimensional (3D) imaging in a single snapshot via the rotation of point spread function (PSF).

Based on a scalar-field analysis, a particular simple version of rotating PSF imagery, which was proposed by my advisor Dr. Prasad, furnishes a practical approach to perform 3D source localization using a spiral phase mask that generates a combination of Bessel vortex beams. For a special annular design of the mask, with the spiral-phase winding number in successive annuli changing by a fixed quantum number, this Bessel-beam combination can yield a shape and size invariant PSF that rotates as a function of the axial position of the source, and possesses a superior depth of field (DOF) when compared to other rotating PSFs.

In the first part of this dissertation, we present a vector-field analysis of an improved rotating PSF design that encodes both the 3D location and polarization state of a monochromatic point dipole emitter for high numerical aperture (NA) microscopy, in which non-paraxial propagation of the imaging beam and the associated vector character of light fields are properly accounted for. By examining the angle of rotation and the spatial form of the PSF, one can simultaneously localize point sources and determine the polarization state of light emitted by them over a 3D field in a single snapshot. We also propose a more advanced approach for doing joint polarimetry and 3D localization using a SAM-OAM conversion device without the need for high NA is also proposed.

A recent paradigm-shifting research proposal has focused on employing the toolbox of quantum parameter estimation for the problem of super-resolution of two incoherent point sources. Surprisingly, the quantum Fisher information (QFI) and associated quantum Cram\'er-Rao bound (QCRB) for estimating the one-dimensional transverse separation of the source pair are both finite constants that are achievable with purely classical measurements that utilize coherent projections of the optical wavefront.

A second important contribution of this dissertation is the generalization of the previous quantum limited transverse super-resolution work to full 3D imaging with more general PSF. Under the assumption of known centroid, we first derive the general expression of $3\times 3$ QFI matrix with respect to (w.r.t.) the 3D pair separation vector, in terms of the correlation of the wavefront phase gradients in the imaging aperture. For a clear circular aperture, the QFI matrix turns out to be a separation-independent diagonal matrix. Coherent-projection bases that can attain the corresponding QCRB in special cases and small separation limits are also proposed with confirmation by numerical simulations.

We next extend our 3D analysis to treat the more general 6-parameter problem of jointly estimating the 3D pair-centroid location and pair-separation vectors. We also present the results of computer simulation of an experimental protocol based on the use of Zernike-mode projections to attain these quantum estimation-limited bounds of performance.

#### Degree Name

Physics

#### Level of Degree

Doctoral

#### Department Name

Physics & Astronomy

#### First Committee Member (Chair)

Sudhakar Prasad

#### Second Committee Member

Keith Lidke

#### Third Committee Member

Arash Mafi

#### Fourth Committee Member

John Grey

#### Language

English

#### Keywords

Three-Dimensional Imaging, Rotating Point Spread Function, Super-resolution, Quantum Fisher Information

#### Document Type

Dissertation

#### Recommended Citation

Yu, Zhixian. "Topics in Three-Dimensional Imaging, Source Localization and Super-resolution." (2019). https://digitalrepository.unm.edu/phyc_etds/217

#### Included in

Atomic, Molecular and Optical Physics Commons, Biological and Chemical Physics Commons, Optics Commons, Quantum Physics Commons