Extended depth of field
Author(s)
Ramirez Hernandez, Pavel
Type
Thesis
Abstract
In this thesis the extension of the depth of field of optical systems is investigated. The
problem of achieving extended depth of field (EDF) while preserving the transverse resolution
is also addressed. A new expression for the transport of intensity equation in the
prolate spheroidal coordinates system is derived, with the aim of investigating the phase
retrieval problem with applications to EDF.
A framework for the optimisation of optical systems with EDF is also introduced,
where the main motivation is to find an appropriate scenario that will allow a convex
optimisation solution leading to global optima. The relevance in such approach is that it
does not depend on the optimisation algorithms since each local optimum is a global one.
The multi-objective optimisation framework for optical systems is also discussed,
where the main focus is the optimisation of pupil plane masks. The solution for the
multi-objective optimisation problem is presented not as a single mask but as a set of
masks. Convex frameworks for this problem are further investigated and it is shown that
the convex optimisation of pupil plane masks is possible, providing global optima to the
optimisation problems for optical systems.
Seven masks are provided as examples of the convex optimisation solutions for optical
systems, in particular 5 pupil plane masks that achieve EDF by factors of 2, 2.8, 2.9, 4
and 4.3, including two pupil masks that besides of extending the depth of field, are super-resolving
in the transverse planes. These are shown as examples of solutions to particular
optimisation problems in optical systems, where convexity properties have been given to
the original problems to allow a convex optimisation, leading to optimised masks with a
global nature in the optimisation scenario.
problem of achieving extended depth of field (EDF) while preserving the transverse resolution
is also addressed. A new expression for the transport of intensity equation in the
prolate spheroidal coordinates system is derived, with the aim of investigating the phase
retrieval problem with applications to EDF.
A framework for the optimisation of optical systems with EDF is also introduced,
where the main motivation is to find an appropriate scenario that will allow a convex
optimisation solution leading to global optima. The relevance in such approach is that it
does not depend on the optimisation algorithms since each local optimum is a global one.
The multi-objective optimisation framework for optical systems is also discussed,
where the main focus is the optimisation of pupil plane masks. The solution for the
multi-objective optimisation problem is presented not as a single mask but as a set of
masks. Convex frameworks for this problem are further investigated and it is shown that
the convex optimisation of pupil plane masks is possible, providing global optima to the
optimisation problems for optical systems.
Seven masks are provided as examples of the convex optimisation solutions for optical
systems, in particular 5 pupil plane masks that achieve EDF by factors of 2, 2.8, 2.9, 4
and 4.3, including two pupil masks that besides of extending the depth of field, are super-resolving
in the transverse planes. These are shown as examples of solutions to particular
optimisation problems in optical systems, where convexity properties have been given to
the original problems to allow a convex optimisation, leading to optimised masks with a
global nature in the optimisation scenario.
Date Issued
2012-07
Date Awarded
2012-08
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Torok, Peter
Sponsor
Consejo Nacional de Ciencia y Tecnología ; SEP
Grant Number
scholarship 189704
Publisher Department
Physics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)