Aims

The aims of the course are to:

• understand how Fourier optics can be used to manipulate light in many applications
• examine the advance of optical techniques into electronic systems for computation and communications.
• investigage the technology behind such potential applications

Objectives

As specific objectives, by the end of the course students should be able to:

• a simple introduction to optical diffraction and Fourier optics.
• apply Fourier techniques to simple optical spatial patterns.
• understand the principles of optical correlation and holography.
• understand the basic principles of liquid crystal phase modulation.
• explain the principles and construction of spatial light modulators (SLMs).
• understand the basic principles of free space optical systems and how to build them
• know the basic function of adaptive optical systems.
• understand the properties of optical aberrations and how to correct them.

Content

The aim of this module is to examine the advance of optical techniques into electronic systems for computation and communications. Two dimensional and three dimensional transmission, storage and processing of information using free space optics are discussed. Applications such as computer generated holography, optical correlation, optical switching and adaptive optics are highlighted through the use of liquid crystal technology.

Fourier Holograms and Correlation (5L)

• Basic diffraction theory, Huygens principle
• Fourier Transforms and Holography introduction and motivation;
• Fourier transforms: theoretical and with lenses: resolution of optical systems;
• Correlation and convolution of 2-dimensional signal patterns;
• Dynamic and fixed phase computer generated holograms.

Electro-Optic Systems (5L)

• Free space optical components; wave plates and Jones matrices
• Fundamentals of liquid crystal phase modulation
• Spatial light modulation and optical systems;
• Holographic interconnects and fibre to fibre switching
• Wavelength filters and routing systems
• The BPOMF and 1/f JTC correlators.

Adaptive optical Systems (4L)

• Adaptive systems in free space optics;
• The power of phase conjugation;
• Adaptive optical interconnects;
• Optical aberrations and optical correction techniques;

Demonstrations in the lectures will include:

1. 2D Fourier transform and diffraction patterns.
2. Computer generated hologram for optical fan-out.
3. Optical beam steering with dynamic holograms on SLMs.
4. The JTC

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

 
Last modified: 23/05/2019 16:01

Aims

The aims of the course are to:

• understand how Fourier optics can be used to manipulate light in many applications
• examine the advance of optical techniques into electronic systems for computation and communications.
• investigage the technology behind such potential applications

Objectives

As specific objectives, by the end of the course students should be able to:

• a simple introduction to optical diffraction and Fourier optics.
• apply Fourier techniques to simple optical spatial patterns.
• understand the principles of optical correlation and holography.
• understand the basic principles of liquid crystal phase modulation.
• explain the principles and construction of spatial light modulators (SLMs).
• understand the basic principles of free space optical systems and how to build them
• know the basic function of adaptive optical systems.
• understand the properties of optical aberrations and how to correct them.

Content

The aim of this module is to examine the advance of optical techniques into electronic systems for computation and communications. Two dimensional and three dimensional transmission, storage and processing of information using free space optics are discussed. Applications such as computer generated holography, optical correlation, optical switching and adaptive optics are highlighted through the use of liquid crystal technology.

Fourier Holograms and Correlation (5L)

• Basic diffraction theory, Huygens principle
• Fourier Transforms and Holography introduction and motivation;
• Fourier transforms: theoretical and with lenses: resolution of optical systems;
• Correlation and convolution of 2-dimensional signal patterns;
• Dynamic and fixed phase computer generated holograms.

Electro-Optic Systems (5L)

• Free space optical components; wave plates and Jones matrices
• Fundamentals of liquid crystal phase modulation
• Spatial light modulation and optical systems;
• Holographic interconnects and fibre to fibre switching
• Wavelength filters and routing systems
• The BPOMF and 1/f JTC correlators.

Adaptive optical Systems (4L)

• Adaptive systems in free space optics;
• The power of phase conjugation;
• Adaptive optical interconnects;
• Optical aberrations and optical correction techniques;

Demonstrations in the lectures will include:

1. 2D Fourier transform and diffraction patterns.
2. Computer generated hologram for optical fan-out.
3. Optical beam steering with dynamic holograms on SLMs.
4. The JTC

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

 
Last modified: 23/08/2018 11:35

Aims

The aims of the course are to:

• Teach some mathematical techniques that have wide applicability to many areas of engineering.

Objectives

As specific objectives, by the end of the course students should be able to:

• Find the SVD of a matrix, and understand how this can be used to calculate the rank and pseudo-inverse of the matrix.
• Calculate the least squares solution of a set of linear equations.
• Understand how to apply Principal Component Analysis (PCA) to a problem.
• Apply PCA to reduce the dimensionality of an optimization problem and/or to improve the solution representation.
• Represent linear iterative schemes using linear algebra and understand what influences the rate of convergence.
• Understand the definitions and application areas of Stochastic Processes.
• Understand the principle of Markov Chains.
• Implement various sampling schemes to enable parameters of stochastic processes to be estimated.
• Understand the concepts of local and global minima and the conditions for which a global minimum can be obtained.
• Understand the algorithms of the different gradient search methods.
• Solve unconstrained problems using appropriate search methods.
• Solve constrained linear and non-linear optimization problems using appropriately selected techniques.
• Understand how Markov Chain-based algorithms can be used to give reasonable solutions to global optimisation problems.

Content

Linear Algebra provides important mathematical tools that are not only essential to solve many technical and computational problems, but also help in obtaining a deeper understanding of many areas of engineering.  Stochastic (random) processes are important in fields such as signal and image processing, data analysis etc. Optimization methods are routinely used in almost of every branch of engineering, especially in the context of design.

Linear Algebra (4L, Prof G Wells)

• Revision of IB material
• Matrix norms, condition numbers, conditions for convergence of iterative schemes
• Positive definite matrices
• Singular Value Decomposition (SVD), pseudo-inverse of a matrix and least squares solutions of Ax = b
• Principal Component Analysis
• Markov matrices and applications

Stochastic Processes (5L, Prof S Godsill)

• Definition of a stochastic process, Markov assumption (with examples), the Chapman-Kolmogorov (CK) equation, conversion of a particular CK integral equation into a differential equation (for the case of Brownian motion)
• The general Fokker-Planck equation with particular examples (Brownian motion, Ornstein-Uhlenbeck process)
• Introduction to sampling Gibbs sampler, Metropolis Hastings, Importance sampling with applications.

Optimization (7L, Luca Magri)

• Introduction: Formulation of optimization problems; conditions for local and global minimum in one, two and multi-dimensional problems
• Unconstrained Optimization: gradient search methods (Steepest Descent, Newton’s Method, Conjugate Gradient Method)
• Linear programming (Simplex Method)
• Constrained Optimization: Lagrange and Karush-Kuhn-Tucker (KKT) multipliers; penalty and barrier functions
• Global optimisation: Simulated Annealing

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

 
Last modified: 08/03/2020 17:41

Aims

The aims of the course are to:

• Teach some mathematical techniques that have wide applicability to many areas of engineering.

Objectives

As specific objectives, by the end of the course students should be able to:

• Find the SVD of a matrix, and understand how this can be used to calculate the rank and pseudo-inverse of the matrix.
• Calculate the least squares solution of a set of linear equations.
• Understand how to apply Principal Component Analysis (PCA) to a problem.
• Apply PCA to reduce the dimensionality of an optimization problem and/or to improve the solution representation.
• Represent linear iterative schemes using linear algebra and understand what influences the rate of convergence.
• Understand the definitions and application areas of Stochastic Processes.
• Understand the principle of Markov Chains.
• Implement various sampling schemes to enable parameters of stochastic processes to be estimated.
• Understand the concepts of local and global minima and the conditions for which a global minimum can be obtained.
• Understand the algorithms of the different gradient search methods.
• Solve unconstrained problems using appropriate search methods.
• Solve constrained linear and non-linear optimization problems using appropriately selected techniques.
• Understand how Markov Chain-based algorithms can be used to give reasonable solutions to global optimisation problems.

Content

Linear Algebra provides important mathematical tools that are not only essential to solve many technical and computational problems, but also help in obtaining a deeper understanding of many areas of engineering.  Stochastic (random) processes are important in fields such as signal and image processing, data analysis etc. Optimization methods are routinely used in almost of every branch of engineering, especially in the context of design.

Linear Algebra (4L, Prof G Wells)

• Revision of IB material
• Matrix norms, condition numbers, conditions for convergence of iterative schemes
• Positive definite matrices
• Singular Value Decomposition (SVD), pseudo-inverse of a matrix and least squares solutions of Ax = b
• Principal Component Analysis
• Markov matrices and applications

Stochastic Processes (5L, Prof S Godsill)

• Definition of a stochastic process, Markov assumption (with examples), the Chapman-Kolmogorov (CK) equation, conversion of a particular CK integral equation into a differential equation (for the case of Brownian motion)
• The general Fokker-Planck equation with particular examples (Brownian motion, Ornstein-Uhlenbeck process)
• Introduction to sampling Gibbs sampler, Metropolis Hastings, Importance sampling with applications.

Optimization (7L, Prof M Girolami)

• Introduction: Formulation of optimization problems; conditions for local and global minimum in one, two and multi-dimensional problems
• Unconstrained Optimization: gradient search methods (Steepest Descent, Newton’s Method, Conjugate Gradient Method)
• Linear programming (Simplex Method)
• Constrained Optimization: Lagrange and Karush-Kuhn-Tucker (KKT) multipliers; penalty and barrier functions
• Global optimisation: Simulated Annealing

This syllabus contributes to the following areas of the UK-SPEC standard:

Toggle display of UK-SPEC areas.

 
Last modified: 28/08/2020 11:10