Thomson, Laura C.
Inverse techniques: problems in optics and gas sensing.
PhD thesis, University of Glasgow.
In this thesis, two, seemingly different, classes of problems are discussed: locating gas sources from downwind gas concentration measurements and designing diffractive optics (i.e. computer generated holograms), which on illumination will produce a desired light beam in the far field. The similarity between these problems is that they are both “inverse problems” and we discuss the use of inverse techniques to solve them.
In many instances within science, it is possible to calculate accurately a set of consequences which result from defined events. In most cases, however, it is math- ematically impossible to analytically calculate the unique set of events which led to the observed consequences. Such problems are termed “inverse problems”. Taking the example of gas dispersion, one sees that a known source leads to a calculable set of downwind concentrations. However, given a single concentration measurement it is impossible to distinguish a specific source and location from a larger, more distant source that would have given the same measured concentration. This is an example of the same consequence resulting from two, or more, different events.
Key to solving inverse problems are iterative algorithms which randomly trial different possible events to find those which best describe the observed consequences. Such algorithms use a search method to postulate possible events, apply a forward model to calculate the anticipated consequences and then use a cost function to compare the postulated with the known consequences. The process is iterated until the optimum value of the cost function is found, at which point the current set of postulated events are taken to be the best estimate of the real events. In this thesis I apply similar iterative algorithms to solve the two classes of problem.
The current demand on the world’s oil resources have encouraged the development of new prospecting techniques. LightTouch is one such solution which is discussed in this thesis and was developed with Shell Global Solutions. LightTouch uses the fact that oil reserves, through microseepages, leak hydrocarbons to their surface. Detection of these hydrocarbons can indicate the presence of oil reserves. LightTouch measures Ethane to sub-part-per-billion sensitivity at multiple positions across a survey area. Locating the source of the Ethane from the sparse downwind concentration measurements is an inverse problem and we deploy algorithms of the type discussed above to locate the Ethane sources. The algorithm is written in LabView and the software, Recon, is currently used by Shell Global Solutions to solve this problem. In appendix B the Recon user interface is shown.
We investigate both the impact of choice of cost function (chapter 3) and forward model (chapter 4), which in this inverse problem is a gas dispersion model, on the algorithm’s ability to locate the gas sources. We find that the choice of cost function is more important to the success of the algorithm than the choice of forward model.
Optical tweezers trap and manipulate particles with light beams. In order to manipulate the particles in a desired way it is necessary for the shape and position of the light beam to be controlled. One way of achieving a desired light beam is to use a spatial light modulator (SLM) which displays a phase pattern (referred to as a computer generated hologram), off which the light is diffracted. Calculating the phase pattern which will result in the desired light beam is an inverse problem and is referred to as holographic light shaping. The forward model in this case is a Fourier transform. In this thesis we use an algorithm similar to that used to solve the gas location problem and the Gerchberg-Saxton algorithm to calculate phase patterns with applications in optical tweezers.
Within an optical tweezers system the highest trap resolution (the smallest distance between neighboring traps) that can be achieved is conventionally dictated by the diffraction limit. In this thesis we investigate two possible ways of beating the diffraction limit: superresolution and evanescent waves.
In chapter 5 we investigate the application of inverse techniques to calculating phase patterns which produce superresolution optical traps. We calculate theoreti- cally the improvements to both relative trap stiffness and trap resolution using the superresolution optical traps. Although both are improved it comes at a cost to trap strength. In chapter 7 we simulate evanescent wave fields and demonstrate shaping three dimensional evanescent optical traps. Similar light shaping techniques are used in chapter 6 to shape light beams which after being disturbed will self-reconstruct.