Project summary: Electromagnetic inverse problems
Liquid crystals (LCs) are organic materials in a phase that is intermediate between liquid and solid and their microstructure gives them fascinating and important optical properties. As LCs play a greater and greater role in technology, so it becomes necessary to predict their optical performance more and more accurately. This is especially true in respect of contrast and resolution.

Dr Polydorides’ research at the University of Manchester (UMIST) was stimulated by the particular new application of LCs in displays for electronic paper. The simplest and commonest LCs are called “nematics” which means they have a rod-like microstructure in which configurations of aligned rods are preferred. Even for this class of LCs the problem of using optical data to understand how the rods align is very challenging mathematically.

The basic problem is that the mathematician has to “work backwards” from the output optical data, the direct problem being that of predicting the optical performance from a given microstructure. This is what theoreticians call an inverse problem or parameter identification, and such problems arise in areas ranging from seismology to volatility estimation. They are notoriously sensitive to the choice of numerical algorithm used in their analysis.

The LC problem has the beauty that there is the prior information that the rods must adopt a stable feasible configuration. This knowledge has been invaluable in filtering out spurious microstructure and hence allowing the construction of a reliable and accurate inversion algorithm. Such an algorithm is currently being used to suggest those sets of optical data that are most important when it comes to inferring the mechanics of the LC.

Chris Newton of Hewlett Packard Laboratories confirms: The project has increased our understanding of the inverse problem and provided us with tools to assess the data requirements for reliable parameter estimation. For stratified media we have also developed code to solve the inverse problem much more quickly and reliably. We are now in a position to explore and understand device behaviour by extracting information from experimental data in a way that was not feasible before.

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