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Southampton Statistical Sciences Research Institute

Research project: Optimal design of experiments for second harmonic generation in chemistry

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Second harmonic generation (SHG) is a nonlinear optical process which is applied in chemistry, physics, electronics and biology. It is used to characterise surfaces and interfaces, for example, solid/liquid or liquid/liquid interfaces, through determining the number and orientation of molecules at the interface.

It has many advantages over other methods, such as spectroscopy, including being relatively simple to apply, allowing in-situ measurements of surfaces, and having high frequency measurements which makes the process suitable for fast dynamic systems.

A joint project between researchers in statistical science and chemistry is investigating optimal designs for experiments on an air/liquid interface via a phenomenological model. The design consists of a set of combinations of input and output polarization angles, together with the number of laser shots for each angle combination. The output is the intensity of the reflected light which is related to the polarization angles through a nonlinear regression model with complex parameters. Research has focussed on finding designs whose performance is robust to the necessary initial estimates of these parameters, particularly when interest is in the estimation of nonlinear combinations of the model parameters. For SHG experiments, the ratios of the parameters are of particular importance. This project arose from the e-Science collaborative grant CombeChem between Chemistry, Electronics and Computer Science, and S3RI.

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