Section 1. Theoretical modelling of biomedical optics
1) Validating and inspiring imaging techniques
Nearly all experiments, in any branch of science and engineering, require validation by a mathematical model. The model’s complexity and realism is dictated by the particular experiment. Biomedical optical experiments are no different: for example, some are adequately modelled by geometrical optics whilst some require a partially coherent electromagnetic description. At OBEL, we have developed tools to model the interaction of light with tissue as well as optical imaging systems. Crucially, these models can be linked to model image formation.
2) Modelling optical imaging systems
Well-designed microscopes are diffraction limited for some region in its field of view, meaning that diffraction limits the resolution of the system. Most of our models, for both illumination and detection, are implementations of established vectorial diffraction theory. For example, we employ the Debye-Wolf integral , a vectorial angular spectrum, to mathematically describe focused beams.
3) Modelling light tissue interaction
Light propagation in tissue is described most realistically using an electromagnetic description. This requires the use of numerical methods since Maxwell’s equations can be solved analytically for a small set of special cases. We employ the finite-difference time-domain and psuedospectral time-domain methods. Both methods enable broadband simulation which significantly reduces the computational complexity required to simulate image formation in optical coherence tomography.
4) Modelling image formation
The models of imaging systems and light tissue interaction may be combined into a model of image formation in optical coherence tomography.
- Richards and E. Wolf, “Electromagnetic diffraction in optical systems ii. structure of the image field in an aplanatic system,” Proc. R. Soc. A 253, 358–379 (1959).
5) Key researchers
6) Key publications
- R.T. Munro, D. Engelke and D.D. Sampson, “A compact source condition for modelling focused fields using the pseudospectral time-domain method”, Opt. Express 22(5): 5599-5613 (2014)
- R.T. Munro, A. Curatolo and D.D. Sampson, “A full wave model of image formation in optical coherence tomography applicable to general samples”, submitted to Opt. Express, 2014.