Modelling tissue optics and imaging

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 [1], a vectorial angular spectrum, to mathematically describe focused beams.

The magnitude of the Cartesian components of the electric and magnetic fields at the waist of a focused Gaussian beam with full width at half maximum of 2.6mm

The magnitude of the Cartesian components of the electric and magnetic fields at the waist of a focused Gaussian beam with full width at half maximum of 2.6mm

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.

Simulation and rendering of the propagation of a beam of light through a numerical model of the epidermis.

Simulation and rendering of the propagation of a beam of light through a numerical model of the epidermis.

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.

Experimental and simulated optical coherence tomography images of a structured phantom for scattering coefficients, within the letters, from top to bottom, of 12.6, 4.3 and 22mm-1.

Experimental and simulated optical coherence tomography images of a structured phantom for scattering coefficients, within the letters, from top to bottom, of 12.6, 4.3 and 22mm-1.

  1. 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

  1. 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)
  2. 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.