Biomedical Imaging

$\frac{{\hslash }^2}{2m}{\nabla }^2\Psi +V\Psi =0,\left(6.40\right)$

obtained for the variable replacement n2k2 → 2m/ℏ2V, with the conventional symbols for the potential V, mass m and (reduced) Planck’s constant ℏ.

Diffraction integrals

For use in biomedical imaging, we need formal solutions of the stationary wave equation, for example, explicit formulas to calculate how a field propagates through an object or in free space. This seems like a formidable task, and no generality can be expected. The solution depends on the precise 3d arrangement of the index of refraction n(r) and the boundary conditions specifying the radiation going into and out of – say – a bound region containing the object. In fact, explicit solutions without approximations can be expected only ...