Physical optics and resolution
The performance of an imaging system is limited by both fundamental and technical constraints.
As we reviewed the basic principles of geometrical optics and ray tracing, treating light as a particle, we learned how aberrations (inherent to the polychromatic spectrum of light, to the nominal curvature of lenses, or introduced by human imperfection) could deform results. In this section, adding the descriptive framework of light as a wave, we'll study other factors that contribute to measurement uncertainty.
Limits of detection in microscopy can be understood as the compound of:
- aberrations
- resolution
- contrast
- detector construction
- noise.
Diffraction
To ray optics, or geometrical optics, that provided intuition and equations to account for reflection and refraction and for imaging with mirrors and lenses, we can add the concepts of wave optics, also dubbed physical optics, and thereby grasp phenomena including interferences, diffraction, and polarization.
Maxwell's equations
- The set of partial differential equations unified under the term 'Maxwell's equations' describe how electric $ \vec E $ and magnetic $ \vec {B} $ fields are generated and altered by each other and by charges and currents.
- $ \nabla \cdot \vec {E} = {\rho \over \varepsilon_0} $
- $ \nabla \cdot \vec {B} = 0 $
- $ \nabla \times \vec {E} = - {\partial \vec {B} \over \partial t} $
- $ \nabla \times \vec {B} = \mu_0 \left ( \vec J + \varepsilon_0 {\partial \vec E \over \partial t} \right ) $
- where ρ and $ \vec J $ are the charge density and current density of a region of space, and the universal constants $ \varepsilon_0 $ and $ \mu_0 $ are the permittivity and permeability of free space. The nabla symbol $ \nabla $ denotes the three-dimensional gradient operator, $ \nabla \cdot $ the divergence operator, and $ \nabla \times $ the curl operator.
- Sinusoidal
