Difference between revisions of "Physical optics and resolution"

From Course Wiki
Jump to: navigation, search
(Created page with "Category:20.309 Category:Optical Microscopy Lab {{Template:20.309}} The performance of an imaging system is limited by both fundamental and technical constraints. As we ...")
 
m
Line 25: Line 25:
 
:<math>\nabla \times \vec {E} = - {\partial \vec {B} \over \partial t}</math>
 
:<math>\nabla \times \vec {E} = - {\partial \vec {B} \over \partial t}</math>
 
:<math>\nabla \times \vec {B} = \mu_0 \left ( \vec J + \varepsilon_0 {\partial \vec E \over \partial t} \right )</math>
 
:<math>\nabla \times \vec {B} = \mu_0 \left ( \vec J + \varepsilon_0 {\partial \vec E \over \partial t} \right )</math>
: where ''&rho;'' and <math>\vec J</math> are the charge and current densities of a region of space, and the universal constants <math>\varepsilon_0</math> and <math>\mu_0</math> are the permittivity and permeability of free space.  The nabla symbol <math>\nabla</math> denotes the three-dimensional gradient operator, <math>\nabla \cdot </math> the divergence operator,  and <math>\nabla \times </math> the curl operator.
+
: where ''&rho;'' and <math>\vec J</math> are the charge density and current density of a region of space, and the universal constants <math>\varepsilon_0</math> and <math>\mu_0</math> are the permittivity and permeability of free space.  The nabla symbol <math>\nabla</math> denotes the three-dimensional gradient operator, <math>\nabla \cdot </math> the divergence operator,  and <math>\nabla \times </math> the curl operator.
  
 
* Sinusoidal
 
* Sinusoidal

Revision as of 13:59, 23 August 2013

20.309: Biological Instrumentation and Measurement

ImageBar 774.jpg


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
From spie.org [1]. Profiles of the transverse electric and magnetic fields of a light wave at an instant of time.


References

  1. http://spie.org/Documents/Publications/00%20STEP%20Module%2004.pdf