User Tools

Site Tools


multi-immersion_objectives

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
multi-immersion_objectives [2019/06/12 12:44]
jon added links to drawings of objectives co-focused
multi-immersion_objectives [2019/06/13 03:25] (current)
jon [Magnification]
Line 55: Line 55:
 Because the magnification depends on the imaging medium, magnification ideally would be measured empirically. ​ However, for most situations estimating the magnification based on the presumed RI of the imaging medium is probably sufficient. Because the magnification depends on the imaging medium, magnification ideally would be measured empirically. ​ However, for most situations estimating the magnification based on the presumed RI of the imaging medium is probably sufficient.
  
-The reason that the effective focal length (and hence magnification) depends on the refractive index of the medium can be understood in a few different ways.  Perhaps the most simple way to understand is to consider the "back aperture"​ of the objective.((The back aperture or pupil is closely related but not identical to the back focal plane)) ​ The NA, the EFL, and the size of the back aperture are related by the following well-known equation BA<​sub>​Ø</​sub>​ = 2 * NA * EFL.  The NA of the objective is proportional to the RI of the media; this is essentially definitional. ​ The back aperture has a fixed size.  For the equation to hold then the EFL must be inversely proportional to the RI, meaning the magnification is proportional to the RI.  An alternative way of understanding is to consider an off-axis ray which passes through the center of the surface between the first objective element and the media. ​ The ray will be refracted off of the glass/media surface with an angle given by [[https://​en.wikipedia.org/​wiki/​Snell'​s_law|Snell'​s law]] which says the ratio of sin θ to RI is constant. ​ For relatively small angles, sin θ ≈ θ, which means that the outgoing angle of the ray is is inversely proportional to the medium'​s RI.  Hence the the displacement from center of that ray at the image plane is inversely proportional to the RI, which is equivalent to saying that the magnification is changed proportionally by the medium'​s RI.+The reason that the effective focal length (and hence magnification) depends on the refractive index of the medium can be understood in a few different ways.  Perhaps the most simple way to understand is to consider the "back aperture"​ of the objective.((The back aperture or pupil is closely related but not identical to the back focal plane)) ​ The NA, the EFL, and the size of the back aperture are related by the following well-known equation BA<​sub>​Ø</​sub>​ = 2 * NA * EFL.  The NA of the objective is proportional to the RI of the media; this is essentially definitional. ​ The back aperture has a fixed size.  For the equation to hold then the EFL must be inversely proportional to the RI, meaning the magnification is proportional to the RI.  An alternative way of understanding is to consider an off-axis ray which passes through the center of the surface between the first objective element and the media. ​ The ray will be refracted off of the glass/media surface with an angle given by [[https://​en.wikipedia.org/​wiki/​Snell'​s_law|Snell'​s law]] which says the ratio of sin θ to RI is constant. ​ For relatively small angles, sin θ ≈ θ, which means that the outgoing angle of the ray is is inversely proportional to the medium'​s RI.  Hence the the displacement from center of that ray at the image plane is inversely proportional to the RI, which is equivalent to saying that the magnification is changed proportionally by the medium'​s RI.  Incidentally,​ the same argument suggests that the magnification varies with RI for **all** objective lenses.
  
 ===== Numerical Aperture and Resolution ===== ===== Numerical Aperture and Resolution =====
multi-immersion_objectives.txt · Last modified: 2019/06/13 03:25 by jon