Oluschinski: Created page with "{{Language_sel|LANG=ger|ARTIKEL=Auflösungsvermögen Mikroskop}} {{PSM_Infobox}} Resolution microscope FORCETOC ==Examination methods in microscopy== Light and electron microscopy methods are used in polymer testing and diagnostics to characterize the structure and morphology (see: microscopic structure) of plastics. The following..."

2026-09-04T12:28:40Z

Created page with "{{Language_sel|LANG=ger|ARTIKEL=Auflösungsvermögen Mikroskop}} {{PSM_Infobox}} Resolution microscope __FORCETOC__ ==Examination methods in microscopy== Light and electron microscopy methods are used in polymer testing and diagnostics to characterize the structure and morphology (see: microscopic structure) of plastics. The following..."

New page

{{Language_sel|LANG=ger|ARTIKEL=Auflösungsvermögen Mikroskop}}
{{PSM_Infobox}}
Resolution microscope
__FORCETOC__

==Examination methods in microscopy==

Light and electron microscopy methods are used in [[Polymer Testing|polymer testing]] and [[Polymer Diagnostic|diagnostics]] to characterize the structure and morphology (see: [[Microscopic Structure|microscopic structure]]) of [[Plastics|plastics]]. The following examination methods are preferred:

* [[Electron Microscopy|Electron microscopy]]
* [[Energy Dispersive X-Ray Spectroscopy (EDX)|Energy dispersive X-ray spectroscopy (EDX)]]
* [[In-situ Ultramicrotomy|In-situ ultramicrotomy]]
* Low-vacuum scanning electron microscopy (see: [[Environmental-SEM (ESEM)|enviromental – SEM (ESEM)]]
* [[Microtomy]]
* [[Atomic Force Microscopy|Atomic force microscopy]]
* [[Scanning Electron Microscopy|Scanning electron microscopy]]
* [[Environmental-SEM (ESEM)|Environmental – SEM (ESEM)]]
* [[Transmission Electron Microscopy|Transmission electron microscopy]]

==Optical parameters for describing the performance of light microscopes==

The optical performance of microscopes is characterized by the following parameters [1]:

* Resolution
*  [[Magnification Microscope|Magnification microscope]]
*  [[Depth of Field Microscope|Depth of field microscope]]

According to ABBE's theory, the following relationships apply to the refraction of light waves at the slit (grating):

{|
|-
|width="20px"|
|width="500px" | <math> sin\alpha =\frac{\lambda }{\delta }</math>
|(1)
|}

with
{|
|-
|''λ''
|width="15px" |
|wavelength of lights 
|-
|''δ''
|
| resolution = smallest distance between two points that can still be distinguished
|}

[[File:aufloesungsvermoegen1.jpg]]
{|
|- valign="top"
|width="50px"|'''Fig. 1''':
|width="600px" |Refraction of light waves
|}

The resolution of the light microscope is as follows:

* for vacuum (or ~ air):

{|
|-
|width="20px"|
|width="500px" | <math> \delta=\frac{\lambda }{\sin \alpha }</math>
|(2)
|}

* in a medium with refraction index n (e.g., immersion oil):

{|
|-
|width="20px"|
|width="500px" | <math> \delta=\frac{\lambda }{n \cdot \sin \alpha }</math>
|(3)
|}

with
{|
|-
|''n'' ⋅ sin ''α''
|width="15px" |
|numerical aperture
|}

For light microscopes, the following applies:

''α'' → 90° corresponds to sin ''α'' → 1,

for ''n'' = 1.4 (immersion oil) and ''λ'' = 0.55 µm (green light),

<math> \delta=\frac{0.55}{1 \cdot 1.4} \sim 0,4 \ \text{µm}</math>, i.e. the resolution of the light microscope (with oil immersion) is 0.4 µm.

==Resolution in electron microscopy==

For [[Transmission Electron Microscopy|transmission electron microscopes]], the following relationships apply to the achievable resolution:

Calculation of the wavelength of fast-moving electrons ''λ''EI:

{|
|-
|width="20px"|
|width="500px" | Energy equation <math> eU=\frac{1}{2}mv^2</math>
|(4)
|}

{|
|-
|width="20px"|
|width="500px" | <math> v=\sqrt{\frac{2e}{m} \cdot U}</math>
|(5)
|}

with
{|
|-
|''e''
|width="15px" |
|charge of the electron 
|-
|''m''
|
|mass of the electron 
|-
|''v''
|
|[[Velocity|velocity]] 
|-
|''U''
|
|acceleration voltage 
|}

The DE BROGLIE equation applies to the wavelength of material waves:

{|
|width="20px"|
|width="500px" | <math> \lambda_{EI}=\frac{h}{m \cdot v}</math>
|(6)
|}

with
{|
|-
|''h''
|width="20px" |
|PLANCK's constant or Planck constant 
|}

Combined, this results in:

{|
|-
|width="20px"|
|width="500px" | <math> \lambda=\sqrt{\frac{h^2}{2em \cdot U}}\sim \sqrt{\frac{1,5}{U}}\ (nm);\ U\ in\ Volt</math>
|(7)
|}

Due to relativistic velocity correction, the actual wavelengths achieved are slightly higher.

Examples:

U = 40 kV: λEI = 0.0060 nm 
U = 100 kV: λEI = 0.0037 nm 
U = 200 kV: λEI = 0.0025 nm

Due to the finite lens errors of electromagnetic lenses (spherical error, aperture error, refraction error, etc.), the achievable values for the numerical aperture α are approximately 10-2 to 10-3, and the point resolution only reaches values of approximately 0.2 to 0.4 nm [1].

==See also==

* [[Measuring Accuracy|Accuracy class]]
* [[Error Limit|Error limits]]
* [[Measuring Uncertainty]]
* [[Resolution Material Testing Machine|Resolution material testing machine]]

==References==

{|
|-valign="top"
|[1]
|Kämpf, G.: Charakterisierung von Kunststoffen mit physikalischen Methoden. Verfahren und praktische Anwendung. Carl Hanser, Munich Vienna (1982), pp. 19–21, (ISBN 978-3-446-13382-2; see [[AMK-Library]] under D 4)
|}

[[Category:Light]]
[[Category:Measurement Testing Technology]]
[[Category:Morphology and Micromechanics]]

Resolution Microscope - Revision history