Resolution Microscope

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Resolution microscope

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 examination methods are preferred:

• Electron microscopy
• Energy dispersive X-ray spectroscopy (EDX)
• In-situ ultramicrotomy
• Low-vacuum scanning electron microscopy (see: enviromental – SEM (ESEM)
• Microtomy
• Atomic force microscopy
• Scanning electron microscopy
• Environmental – SEM (ESEM)
• 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
• 
Depth of field microscope

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

$sin\alpha ={\frac {\lambda }{\delta }}$

(1)

with

λ		wavelength of lights
δ		resolution = smallest distance between two points that can still be distinguished

Fig. 1:

Refraction of light waves

The resolution of the light microscope is as follows:

• for vacuum (or ~ air):

$\delta ={\frac {\lambda }{\sin \alpha }}$

(2)

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

$\delta ={\frac {\lambda }{n\cdot \sin \alpha }}$

(3)

with

n ⋅ sin α

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),

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

Resolution in electron microscopy

For transmission electron microscopes, the following relationships apply to the achievable resolution:

Calculation of the wavelength of fast-moving electrons λ_EI:

Energy equation $eU={\frac {1}{2}}mv^{2}$

(4)

$v={\sqrt {{\frac {2e}{m}}\cdot U}}$

(5)

with

e		charge of the electron
m		mass of the electron
v		velocity
U		acceleration voltage

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

$\lambda _{EI}={\frac {h}{m\cdot v}}$

(6)

with

h

PLANCK's constant or Planck constant

Combined, this results in:

$\lambda ={\sqrt {\frac {h^{2}}{2em\cdot U}}}\sim {\sqrt {\frac {1,5}{U}}}\ (nm);\ U\ in\ Volt$

(7)

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

Examples:

U = 40 kV: λ_EI = 0.006₀ nm
U = 100 kV: λ_EI = 0.003₇ nm
U = 200 kV: λ_EI = 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

• Accuracy class
• Error limits
• Measuring Uncertainty
• Resolution material testing machine

References

[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)