https://en.formulasearchengine.com/w/api.php?action=feedcontributions&feedformat=atom&user=24.162.111.164formulasearchengine - User contributions [en]2026-07-10T11:14:51ZUser contributionsMediaWiki 1.47.0-wmf.7https://en.formulasearchengine.com/w/index.php?title=Quantum_mechanics_of_time_travel&diff=26271Quantum mechanics of time travel2014-01-29T05:03:07Z<p>24.162.111.164: </p>
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<div>{{expert-subject|date=January 2011}}<br />
{{refimprove|date=January 2011}}<br />
The Optical Unit is a dimensionless units of length used in optical microscopy. Because every diffraction limited system have their resolution proportional to wavelength / [[Numerical aperture|NA]], it is convenient for comparison to use this unit.<br />
There are actually 2 units, one "axial" (along the optical axis of the objective) and one "radial".<br />
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== Equation ==<br />
<br />
<math>u_\mathrm{axial} = \frac{8 \pi n}{\lambda} \sin^2(\frac{\alpha}{2}) z</math><br />
<br />
<math>v_\mathrm{radial} = \frac{2 \pi}{\lambda} \frac{n \sin \alpha}{M_\mathrm{tot}} r</math><br />
<br />
where :<br />
* <math>n</math> is the [[refractive index]]<br />
* <math>\lambda</math> is the wavelength<br />
* <math>\alpha</math> the beam conus angle<br />
* <math>M_\mathrm{tot}</math> is the total magnification (<math>M</math> is 1 if you want the size in the sample)<br />
<br />
Note : <math>n * \sin \alpha</math> = [[numerical aperture]]<br />
<br />
== References ==<br />
* James B. Pawley in ''Handbook of biological confocal microscopy'' ; second edition; Appendix I<br />
* http://www.ntmdt.com/spm-basics/view/classical-optical-microscopy (see equation 3 and 4)<br />
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[[Category:Microscopy]]</div>24.162.111.164