Optical unit

The Optical Unit is a dimensionless units of length used in optical microscopy. Because every diffraction limited system have their resolution proportional to wavelength / NA, it is convenient for comparison to use this unit. There are actually 2 units, one "axial" (along the optical axis of the objective) and one "radial".

In radial optical unit, the radius of the first Airy minimum (radius) is 3,77. It is also approximatively the same for the FWHM of Airy function.

Equation

$u_{axial} = \frac{8 \pi n}{\lambda} sin^2(\frac{\alpha}{2}) z$

$v_{radial} = \frac{2 \pi}{\lambda} \frac{n sin \alpha}{M_{tot}} r$

where :

• n is the refractive index
• λ is the wavelength
• α the beam conus angle
• M_tot is the total magnification (M is 1 if you want the size in the sample)

Note : n * sin α = numerical aperture

References

• James B. Payley in Handbook of biological confocal microscopy ; second edition; Appendix I
• http://www.ntmdt.com/spm-basics/view/classical-optical-microscopy (see equation 3 and 4)