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f/#, NA, and spot size

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Optics index
f/#, NA, and spot size diagram
The f/# and NA are calculated from the aperture size (or Gaussian 1/e² beam width) and the focal length in air. Known ratios, together with the light wavelength, allow spot size calculations. This calc is accurate to ~2 significant figures.
Focal length
Aperture diameter

Airy disk diameter
Gaussian waist size
Gaussian FWHM
Rayleigh length
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For a Gaussian beam (as opposed to a homogemeous beam), the "Aperture diameter" is the 1/e² diameter, and a large lens size is assumed. For a truncated beam, the appropriate spot size ratio should be applied (see the relevant calc, e.g. 1.12 for truncation at the 1/e² diameter). The resolving power is considered to be 1/2 of the Airy disk diameter, and the Rayleigh length is calculated here in air.