# Rayleigh vs. Nyquist

Started by December 12, 2017
```Consider the Nyquist criterion for sampling a continuous=20
waveform - 2x bandwidth - then the Rayleigh resolution=20
principle - peaks must separate by at least 1 wavelength. =20

Don't these look much analogous? =20
Especially as =CE=BB =3D 1/f

Ruminating  a bit more... Nyquist sampling can be=20
viewed as a mandate to sample each period, at least=20
twice.  And, Rayleigh mandates that the image be=20
'sampled' twice, in the sense of a peak and trough.

It strikes me they may be equivalent, in some deeper=20
sense.  Has anyone ever tried to derive such a result,=20
mathematically?

I can't be the first to ever conjecture this - =20

--
Rich

```
```On Wednesday, December 13, 2017 at 12:40:53 PM UTC+13, RichD wrote:
> Consider the Nyquist criterion for sampling a continuous=20
> waveform - 2x bandwidth - then the Rayleigh resolution=20
> principle - peaks must separate by at least 1 wavelength. =20
>=20
> Don't these look much analogous? =20
> Especially as =CE=BB =3D 1/f
>=20
> Ruminating  a bit more... Nyquist sampling can be=20
> viewed as a mandate to sample each period, at least=20
> twice.  And, Rayleigh mandates that the image be=20
> 'sampled' twice, in the sense of a peak and trough.
>=20
> It strikes me they may be equivalent, in some deeper=20
> sense.  Has anyone ever tried to derive such a result,=20
> mathematically?
>=20
> I can't be the first to ever conjecture this - =20
>=20
> --
> Rich

https://svi.nl/NyquistRate
```