A245461 Decimal expansion of constant in the Rayleigh criterion: first zero of J_1, divided by Pi.

1, 2, 1, 9, 6, 6, 9, 8, 9, 1, 2, 6, 6, 5, 0, 4, 4, 5, 4, 9, 2, 6, 5, 3, 8, 8, 4, 7, 4, 6, 5, 2, 5, 5, 1, 7, 7, 8, 7, 9, 3, 5, 9, 3, 3, 0, 7, 7, 5, 1, 1, 2, 1, 2, 9, 4, 5, 6, 3, 8, 1, 2, 6, 5, 5, 7, 6, 9, 4, 3, 2, 8, 0, 2, 8, 0, 7, 6, 0, 1, 4, 4, 2, 5, 0, 8, 7

Offset

1,2

Comments

The angular resolution (diffraction limit), in radians, is this constant times the wavelength of the light used divided by the aperture diameter. That is: objects closer than this angle cannot be resolved as separate objects.

Note that the small angle approximation sin(theta) =~ theta can be used. Also, a commonly used approximation to this constant is 1.220. - John W. Nicholson, Jul 29 2014

For example, a radio telescope with a 300-meter aperture observing at the hydrogen line (21.106... cm) can distinguish objects at most 0.04916... degrees apart. - Charles R Greathouse IV, Mar 08 2018

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

COSMOS - The SAO Encyclopedia of Astronomy, Rayleigh Criterion

Rene Kay, Todd Kay, Planet Seeker Interferometer (PSI), hal-02870885v2 [astro-ph.IM], 2020.

Wikipedia, Angular resolution

Wikipedia, Diffraction-limited system

Example

1.21966989126650445492653884746525517787935933077511...

Mathematica

RealDigits[ BesselJZero[1, 1]/Pi, 10, 111][[1]] (* Robert G. Wilson v, Jul 23 2014 *)

Prog

(PARI) solve(x=3, 4, besselj(1, x))/Pi
(PARI) besseljzero(1)/Pi \\ Charles R Greathouse IV, Aug 09 2022

Crossrefs

Cf. A115369, A221210.

Sequence in context: A246323 A201685 A120671 * A086572 A349035 A316606

Adjacent sequences: A245458 A245459 A245460 * A245462 A245463 A245464

Keyword

nonn,cons

Author

Charles R Greathouse IV, Jul 22 2014

Status

approved