

A245461


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


2



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
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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 300meter 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), hal02870885v2 [astroph.IM], 2020.
Wikipedia, Angular resolution
Wikipedia, Diffractionlimited 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


CROSSREFS

Cf. A115369, A221210.
Sequence in context: A246323 A201685 A120671 * A086572 A316606 A016632
Adjacent sequences: A245458 A245459 A245460 * A245462 A245463 A245464


KEYWORD

nonn,cons


AUTHOR

Charles R Greathouse IV, Jul 22 2014


STATUS

approved



