[seqfan] Re: Optics sequence

[Wouter Meeussen]

http://en.wikipedia.org/wiki/Angular_resolution
"The factor 1.220 is derived from a calculation of the position of the first 
dark circular ring surrounding the central Airy disc of the diffraction 
pattern. " compares nicely with your:
"The angular resolution, 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."

Mathematica %t line:
BesselJZero[1, 1]/ Pi  ~ N ~ 87
(*1.21966989126650445492653884746525517787935933077511212945638126557694328028076014425087*)

Wouter.


-----Original Message----- 
From: Charles Greathouse
Sent: Tuesday, July 22, 2014 10:24 PM
To: Sequence Fanatics Discussion list
Subject: [seqfan] Optics sequence

I have just submitted a sequence
https://oeis.org/draft/A245461
for review: "Constant in the Rayleigh criterion: first zero of J_1, divided
by Pi". If anyone has appropriate background to look this over I would
appreciate it. At this point I don't think I can be picky: if you work in
physics, or have taken even a single undergrad class in optics, you qualify.

I thought the sequence was important enough to submit but don't really know
enough to be sure of my own submission. In particular: (1) Is my
description of the criterion essentially correct? (2) Is there a good
reference to include? (A quick Google search didn't find much.) (3) Should
Sparrow's limit be mentioned, and does it have a similar closed form?

Of course help and advice are welcome from all, even if (like me) you
haven't studied optics. Feel free to edit the entry or email me directly.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

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