calculate spacing of airy rings

[00000254aaf46f51-dmarc-request]

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Dear list,

I have to pick your brains on a maybe trivial question:

How do I calculate the spacing between airy rings for a given objective NA, pinhole size (and shape, we are having hexagonal pinhole) and wavelength.
Or is there some (Matlab) code to calculate the whole pattern?

Thanks!

Jens

[Sripad Ram-2]

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Hi Jens,
If my memory serves right, the first few radial distance values pertaining
to the zeros of an Airy profile are listed in the Born and Wolf textbook on
Optics. The radial distance values will be expressed in a normalized
coordinate system (scaled by na and lambda) which can be converted back to
real units. The scaling factor for the conversion should also be in the
book.

Hope this helps.
Sripad


On Thu, Dec 6, 2018 at 4:22 AM <[hidden email]>
wrote:

> *****
> To join, leave or search the confocal microscopy listserv, go to:
> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
> Post images on http://www.imgur.com and include the link in your posting.
> *****
>
> Dear list,
>
> I have to pick your brains on a maybe trivial question:
>
> How do I calculate the spacing between airy rings for a given objective
> NA, pinhole size (and shape, we are having hexagonal pinhole) and
> wavelength.
> Or is there some (Matlab) code to calculate the whole pattern?
>
> Thanks!
>
> Jens

[Craig Brideau]

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The distribution is a Bessel function I believe. Here is a primer I found
fairly quickly:
www.physics.usyd.edu.au/teach_res/mp/op/doc/op_bessel1.pdf
<https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=7&cad=rja&uact=8&ved=2ahUKEwimgeX9k4zfAhUWJjQIHcKnBm8QFjAGegQIBxAC&url=http%3A%2F%2Fwww.physics.usyd.edu.au%2Fteach_res%2Fmp%2Fop%2Fdoc%2Fop_bessel1.pdf&usg=AOvVaw0eRoNyEXXpS6fO6fHyAPzY>

Also this one which is more general:
web.ipac.caltech.edu/staff/fmasci/home/astro_refs/PSFtheory.pdf
<https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=8&ved=2ahUKEwimgeX9k4zfAhUWJjQIHcKnBm8QFjAHegQICRAC&url=http%3A%2F%2Fweb.ipac.caltech.edu%2Fstaff%2Ffmasci%2Fhome%2Fastro_refs%2FPSFtheory.pdf&usg=AOvVaw3hVr7O1zz2vXL6hwmXEHkF>

Craig

On Thu, Dec 6, 2018 at 12:35 PM S Ram <[hidden email]> wrote:

> *****
> To join, leave or search the confocal microscopy listserv, go to:
> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
> Post images on http://www.imgur.com and include the link in your posting.
> *****
>
> Hi Jens,
> If my memory serves right, the first few radial distance values pertaining
> to the zeros of an Airy profile are listed in the Born and Wolf textbook on
> Optics. The radial distance values will be expressed in a normalized
> coordinate system (scaled by na and lambda) which can be converted back to
> real units. The scaling factor for the conversion should also be in the
> book.
>
> Hope this helps.
> Sripad
>
>
> On Thu, Dec 6, 2018 at 4:22 AM <
> [hidden email]>
> wrote:
>
> > *****
> > To join, leave or search the confocal microscopy listserv, go to:
> > http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
> > Post images on http://www.imgur.com and include the link in your
> posting.
> > *****
> >
> > Dear list,
> >
> > I have to pick your brains on a maybe trivial question:
> >
> > How do I calculate the spacing between airy rings for a given objective
> > NA, pinhole size (and shape, we are having hexagonal pinhole) and
> > wavelength.
> > Or is there some (Matlab) code to calculate the whole pattern?
> >
> > Thanks!
> >
> > Jens
>