Formula for Resolution

[frank....@dol.net]

In Astronomy and Telescopes there is formula for calculating the optical
resolution as a function of the aperture of the objective lens (or
mirror ). This resolution is smallest angle detectable between 2
points and is usually expressed in arc seconds. The formula something
like:

R (arc seconds) = 2,5 X 10 to the 5th X Wavelength / Obj Diameter

where the wavelength and diameter are in meters.

Is this formula (or a similar one) functional with all optical lenses
like say a camera? What brought this up was that many amateur
astronomers put reduced aperture sun filters over their objectives to
view sunspots. I maintained they are losing resolution by masking down
and they reply this formula is only valid in resolving points (like
stars)
Any comments appreciated.
Frank

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[OpticsNotes.Com]

In article <8ekkj7$oj2$1...@nnrp1.deja.com>,

Hi Frank,

Indeed when you aperture down any diffraction limited optic, the
minimum resolvable feature size grows. When you are looking at
splitting binary stars, your telescope resolution (and
atmospheric "seeing") is very important. However, when you aperture
down when looking at the sun, your resolution does degrade,
theoretically, but practically you don't care because the feature size
you are looking for on the sun (sunspots, corona, etc.) is much smaller
than those binary stars you may want to split.

Bruce

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[Bob May]

One of the other things to remember is that if the telescope is much
larger than the "seeing cells" then the resolution degrades to the
smaller size and then some anyway. Thus it becomes that the smaller
aperture acutally gives a better REAL image resolution than the larger
scope. Weird but true.
--
Bob May

Don't subscribe to ACCESS1 for your webserver for the low prices. The
service has
been lousy and has been poor for the last year. Bob May

[Dr Morpheus]

frank....@dol.net wrote:
[snip]

> Is this formula (or a similar one) functional with all optical lenses
> like say a camera?

Not always. In spectroscopes the formula for the resolution is quite
different. (And there IS a telescope involved in this case - The viewing
Telescope). Although, if one wants to be technically accurate in the
case of spectroscopes, one should consider that limit to be:
max{R,DeltaLambda}
where R is the resolution of the viewing telescope as you have above and
DeltaLambda is the prism's resolution as defined by Lord Rayligh's
formula. Of course, one should convert both to similar units first.

>What brought this up was that many amateur
> astronomers put reduced aperture sun filters over their objectives to
> view sunspots. I maintained they are losing resolution by masking down
> and they reply this formula is only valid in resolving points (like
> stars)

You are correct, if the size of the sunspot is close to the telescope's
resolution limit. If it is larger, the reduction of apperture will
affect only the "grainy" appearance of the sunspot's internal
appearance. If it is smaller, it won't matter, because you won't be able
to see it anyway, and reducing the apperture from x to x-y inches would
give you a smaller appreciable amount of small sunspots. Statistically
speaking, the amount of sunspots that will have sizes equal EXACTLY to
the limit of the unreduced apperture will be very small.

> Any comments appreciated.
> Frank

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