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Doesn't an infinitely sharp edge require infinite frequency content?
Therefore infinite data?

Craig

On Mon, Feb 13, 2017 at 6:57 PM, JAMES B PAWLEY <[log in to unmask]> wrote:

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> Hi all,
>
> Those attending the sadly-gone UBC 3D-course may remember that our first
> slogan was, "If it isn’t diffraction, it’s statistics.”
>
> Colin’s wonderful, inclusive paper does indeed wrap up the diffraction
> part superbly.
>
> But how many photons/nm*3 would you have to collect in order to obtain
> data that would allow you to fill in those beautifully narrow lines?
> Millions? (if the line width is say 1% of its “value” surely you need
> 10,000 detected photons to determine it  And how big must a pixel be to
> trace out these lovely curves without them looking blocky? Given that
> biologists habitually work with specimens capable of producing at most tens
> of detectable photons/pixel, surely it is the statistics that places the
> most severe spatial limits on the data we finally obtain.
>
> Where is the young mathematician (statistician?) who can give us an
> equally comprehensive analysis of the number of photons  per cubic nm that
> we must elicit and detectin order to “resolve” two closely spaced point
> objects? And why do we always assume that these two objects have the same
> intensity when this is so seldom the case? What visibility criteria would
> be appropriate to model the problem of seeing the Earth from Alpha Centauri?
>
> Please someone take up this quest.
>
> Jim Pawley
>
> James and Christine Pawley, 5446 Burley Place, Box 2348, Sechelt BC,
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> 1-604-885-0840, cell 1-604-989-6146
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>
>
> On Feb 13, 2017, at 7:11 AM, Alberto Diaspro <[log in to unmask]<mailto:
> [log in to unmask]>> wrote:
>
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> Dear
> following a discussion with the MRT staff and Wiley, they informed me that
> the paper is now available for free for one month. Hope this can help.
> Please, have a check and let me know if it works at
> http://onlinelibrary.wiley.com/doi/10.1002/jemt.22834/full
>
> Best
> Alby
>
>