Re: Observing, one photon at a time

Now.... this is why I love this group! What a fascinating tidbit of
trivia to talk about at star parties. Thanks for going to the trouble
for the research.

I just love hanging out with smart people.

I think that someday...maybe some of it will rub off on me.

Michelle

On Tue, Jun 30, 2009 at 8:47 PM, David Cooper<david.cooper@No-Spam> wrote:
> While recently perusing the 2009 Observer’s Handbook I was struck by the
> following statement: “When a typical backyard telescope is aimed at an
> average star in the night sky, at any instant there is seldom more than one
> photon from that star in transit through the telescope.”  This is a
> remarkable fact (if true) and one, I must admit, I had never thought about
> before.  Being a physicist, I could not resist checking this result – it’s a
> simple calculation. And, it turns out to be true.
>
>
>
> The same resource provides an expression for the illuminance, E (in Lux) of
> a star of visual magnitude m: logE = -0.4(m+13.99).   At a wavelength of 555
> nm (the peak response of the dark adapted human eye) the illuminance can be
> converted into the radiance (in milliwatts per square meter) through
> multiplication by the factor 1.464.  Division of the result by the energy of
> a single 555 nm photon (in millijoules) gives the photon flux (in photons
> per square meter per second).  For a second magnitude star, this calculates
> to be about 1.6 billion photons per square meter per second.
>
>
>
> For my AP155, which has a 0.019 square meter collection surface area, the
> second magnitude star delivers about 310 million photons per second through
> the tube.  Dividing this number by the speed of light gives the average
> number of photons per meter, which is 0.1.  That is, on average the photons
> arriving from that star are separated by ~ 10 meters – so there is only a
> single photon in my (~ 1 m) tube assembly about 10% of the time!  Those of
> you blessed with 18” Dobsonians fare a little better – the same second
> magnitude star results in a single photon in the tube about 90% of the time.
>
>
>
> The perceptive reader may note that I have ignored photon statistics in this
> calculation.  Indeed I have, but it turns out that it does not make much
> difference.  If we use the quantum mechanically correct Bose-Einstein
> probability distribution, it turns out that when looking at that same 2nd
> magnitude star through my AP155, the probability that there is a single
> photon in my tube assembly at any instant of time is about 8.5% (as opposed
> to the 10% calculated above).
>
>
>
> When observing a 12th magnitude object it is also interesting to contemplate
> that on average the photons arriving at the telescope are separated by ~ 100
> km.  So when the first photon strikes your eye, the next one to arrive is
> still 100 km above the telescope – it’s still in space!  Amazing to
> contemplate.
>
>
>
> No wonder we feel photon starved most of the time – we truly are observing
> most objects a single photon at a time!
>
> ---
>
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June 28, 2009: TAC Web Page Updated http://observers.org/TAC.cgi/Announcements/
Star Party! CalStar: Sept 17-20: http://www.observers.org/CalStar
TAC mailing list - to join, manage, or leave: http://nine.pairlist.net/mailman/listinfo/tac