Re: Observing, one photon at a time

i think that if your photons arrive just right that the binoculars may jist show you TWO stars at once greg .... LOL

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------Original Message------
From: Greg LaFlamme <greg.laflamme@No-Spam>
To: "'TAC mailing list'" <tac@No-Spam>,"Greg LaFlamme" <greg.laflamme@No-Spam>
Date: Wed, Jul 1, 3:43 PM -0700
Subject: Re: [TAC] Observing, one photon at a time

Ah yes, the ole Bose-Einstein probability distribution thingy. Sounds like
its in good hands! Hey, what about my 7x50 binocs? Can I still see a star? I
may need bigger ones!
 
 
GML

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From: tac-bounces@No-Spam [mailto:tac-bounces@No-Spam]
On Behalf Of Peter Natscher
Sent: Wednesday, July 01, 2009 6:43 AM
To: [TAC]
Subject: Re: [TAC] Observing, one photon at a time

And I'll be camping next to this guy? Whew!!!

Peter N

  _____

From: David Cooper <david.cooper@No-Spam>
Reply-To: TAC mailing list <tac@No-Spam>
Date: Tue, 30 Jun 2009 20:47:26 -0700 (PDT)
To: TAC <tac@No-Spam>
Subject: [TAC] Observing, one photon at a time

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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