Re: Observing, one photon at a time

Yes, but at the speed of light, the next photon to hit your eye will do so almost instantaneously........and the
one after that........and the one after that........and before you can move your eye away from the eyepiece,
you'll have collected more than enough to cure your photon deprivation.......... ;-)

Jim ……….. :-)

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Jim Bartolini nytgems@No-Spam
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  ----- Original Message -----
  From: David Cooper
  To: TAC
  Sent: Tuesday, June 30, 2009 8:47 PM
  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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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