Re: Observing, one photon at a time

Sounds like that AP155 is broken and needs to be sold off at once!
Paul
 
 
In a message dated 7/1/2009 3:43:50 P.M. Pacific Daylight Time,
greg.laflamme@No-Spam writes:

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

 
____________________________________
 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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