by henk21cm » Thu Apr 24, 2008 7:38 pm
watch24 wrote:Unfortunately, being a time exposure, it doesn't answer my question about naked-eye observation at those altitudes.
G'day Marty,
I cannot answer your question from first hand experience. I live 5 m below see level, and the highest point i ever saw a star was when i was just a few hundreds of meters high.
There are reasons which tell me that the height and thus air pressure is of no importance. We could ask Serge Brunier, he has been there.
Each optical element (mirror or lens) has to endure Airy diffraction. The separation angle i told you yesterday is roughly the angle caused by this type of diffraction. See e.g.
http://en.wikipedia.org/wiki/Airy_disc. Even the eye has Airy diffraction. The Airy angle in our eye will be roughly 600 nm / 4 mm = 150 micro radians. The radius of our eye is 2.5 cm. Such an angle will lead to a distance on the retina of 1.5E-4 * 2.5E-2 = 4 E-6 m.
Our eye has approximatedly 100 millions light sensitive cells. The surface of the retina is approximately 5 square centimeters. Each cell will, on average, occupy roughly 5E-8 square centimeters, that is 5E-12 square meters. The size (length, width, radius) of such a cell is therefore about 2E-6 m, that is the same order of magnitude as the center part of the Airy disk. Thus the limitations of optics (i.e. ideal optics) will cause diffraction of a point source, and spread the light out over at least one cell.
So the projection of a point source on the retina 'always hits a light sensitive cell', it never falls in between of the cells. That would be the obvious reason why you would miss a star. You can compare it with a bed of nails, as used by some artists/performers. When you drop from a few meters high a marble on the bed of nails, the marble has a chance to fall between the nails. Now we add optics to the equation. The limitation to optics (Airy diffraction) makes the marble larger: they become melons. A melon -when dropped on a bed of nails- will always hit a nail.
Whether the light is diffracted by the atmosphere, is of no importance, since not the atmosphere is the dominant player, the optical limitations in the human eye are.
I read in a publication of the JPL about the Spitzer telescope (Bachus, Velusamy, Thompson and Arballo, 2005). The Airy diffraction, as projected on the CCD, has a size which is comparable with the size of one element of the CCD. This situation is the same as in the human eye. Much smaller CCD elements are useless, since the Airy pattern would spread out the light over many cells, not adding information.
Regards,
Henk
[quote="watch24"]Unfortunately, being a time exposure, it doesn't answer my question about naked-eye observation at those altitudes.[/quote]
G'day Marty,
I cannot answer your question from first hand experience. I live 5 m below see level, and the highest point i ever saw a star was when i was just a few hundreds of meters high.
There are reasons which tell me that the height and thus air pressure is of no importance. We could ask Serge Brunier, he has been there.
Each optical element (mirror or lens) has to endure Airy diffraction. The separation angle i told you yesterday is roughly the angle caused by this type of diffraction. See e.g. [url]http://en.wikipedia.org/wiki/Airy_disc[/url]. Even the eye has Airy diffraction. The Airy angle in our eye will be roughly 600 nm / 4 mm = 150 micro radians. The radius of our eye is 2.5 cm. Such an angle will lead to a distance on the retina of 1.5E-4 * 2.5E-2 = 4 E-6 m.
Our eye has approximatedly 100 millions light sensitive cells. The surface of the retina is approximately 5 square centimeters. Each cell will, on average, occupy roughly 5E-8 square centimeters, that is 5E-12 square meters. The size (length, width, radius) of such a cell is therefore about 2E-6 m, that is the same order of magnitude as the center part of the Airy disk. Thus the limitations of optics (i.e. ideal optics) will cause diffraction of a point source, and spread the light out over at least one cell.
So the projection of a point source on the retina 'always hits a light sensitive cell', it never falls in between of the cells. That would be the obvious reason why you would miss a star. You can compare it with a bed of nails, as used by some artists/performers. When you drop from a few meters high a marble on the bed of nails, the marble has a chance to fall between the nails. Now we add optics to the equation. The limitation to optics (Airy diffraction) makes the marble larger: they become melons. A melon -when dropped on a bed of nails- will always hit a nail.
Whether the light is diffracted by the atmosphere, is of no importance, since not the atmosphere is the dominant player, the optical limitations in the human eye are.
I read in a publication of the JPL about the Spitzer telescope (Bachus, Velusamy, Thompson and Arballo, 2005). The Airy diffraction, as projected on the CCD, has a size which is comparable with the size of one element of the CCD. This situation is the same as in the human eye. Much smaller CCD elements are useless, since the Airy pattern would spread out the light over many cells, not adding information.
Regards,
Henk