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The twinkling of stars, or scintillation, occurs because the optical path length of the atmosphere varies in both space and time due to turbulence.

This means that when the wavefront from a distant star enters a telescope, it is distorted from the flat wavefront expected for an object at infinity.

Because the fundamental Fourier mode of this wavefront varies in time, the average position of the PSF on the retina of a human observer also changes in time; the star appears to shake back and forth. (By this I mean that the wavefront at the telescope may be considered a superposition of plane waves. One particular plane wave is the strongest, or is the median; that is the one I mean by "fundamental Fourier mode". I'm not sure if I'm using exactly the right term. When I worked with an adaptive optics team one summer, we had a "tip-tilt mirror" specifically to correct for this mode, and then the deformable mirror corrected for higher-order aberrations. )

That much makes sense to me. However, I have read on Wikipedia that this is not the dominant effect in what we observe as scintillation. Instead, the overall apparent brightness of the star varies.

I presume this has essentially the same physical origin. The wavefront is complicated and dynamic, and so interference effects sometimes reduce and sometimes increase the brightness. What are the details of how this works? How can one work out that this effect should occur? Perhaps a specific example of what a wavefront might do and how this would result in varying brightness would be helpful.

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Answer is in link below. Short version: Refractive gradients in the mixed atmosphere, thousands of meters above the surface, are far too small to act as lenses and prisms, and scintillation is not a geometric optics phenomenon. It results from interference effects of plane-wave light (spatially coherent light, like starlight or laser light) as the wavefront is distorted by tiny refractive gradients associated with Kolmogorov turbulence. This accounts for both the intensity and color fluctuations seen by eye, and also explains why the larger planets, whose light is far from coherent, do not scintillate. Little's paper anticipates by a decade the works of Kolmogorov, Tatarski and Rytov. It also anticipates speckle, seen in larger apertures, where the distorted wavefront breaks up the Airy disc into tiny pieces that fluctuate on millisecond time scales.

http://adsabs.harvard.edu/full/1951MNRAS.111..289L

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I think you have the seeds of your answer within the question. The apparent brightness variations are caused by essentially the same phenomenon, but maybe with a larger amplitude than you've allowed for.

If you think of the atmosphere as a collection of lenses between you and the star, you get the general idea of what causes twinkling. Lenses bring the light to a focus - i.e. all of the light from a plane wave goes to one point - but they also prevent that light from going straight through. When you use a magnifying glass to focus sunlight, the glass has a shadow.

As you point out, the average position of the PSF can move on the retina. However, twinkling can also focus the light away from the retina. This phenomenon can cause stars to appear brighter and fainter.

Telescopes are generally not subject to the same effect. For a telescope, the relative position of the star matters, but all of the light from the star will still be collected. Since your eye is small (about 1 cm), the tiny lenses in the atmosphere can focus the light outside your eye aperture, but for telescopes with apertures >a few cm (probably even for good binoculars), the light just gets moved to a different part of the mirror.

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For telescopes, it may not matter in terms of light gathering power, if they are big enough; the light gets deviated but still ends up captured. But it does matter in terms of resolving power; even a very large telescope is affected by "seeing", perhaps even more frustratingly so than small telescopes, since a big aperture could deliver a lot of resolving power, yet it's stopped down by seeing. –  Florin Andrei Dec 6 '11 at 20:33
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