# What exactly causes "color twinkling" and why does it seem that any color might be furthest refracted for a moment?

In this answer to Betelgeuse appears in a rainbow of colors through a Newtonian telescope I link to a video of a bright star imaged at perhaps video rate (I think) through a telescope. In addition to the saturated central white spot the edges show twinkling (i.e. scintillation or astronomical seeing effects) which shows up in the color camera and unknown amount of color "correction" or chroma boost as lots of vibrant colors at the edges of the image. Red, blue, green, yellow, orange, violet, etc.

The underlying phenomenon is refraction through turbulent and variable density air primarily at scales scales of centimeters to tens of centimeters.

Like all transparent dielectrics1 air has chromatic dispersion with the index of refraction slightly increasing monotonically from red to blue, so naively I would assume that the edges of these images would all be slightly bluish because whatever refraction is happening to cause rays to deviate that far, it would be strongest for the shortest visible wavelengths.

In fact for the average effects of refraction when observing far from the zenith some observatories use a variable dispersion prism apparatus to cancel atmospheric dispersion:

And yet in these images all the colors of the rainbow end up at the extrema at different moments, as if dispersion weren't monotonic.

Before we challenge the chroma settings on the video, recall that the reason I posted this answer was to explain why bright stars seen through a particularly large amount of turbulence (say low to the horizon over a desert (natural or urban) after sunset after a scorching day) will definitely twinkle in color.

Question: What exactly causes "color twinkling" and why does it seem that any color might be furthest refracted for a moment?

1 I'm not familiar with any transparent dielectrics where the real index of refraction does not monotonically increase from red to blue, but I'd be happy to find out if there is such a thing!

Fig. 5 The refractive index calculated as a function of the wavelength using (blue solid line) the standard Sellmeier equation for N2 (a), O2 (b), Ar (c), and [Eq. (2)] for air (d) and (pink dashed line) Eq. (5) including only the terms with r = 12, 13, 14, 15 with parameters as specified in Table 1 for (a) N N2 = 2.688 @BULLET 10 19 cm −3 , (b) N O2 = 2.504 @BULLET 10 19 cm −3 , (c) N Ar = 2.879 @BULLET 10 19 cm −3 , and (d) the standard gas content of atmospheric air with parameters as specified in Fig. 1.

Fig. 1 The refractive index (a-d) and the group-velocity dispersion (e-h) calculated as functions of the wavelength using the full model of air refractivity based on Eq. (1) including the HITRAN-database manifold of atomic and molecular transitions (blue line) and Eq. (5) including M = 15 terms with parameters as specified in Table 1 (pink line): (a,e) visible and near-IR, (b,f) near-IR, (c,g) mid-IR, and (d,h) mid-IR and LWIR ranges. Absorption spectrum of air is shown by grey shading. Atmospheric air is modeled as a mixture of molecular and atomic gases with densities N N2 = 1.987 • 10 19 cm −3 , N O2 = 5.3291 • 10 18 cm −3 , N Ar = 2.3763 • 10 17 cm −3 , N H2O = 7.0733 • 10 16 cm −3 (10% humidity), and N CO2 = 9.4136 • 10 15 cm −3. The temperature is 296 K, n0 = 1.000273.

Screenshot from the YouTube video "Stars through a telescope 1" linked below:

cued at 12:23 watch for about 30 seconds to see the color scintillations.

• There are certainly a variety of glass types with negative dispersion. I don't think you'll see that in atmospheric effects as those are almost entirely Rayleigh and related scattering mechanisms. To clarify I'm only saying that if a series of images show different direction of red-to-blue, that is unlikely to be of atmospheric origin. Jun 6, 2022 at 13:19
• @CarlWitthoft can you produce a single example of a transparent "glass typ(e) with negative dispersion"? If so, then achromatic lenses would not need to be made from one positive lens and one negative lens. I'm always delighted to be found wrong because I learn something, and this will be a very interesting material to learn about indeed! A quick way would be to find a glass with a negative Abbe number. If you can't then it will be a more difficult search and you may have to reevaluate.
– uhoh
Jun 6, 2022 at 21:07
• rare but possible without "exotic materials" , so yeah you won't find them in any commercial lens system. patents.google.com/patent/FR2691961A1/en patents.google.com/patent/US9771299 opg.optica.org/ao/abstract.cfm?uri=ao-58-2-428 Jun 7, 2022 at 12:26
• @CarlWitthoft It's late so I won't try to figure out what "negative anomalous dispersion $\Delta P_{g, F}$" means exactly, and if that really means that the index ever actually decreases towards the blue or not. cf. Eq. 9 in Schott TIE-29 Refractive Index and Dispersion for the expression for $\Delta P_{g, F}$.
– uhoh
Jun 7, 2022 at 13:08

## 1 Answer

This is more a hypothesis rather than a definitive answer. Below is a photo of a prism with the camera in the path of the separated colors. Only a small part of the spectrum actually falls on the lens. The lens in this case was about a quarter of an inch wide, while the full spectrum was about 1 foot wide, so all we see here is blueish green. This prism was able to spread the spectrum over a foot in just a short distance, when a star gets refracted through the atmosphere, the refraction starts at least a hundred miles away, so your eye/telescope is only going to pick up very small fraction of the spectrum.

This can't be a full explanation though, as the video shows multiple colors in the same image. I have a few wild guesses, from attributing them to the telescope/camera lens, to multiple paths of refraction through the atmosphere.

• I think the reason that the colours change is that the air is always moving, analogous to what you would see if the prism in the answer above were rotating. Since the air is moving, different parts of the spectrum sweep by the telescope, producing the changing colours. Jun 4, 2022 at 19:44
• This is an excellent thought-provoking answer! I'm not certain that "multiple paths of refraction through the atmosphere" is the solution; there's not just one "prism" between the star and the telescope, there are many, and since they are irregularly shaped they will have some weak lensing effects as well.
– uhoh
Jun 4, 2022 at 21:03
• correction: I AM certain that "multiple paths of refraction through the atmosphere" is the solution. The "I'm not" should have been cleaned up during proofs :-)
– uhoh
Jun 5, 2022 at 1:35