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George
2017-Dec-02, 06:42 PM
Yes, we love the nice sunsets where the Sun can be seen becoming more and more yellow near the sunset. [Feel free to wax poetically. I enjoy such things.] With higher and higher particle counts, the Sun will become more orange and, on rare occasions, somewhat red.

But these color variations don’t represent its “true color” – seen from space (above atmospheric color-distorting effects) and at a comfortable attenuation.

Also, we aren’t discussing any other star since the Sun is unique in that it is an extended (not a point-source of light) object. Point-sources are seen far more by our fovea region of the retina and a combination of things, apparently, cause a slight redshift in color even if we adjust for atmospheric extinctions.

Hard facts:
1) The spectral irradiance of the Sun has a number of “peaks”, all in the blue end (and closer to violet):
...nm........w/m^2
449.43.....2,051.1
450.23.....2,064.7
451.04.....2,069.3
451.85.....2,061.1
452.66.....2,050.7
453.48.....2,045.2
454.3.......2,044.5
455.13.....2,044.7
455.96.....2,048.4
456.8.......2,056.2
457.64.....2,063.7
458.48.....2,069.5
459.33.....2,073.6
460.19.....2,079.1
461.05.....2,081.6
461.92.....2,083.1
462.79.....2,078.8
463.66.....2,071.2
464.54.....2,061.0
465.43.....2,050.0

2) Because the Sun is dynamic, these values can change over time, but only slightly. Overall, the Sun doesn’t vary (luminosity) more than about 0.1%. Variation for higher blue-end wavelengths, more for violet and UV, will vary considerably more. For the above, on this day, per SORCE data, the peak wavelength was at 461.92nm.

3) Rather than an energy distribution, a photon flux density distribution is the better model regarding how we see things. This dramatically changes the color distribution. Since E=hf (f is freq.) then the blue-end gets slashed in values. Why? A photon that is twice the frequency of another will require twice the amount of energy. [For wavelengths, a photon with Ĺ the wavelength of another will have twice the amount of energy.] So the strong blue colors in the energy distribution will present a greatly reduced level for a photon distribution than the lower energy “red” photons.

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4) The photon flux distribution is very flat. For those who love peaks, it does have a peak, of course. Not eschewing obfuscation, its peak is yellow (*cough*). But it isn’t really a peak, but a tiny pimple. So treat it accordingly. [The crudeness of the graph shows orange, but it’s actually yellow.]

5) Color is the product of the spectral emission entering the eye and the spectral sensitivity of the eye, which isn’t flat. Saying one distribution is ideal is only a guess, or close approximation, unless substantial empirical evidence is presented to support any particular color model, including computer models.

6) The Sun is white. My avatar is a solar image taken by Dr. Potter and Roy Lorenz at the McMath-Pierce observatory on one of their projection tables. I had requested they place a red, green, and blue something, if possible, to demonstrate that this is a “true” color image. Also, this telescope uses no filters, at least for this image.

7) The Sun is very white. Look at the avatar again, but this time look at the solar limb (edge). It too is white. This is very important. The Sun’s limb temperature drops all the way down to 5000K, so this is where the yellow tint would be dominant, yet the limb is still white. Think about that a little more. Our atmosphere removes mostly what colors from sunlight? Blue, right? So if we add those blues back into this terrestrial white image, could we ever get a yellow result? Not no way; not no how!

8) A bright light source is color shifted toward white (see color constancy). The retinex (eye-brain process for color) color adjusts to make the main light source white. You can easily test this by looking at an incandescent light (older car headlight) at night verses in bright sunlight. The yellowish daytime light shifts to a much whiter light. Color processing does something similar. This would cause the Sun to appear white even if it was actually slightly yellow. [It would take a hotter, more white, light to make it look yellow, and I'm not sure this is possible. Perhaps the Sun is perfectly white.]

Erroneous claims regarding its true color:
1) The Sun is yellow because its peak wavelength is yellow.
False. I suspect this is reverse logic. They are convinced the Sun is yellow, perhaps from reading older astronomy text books that call the Sun a “yellow dwarf”, or from seeing countless images and illustrations of a yellow Sun. So it must be strong in the yellow band and it may be assumed that this is where the peak must be. [You can create a yellow appearance with no yellow emission (see metamers).] [The "yellow dwarf" label is a quirk in astronomy, IMO, but it can better be understood as more a reference to its spectrum being in the type of stars that do actually appear yellow. Father Secchi placed it with Capella, and this may have given the color assignment more cement than it should have. Black and white imaging soon followed and color got lost in the process a bit, I suspect.]

2) The Sun has a peak wavelength of green.
False. This is a more common mistake. If the Sun were a perfect blackbody emitter, given its temperature of 5777K, then its peak would be in the green (501.6nm). [See Wien’s law or use Planck’s equation.] Since we have space telescopes that give very accurate data, why not use the Sun’s actual spectrum and not the blackbody equation? The actual data reveals...it’s always in the blue band (energy distribution).

3) The Sun is yellow because other sun-like stars are yellow.
False. Observe solar twins such as 18 Sco.
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Eta Cas is just a little hotter and it’s fun to look at since it has a red dwarf neighbor. [It's important to note, however, that stars similar to the Sun can vary from white to a strong tint of yellow or gold due to atmospheric effects and the fact that they are point sources. ] Interestingly, this seems to be how the Sun first got labeled as yellow since its spectrum, which was first taken in the late 1800s, was a closer match to Capella (yellow) than the other color reference stars. Vega was considered to be the model white star.

4) The Sun is whiter because it emits all the colors of the spectrum.
False. But it’s half true. All stars emit all the colors of the spectrum, but not all stars are white, right? It is the intensity of each color that affects our color determination. For instance, blue-white stars emit copious amounts of “blue” photons, more than the other colors, so a blue tint is seen.

5) The Sun’s color is subjective so no definitive color need be assigned to it.
False. Although there is some subjectivity when talking about the world of colors, a very red rose is nor more subjective than its thorns. Of course, when only slight tints of color is found for any one star, other viewers may easily see something a little different. Color contrasting doubles can plan an even bigger roll for star colors.

George
2017-Dec-02, 06:46 PM
It is very likely that this is unique to Cosmoquest (formerly Bad Astronomy, then merged with Universe Today). It began somewhat when Phil was clearly reluctant to assign color to the Sun. [I first read an article in a science magazine claiming the Sun was green, which surprised me.]

So it may not be big science, Cosmoquest deserves, IMO, most the credit for this colorful enterprise. So thank Frasier and Phil
and me (and many other contributors, which I would enjoy naming) if you think it is of value. Otherwise, it's their fault.

Hornblower
2017-Dec-04, 01:54 AM
Did you judge the McMath image to be neutral white by comparing it with some sort of laboratory standard, or is it more like an umpire's "I call it as I see it"?

The effective temperature drops from about 6300K at the center to 5000K at the limb. If the upper wisps of the photosphere that dominate at the limb are more strongly nonthermal than the deep layers we see at the center, in such a way as to boost the blue band compared to that of a blackbody at the same temperature, perhaps that could equalize the hue. Your camera, provided you don't overexpose, would record hue differences that might elude your eyes when looking at such a large, bright projection up close. This would be interesting to check out in theory.

schlaugh
2017-Dec-04, 03:20 AM
FWIW, and a digression, many of us were indoctrinated into the "yellow sun" myth by Superman comics. Superman gains his powers by living near a yellow star.
(http://superman.wikia.com/wiki/Yellow_Stars)

Solar energy from the yellow sun is the source of energy for Kryptonian powers. When Superman is exposed to large amounts of sunlight, his powers can be greatly magnified. If a Kryptonian is powerless, absorbing a large amount of sunlight radiation can regenerate their powers.

George
2017-Dec-04, 03:28 PM
Did you judge the McMath image to be neutral white by comparing it with some sort of laboratory standard, or is it more like an umpire's "I call it as I see it"? The sunlight on the projection table was both the brightest light in the viewing area and the whitest object. The florescent, IIRC, lighting was much weaker on the table and it wasn't whiter. Sunlight typically is the whitest light and I'm not sure what "white" light would make it look any other color. The lighting industry establishes their index (CRI -- Color Rendering Index) to sunlight (daylight). The brightest light, if it is close to white, will appear more white-shifted, if you will, to the eye rendering colors more accurately. It's pretty amazing to me that our brains can do this, though it can be fooled at times. Cameras process colors similarly.

Also, I later bought a light meter and sent it to them to assure that the photopic level wasn't too high since even yellow objects will appear white if their intensity is high enough. The solar projection was comfortable to look at so I was confident it was fine, but I did get a quantitative result that showed it was well within the photopic range.


The effective temperature drops from about 6300K at the center to 5000K at the limb. Yes, though 6390K is more accurate for the central zone. This hot central region presents the question of whether it, by itself, might look bluish-white, but I think not since the photon flux would likely make the depressed blue end in a photon flux distribution come up to flat. It would be interesting to see just what a photon flux distribution would look like for a bluish white star, perhaps Rigel, to see how much of a bump is needed from a flat distribution. My goal, however, was to de-yellow the Sun, so I haven't fooled with it much, but I doubt 6390K will give us a bluish-white color result.

If one matches the blue sky spectrum to a blackbody, you will discover the temperature won't be 8500K as photorgraphers like to set it, but closer to 15 million kelvins, which, interestingly, would make the core of the Sun a saturated blue, given proper attenuation and gamma ray protection. :)


If the upper wisps of the photosphere that dominate at the limb are more strongly nonthermal than the deep layers we see at the center, in such a way as to boost the blue band compared to that of a blackbody at the same temperature, perhaps that could equalize the hue. Your camera, provided you don't overexpose, would record hue differences that might elude your eyes when looking at such a large, bright projection up close. This would be interesting to check out in theory.This low limb temperature (thus much weaker in luminosity) may limit this, and I assume it is a small region compared to the rest of the disk. And it may be more an opposite effect, perhaps. The sp. irr. of the Sun is much weaker in the blue band when compared to a blackbody profile. Something is going on. Perhaps your point about nonthermal regions, limb or otherwise, is a good one to address this.

George
2017-Dec-04, 03:36 PM
FWIW, and a digression, many of us were indoctrinated into the "yellow sun" myth by Superman comics. Superman gains his powers by living near a yellow star.
(http://superman.wikia.com/wiki/Yellow_Stars) A white star would better explain his jumps and speeds. :) It would be interesting to know what percent of the times comic artists colored the Sun as white? Also, what percent of mankind used a yellow crayon as their first color of choice for the Sun?

Hornblower
2017-Dec-07, 02:56 AM
First things first. I did a rough experiment, projecting the Sun onto a white card in a blacked out room. I am satisfied that it looked neutral white, and thus I would be comfortable in calling either this spectrum or a true blackbody that matches the sensation neutral white by definition, should it be scientifically useful to do so. I will firm up the testing by cleaning the window for maximum contrast (It was dreadfully dirty today), covering it with a sheet of plywood with a 1.25 inch hole in an otherwise total blackout cover, and using binoculars for projecting a large image on the screen. I will then photograph that image with my digital camera, bracketing to get an image that is not overexposed at the center so I can get a good look at the limb darkening. I will then use my PaintShop Pro software to read the hue all over the image, to check for any yellowish or brownish shift toward the limb.

If I am not mistaken, George asserted that there would be no way to make the image of the Sun look bluish white. I beg to disagree since I observed it myself today. A slender beam of sunshine was shining through cracks in the blinds and making spots on a surface that otherwise looked neutral white in the overwhelming 3200K ambient light in the room. The sunlight looked as blue as an image of an early B star in a telescope. When I opened the blinds enough to make the sunshine dominant, it started looking neutral and the surface catching only the interior lighting became yellowish white.

George asserted that the core of the Sun, at millions of degrees K, should be saturated blue. No way. The tint of a blackbody emitter asymptotically approaches a limit that is only modestly bluer than an O or B star. I verified this myself with the Planckís law equation in my computer. It is my understanding that an opaque interior like this is thoroughly thermalized and that in a brief exposure it would match a true blackbody.

George can keep on stressing the nearly flat photon flux distribution of the Sunís light until doomsday and it will not shake my confidence in my hypothesis. I know from observation that a sheet of paper that looks neutral white in daylight looks just as neutral white in 3200K indoor lighting at night, even though the relative photon flux in the blue end is down by a factor of 10 or so in the latter. My color vision system retunes to it with ease. I also know that a star of 6000K or so looks neutral white in a dark surrounding. For whatever reason the system seems to remember the daylight hue as a primary standard in the absence of ambient light at a different temperature. Once again, suppose we had evolved for eons in 3200K daylight instead of what we actually did. I cannot see any reason from first principles to rule out the possibility that the visual system could perceive a star of that temperature as neutral white. Of course my line of thought is a hypothesis with no practical way to test it, as we have no means of turning the clock back and changing the color of the Sun before the emergence of trichromat mammals.

George, can you offer any argument from first principles against my hypothesis?

Hornblower
2017-Dec-07, 01:37 PM
I now have the window boarded up with just a pinhole for looking at the blue sky, and it looks much like a B or an A star. The difference between the 8500K used by photographers for the sky and some 30000K for an early B star is only a slight increase in the blue end of the spectrum. Now it's "hurry up and wait" for the Sun to come around to where I can project it with the binoculars, with an objective up against the board at the entrance hole.

Hornblower
2017-Dec-07, 04:58 PM
Here is an image of the Sun, adjusted in PaintShop Pro to make the center PSP's version of neutral light gray. To the upper left are three swatches from the image. The center swatch is from the center of the disk and the top one is from just inside the limb. Note how much more striking the limb darkening is with a sharp edge between the swatches than with the broad gradation on the disk. The bottom swatch is the limb brightened to the level of the center, to show the yellowing. I deliberately exposed the image so the center would not be blocked up. Overexposure could easily obliterate the limb darkening.
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George
2017-Dec-07, 05:07 PM
First things first. I did a rough experiment, projecting the Sun onto a white card in a blacked out room. I am satisfied that it looked neutral white, and thus I would be comfortable in calling either this spectrum or a true blackbody that matches the sensation neutral white by definition, should it be scientifically useful to do so. This supports Newton's claim that sunlight is white ("perfectly white"). I'm curious what the solar altitude was since air mass will redshift it some. The extinctions from our atmosphere don't normally cause a yellow tint for any projection, I assume, until the altitude is close to the horizon. There probably is a way to quantify the color metamorphosis if both altitude (air mass) and particle count is determined. Particle sizes could be important but maybe it's not that critical. Extensive observations would tweak this, perhaps, since pollen, aerosols, etc. can be seasonal, but, again, maybe the net tint effect would be minor.


I will firm up the testing by cleaning the window for maximum contrast (It was dreadfully dirty today), covering it with a sheet of plywood with a 1.25 inch hole in an otherwise total blackout cover, and using binoculars for projecting a large image on the screen. I will then photograph that image with my digital camera, bracketing to get an image that is not overexposed at the center so I can get a good look at the limb darkening. I will then use my PaintShop Pro software to read the hue all over the image, to check for any yellowish or brownish shift toward the limb. I am a little dubious about using binoculars. Wouldn't the coatings and achromatic aberration be color perturbers? I suppose if white is the result regardless, then perhaps not.


If I am not mistaken, George asserted that there would be no way to make the image of the Sun look bluish white. I beg to disagree since I observed it myself today. Okay, but consider the context of my statement. If you add blue paint to a white bucket of paint, will you ever get a yellowish colored paint from it? This would be true of any spectrum itself. Increasing the blue photon flux to a white photon flux distribution will not create a yellow result, right? This will not always be true, however, if you allow other effects to come into play, which is an interesting effect you have found, apparently...

[Added: I have stated in the past that perhaps the hotter central zone might have a tint of blue, but I expressed doubt due to the fact that the photon distribution would not bump into the blue much if at all, and color constancy favors a bright white light source. My main arguments are anti-yellow ones.]


A slender beam of sunshine was shining through cracks in the blinds and making spots on a surface that otherwise looked neutral white in the overwhelming 3200K ambient light in the room. The sunlight looked as blue as an image of an early B star in a telescope. When I opened the blinds enough to make the sunshine dominant, it started looking neutral and the surface catching only the interior lighting became yellowish white.That's interesting. The higher temperature and brighter surface brightness from the spot of sunlight should have made your retinex adjust it to a white spot and the adjacent area would yellow shift a little as a result. The whiter appearance of car lights when seen at night vs. in bright daylight is a similar case. But it's not always this simple. This isn't an area I've researched much. Some of Dr. Lamb's (Polaroid) work, for instance, can be found on line and it shows how changes in ambient light color can have some interesting color effects. Could diffraction also be a factor for "crack" light?

You might enjoy using a cyanometer (https://en.wikipedia.org/wiki/Cyanometer) for some of your work. This goes back to the late 1700s to note variations in blue saturation to better understand the cause of the blue sky, I think. It was carried atop the highest mountains with recordings of hue variations along the way.


George asserted that the core of the Sun, at millions of degrees K, should be saturated blue. No way. The tint of a blackbody emitter asymptotically approaches a limit that is only modestly bluer than an O or B star. I verified this myself with the Planck’s law equation in my computer. It is my understanding that an opaque interior like this is thoroughly thermalized and that in a brief exposure it would match a true blackbody. Attenuation may be what you are missing. Here is a BB comparison with an O star (25,000 K) versus the solar core temperature.

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The 15M K plot is reduced by a factor of 90,000, 25,000K plot by 100 to match at 750nm.

[Note: This is the corrected version, thanks to Hornblower catching the error in the original graph.]


George can keep on stressing the nearly flat photon flux distribution of the Sun’s light until doomsday and it will not shake my confidence in my hypothesis. I know from observation that a sheet of paper that looks neutral white in daylight looks just as neutral white in 3200K indoor lighting at night, even though the relative photon flux in the blue end is down by a factor of 10 or so in the latter. My color vision system retunes to it with ease. Mine too. This is known as color constancy, which is the "retuning" effect you mention. I have mentioned this many times. This is yet another reason why the Sun will be favored as white since even low temperature lighting will color shift to white if it is the brighter source of ambient light.

On a bright blue-sky day, look at your white paper while in the shade. The much stronger blue light of the skylight (no direct sunlight) will overcome the color constancy effect and produce a noticeable blue hue. Color constancy has limits.


I also know that a star of 6000K or so looks neutral white in a dark surrounding. Yet you've convinced me otherwise, but this seems to be very dependent on atmospheric extinctions. My example case is eta Cas which varies from a distinct yellow or gold hue to white, depending on the variation in extinctions, no doubt.


For whatever reason the system seems to remember the daylight hue as a primary standard in the absence of ambient light at a different temperature. I don't think its memory but the ability to always whiten the bright light source. Yet there are variations to this as you note above in your bluish white result, though the ambient light, in this case, may have been bright enough for the brain to accept it as the white source, thus giving you a color contrast of blue for the hotter sunlight spot. Your dark room result of white is consistent with this view, I think.


Once again, suppose we had evolved for eons in 3200K daylight instead of what we actually did. I cannot see any reason from first principles to rule out the possibility that the visual system could perceive a star of that temperature as neutral white. I agree that it would seem likely given enough evolutionary time. The variation in vision with other species might disagree with this idea, however. The earlier views of evolution (e.g. Lamark) argued that evolution would always improve things. Darwin showed that it was passive, so imperfection is possible if it doesn't mean extinction is a result.


George, can you offer any argument from first principles against my hypothesis?Do we not have enough objective evidence in other, even more evolved, species to suggest otherwise? This isn't evidence you are wrong only that there are limited guarantees with evolution.

George
2017-Dec-07, 05:34 PM
Here is an image of the Sun, adjusted in PaintShop Pro to make the center PSP's version of neutral light gray. To the upper left are three swatches from the image. The center swatch is from the center of the disk and the top one is from just inside the limb. Note how much more striking the limb darkening is with a sharp edge between the swatches than with the broad gradation on the disk. The bottom swatch is the limb brightened to the level of the center, to show the yellowing. I deliberately exposed the image so the center would not be blocked up. Overexposure could easily obliterate the limb darkening.
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The CLV (center to limb variation ) is dramatic. There is, as you know, a lot of flux difference between a 5000K source and a 6390K source, given the 4th power results for luminosity with temperature.

Your yellowing effect is likely due to extinctions, which is more than I would have expected. It would be interesting to see how this varies as the Sun sinks toward the horizon.

Here is one I took using a Sunspotter. The blue background, though more saturated in this image than of the eye, is the blue sky only shining on in the shade portion of the Sunspotter. But the brighter sunlight prevented any color contrast effect that would cause the Sun to appear more yellow.

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[Added: (Sorry my posts are rushed, due to work loads) I want to compliment you on this picture since I have been wanting to see an image as extinctions cause the cooler limb to turn yellow. A set of pictures from this point to a full yellow or orange Sun as it sinks over the horizon would be cool. It wouldn't shock me if no one has ever done this since I think I would have remembered seeing it if someone had.]

Hornblower
2017-Dec-08, 02:41 AM
First things first. I did a rough experiment, projecting the Sun onto a white card in a blacked out room. I am satisfied that it looked neutral white, and thus I would be comfortable in calling either this spectrum or a true blackbody that matches the sensation neutral white by definition, should it be scientifically useful to do so.

This supports Newton's claim that sunlight is white ("perfectly white"). I'm curious what the solar altitude was since air mass will redshift it some. The extinctions from our atmosphere don't normally cause a yellow tint for any projection, I assume, until the altitude is close to the horizon. There probably is a way to quantify the color metamorphosis if both altitude (air mass) and particle count is determined. Particle sizes could be important but maybe it's not that critical. Extensive observations would tweak this, perhaps, since pollen, aerosols, etc. can be seasonal, but, again, maybe the net tint effect would be minor.
The elevation was about 25 degrees. I have seen sources that reported that clear air shifts the B-V color index by about 0.3 at the zenith and more at lower elevations. That means some yellowing even at the zenith. My image was about 8 inches in diameter and bright enough that my color constancy was probably starting to kick in, whitening something that probably would have looked slightly yellowish white in a tiny speck.

Hornblower
2017-Dec-08, 02:54 AM
I will firm up the testing by cleaning the window for maximum contrast (It was dreadfully dirty today), covering it with a sheet of plywood with a 1.25 inch hole in an otherwise total blackout cover, and using binoculars for projecting a large image on the screen. I will then photograph that image with my digital camera, bracketing to get an image that is not overexposed at the center so I can get a good look at the limb darkening. I will then use my PaintShop Pro software to read the hue all over the image, to check for any yellowish or brownish shift toward the limb.

I am a little dubious about using binoculars. Wouldn't the coatings and achromatic aberration be color perturbers? I suppose if white is the result regardless, then perhaps not.
Some optical systems cause a slight yellowing of the transmitted light, but I was not concerned about the absolute color index here. I was looking for differences between the center and the limb. I had to get the Sun exactly centered in the glass because of a bit of off-axis lateral chromatic aberration, but once I got it centered there was no color fringe on the limb. I was using the only practical instrument I have for this task.

Hornblower
2017-Dec-08, 03:07 AM
If I am not mistaken, George asserted that there would be no way to make the image of the Sun look bluish white. I beg to disagree since I observed it myself today.

Okay, but consider the context of my statement. If you add blue paint to a white bucket of paint, will you ever get a yellowish colored paint from it? This would be true of any spectrum itself. Increasing the blue photon flux to a white photon flux distribution will not create a yellow result, right? This will not always be true, however, if you allow other effects to come into play, which is an interesting effect you have found, apparently...

[Added: I have stated in the past that perhaps the hotter central zone might have a tint of blue, but I expressed doubt due to the fact that the photon distribution would not bump into the blue much if at all, and color constancy favors a bright white light source. My main arguments are anti-yellow ones.]
Whatever happens when we mix paint is irrelevant here. Opening the blinds made the overall ambient light bluer, but did not completely obliterate the illumination of that white cabinet by the room light. White surfaces close to the window started looking more nearly neutral, while those in the far side of the room where the light bulbs still provided most of their light started looking yellower then when there was very little sunlight getting into the room. A photo taken with the white balance feature in the camera turned off would have shown the latter less yellow than before I opened the blinds.

Hornblower
2017-Dec-08, 03:20 AM
A slender beam of sunshine was shining through cracks in the blinds and making spots on a surface that otherwise looked neutral white in the overwhelming 3200K ambient light in the room. The sunlight looked as blue as an image of an early B star in a telescope. When I opened the blinds enough to make the sunshine dominant, it started looking neutral and the surface catching only the interior lighting became yellowish white.

That's interesting. The higher temperature and brighter surface brightness from the spot of sunlight should have made your retinex adjust it to a white spot and the adjacent area would yellow shift a little as a result. The whiter appearance of car lights when seen at night vs. in bright daylight is a similar case. But it's not always this simple. This isn't an area I've researched much. Some of Dr. Lamb's (Polaroid) work, for instance, can be found on line and it shows how changes in ambient light color can have some interesting color effects. Could diffraction also be a factor for "crack" light?
These spots covered perhaps 1/1000th of the surface in that room and were not very bright. This was essentially pinhole projection, and the Sun was already considerably dimmed by shining through the crowns of large trees. Before I opened the blinds these little spots were nowhere near enough to take over from the room light in dominating my color constancy function, just as distant car headlights in daylight are nowhere near enough to to a similar takeover. As for effects of diffraction, I doubt it.

Hornblower
2017-Dec-08, 03:37 AM
George asserted that the core of the Sun, at millions of degrees K, should be saturated blue. No way. The tint of a blackbody emitter asymptotically approaches a limit that is only modestly bluer than an O or B star. I verified this myself with the Planck’s law equation in my computer. It is my understanding that an opaque interior like this is thoroughly thermalized and that in a brief exposure it would match a true blackbody.

Attenuation may be what you are missing. Here is a BB comparison with an O star (25,000 K) versus the solar core temperature.

Click image for larger version.

Name: Solar core color.jpg
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Size: 669.2 KB
ID: 22794

The 15M K plot is reduced by a factor of 30k.
I am reasonably certain that whoever plotted that graph bungled it severely. The white curve is closer to 7500K than 25000K. At the latter temperature the peak of the curve should be way over in the ultraviolet, around 120nm or so. The blue curve should not rise that steeply from the red to the blue end of the visible range. When I get a chance I will run my Planck calculator and attenuate the core curve enough to equalize them at the red end, and upload a scan of my graph.

Hornblower
2017-Dec-08, 03:43 AM
[Added: I have stated in the past that perhaps the hotter central zone might have a tint of blue, but I expressed doubt due to the fact that the photon distribution would not bump into the blue much if at all, and color constancy favors a bright white light source. My main arguments are anti-yellow ones.]
My bold. At the higher temperature the blue end of the spectrum is brightened by the largest factor. The red portion is brightened the least and the green portion by an intermediate amount.

Hornblower
2017-Dec-08, 03:59 AM
George can keep on stressing the nearly flat photon flux distribution of the Sun’s light until doomsday and it will not shake my confidence in my hypothesis. I know from observation that a sheet of paper that looks neutral white in daylight looks just as neutral white in 3200K indoor lighting at night, even though the relative photon flux in the blue end is down by a factor of 10 or so in the latter. My color vision system retunes to it with ease.

Mine too. This is known as color constancy, which is the "retuning" effect you mention. I have mentioned this many times. This is yet another reason why the Sun will be favored as white since even low temperature lighting will color shift to white if it is the brighter source of ambient light.

On a bright blue-sky day, look at your white paper while in the shade. The much stronger blue light of the skylight (no direct sunlight) will overcome the color constancy effect and produce a noticeable blue hue. Color constancy has limits.I checked it out today, and yes indeed, ambient light of that color is beyond the upper limit of my color constancy. I would say that 6000K is at or very near that upper limit. I think my lower limit is somewhat below 3200K, based on test brownouts I have done with a Variac to reduce the voltage going into a tungsten lamp.

Hornblower
2017-Dec-08, 04:03 AM
I also know that a star of 6000K or so looks neutral white in a dark surrounding.

Yet you've convinced me otherwise, but this seems to be very dependent on atmospheric extinctions. My example case is eta Cas which varies from a distinct yellow or gold hue to white, depending on the variation in extinctions, no doubt.
I meant to specify as seen from out in space. My own observations in good air quality find that an early F star, about 7500K, is a better neutral white. In really foul air I have seen them look yellowish.

Hornblower
2017-Dec-08, 04:21 AM
Once again, suppose we had evolved for eons in 3200K daylight instead of what we actually did. I cannot see any reason from first principles to rule out the possibility that the visual system could perceive a star of that temperature as neutral white.

I agree that it would seem likely given enough evolutionary time. The variation in vision with other species might disagree with this idea, however. The earlier views of evolution (e.g. Lamark) argued that evolution would always improve things. Darwin showed that it was passive, so imperfection is possible if it doesn't mean extinction is a result.
I don't have any bright ideas about how to investigate this phenomenon with other species. I am not Dr. Dolittle, so an animal cannot tell me what sort of star it perceives as neutral white.

I just thought of something closer to home timewise than long term evolution. Perhaps our exposure to lots of daylight in infancy was a factor in wiring us to see colors the way we do. If a baby never sees anything but 3200k ambient light during those first critical weeks and months, he or she just might have a perception of star colors that is different from mine.

Hornblower
2017-Dec-08, 04:56 AM
Here is an image of the Sun, adjusted in PaintShop Pro to make the center PSP's version of neutral light gray. To the upper left are three swatches from the image. The center swatch is from the center of the disk and the top one is from just inside the limb. Note how much more striking the limb darkening is with a sharp edge between the swatches than with the broad gradation on the disk. The bottom swatch is the limb brightened to the level of the center, to show the yellowing. I deliberately exposed the image so the center would not be blocked up. Overexposure could easily obliterate the limb darkening.

The CLV (center to limb variation ) is dramatic. There is, as you know, a lot of flux difference between a 5000K source and a 6390K source, given the 4th power results for luminosity with temperature.
Your yellowing effect is likely due to extinctions, which is more than I would have expected. It would be interesting to see how this varies as the Sun sinks toward the horizon.

Here is one I took using a Sunspotter. The blue background, though more saturated in this image than of the eye, is the blue sky only shining on in the shade portion of the Sunspotter. But the brighter sunlight prevented any color contrast effect that would cause the Sun to appear more yellow.

22797

[Added: (Sorry my posts are rushed, due to work loads) I want to compliment you on this picture since I have been wanting to see an image as extinctions cause the cooler limb to turn yellow. A set of pictures from this point to a full yellow or orange Sun as it sinks over the horizon would be cool. It wouldn't shock me if no one has ever done this since I think I would have remembered seeing it if someone had.]
My bold. I don't get your point about extinction. Suppose for the sake of argument that the Sun's hue is the same at the limb as at the center, just darker. Any atmospheric extinction would change the overall color but still leave the limb and the center the same color. The yellowing toward the limb is from extinction in the Sun's photosphere, not in our atmosphere. The light from the hotter deep layers is attenuated more in going slantways from near the limb than in going straight up at the center.

My hunch is that the inherent yellowing of the limb will be masked by strong atmospheric yellowing near the horizon. I have some yellow images as a result of the characteristics of my solar filter which I used when photographing the eclipse in August. I will read the color content in PaintShop Pro when I get a chance.

George
2017-Dec-08, 03:22 PM
My bold. I don't get your point about extinction. Suppose for the sake of argument that the Sun's hue is the same at the limb as at the center, just darker. Any atmospheric extinction would change the overall color but still leave the limb and the center the same color.Right, but we know that's not true. From space (AM0), the difference in sp. irr. between the limb and the center is significant when we talk about reaching color changing thresholds after atmospheric extinctions, which are due to things like lower solar elevation, increased extinctions due to more dusty, or other, conditions.


The yellowing toward the limb is from extinction in the Sun's photosphere, not in our atmosphere. The light from the hotter deep layers is attenuated more in going slantways from near the limb than in going straight up at the center. Correct, from space the limb's 5000K is more yellow (redshifted) compared with the hot 6390K central zone due to the fact that we are only viewing the very tip-top region of the limb's region of the photosphere due to our angle to the spherical photosphere there. We can see, reportedly, about 200km deep into the photosphere's interior when viewing the central region, thus we see a much hotter region, which bumps the blue end photon flux for the central region.

22798

[The Sun varies from a BB more than many realize especially in the blue end of the visible spectrum. I would enjoy seeing an actual sp. irr. of both these regions.]


My hunch is that the inherent yellowing of the limb will be masked by strong atmospheric yellowing near the horizon.If I understand you, I disagree. With greater and greater atmospheric extinctions as the Sun sinks over the edge, the solar limb light will begin to turn yellow prior to the hotter (bluer) central zone. The greater blue-end flux of the hotter central zone will delay it from appearing yellow as soon as the limb does. I think this is what we are seeing in your picture. This may or may not happen fairly quickly since air mass increases quickly near the horizon, and increase in air mass means an exponential rate for extinctions, blues go first. [We'll ignore the violets.] [It would be very interesting to see this color metamorphosis in pictorial form. hint. ;)]

George
2017-Dec-08, 03:48 PM
The elevation was about 25 degrees. I have seen sources that reported that clear air shifts the B-V color index by about 0.3 at the zenith and more at lower elevations. That means some yellowing even at the zenith. My image was about 8 inches in diameter and bright enough that my color constancy was probably starting to kick in, whitening something that probably would have looked slightly yellowish white in a tiny speck.

[Oops, I missed your other posts...]

That is helpful information. I would not have guessed that an AM1 would have been quite that much of a color shift but I'm not that surprised. The Solar Constant drops significantly for even an AM1 reduction.

George
2017-Dec-08, 03:55 PM
Whatever happens when we mix paint is irrelevant here. Opening the blinds made the overall ambient light bluer, but did not completely obliterate the illumination of that white cabinet by the room light. White surfaces close to the window started looking more nearly neutral, while those in the far side of the room where the light bulbs still provided most of their light started looking yellower then when there was very little sunlight getting into the room. A photo taken with the white balance feature in the camera turned off would have shown the latter less yellow than before I opened the blinds.Agreed, sunlight, being the hotter and whiter light will cause us and cameras to make it the white-balanced source of light, causing lower temperature light areas to yellow-shift, which is the analogy of the car lights being whiter at night and much more yellow in daylight.

The best argument that the Sun is not yellow, though I'm digressing away from your points, is the fact that projections are white even at the limb. Adding the atmospheric extinctions, which are far more blue-end light, back into the white disk will never give us a yellow Sun. [I know you get this, but it is the most powerful argument I know to convince others that we don't have a yellow Sun.]

George
2017-Dec-08, 03:58 PM
Some optical systems cause a slight yellowing of the transmitted light, but I was not concerned about the absolute color index here. I was looking for differences between the center and the limb. I had to get the Sun exactly centered in the glass because of a bit of off-axis lateral chromatic aberration, but once I got it centered there was no color fringe on the limb. I was using the only practical instrument I have for this task.
That's interesting. It seems you have a way to simulate greater extinctions with your viewing angles. If this method is a close fit with actual extinctions it would make the color metamorphosis go quicker. But is does represent what we ought to see -- the limb becoming yellow sooner than the hotter central region.

George
2017-Dec-08, 04:05 PM
I don't have any bright ideas about how to investigate this phenomenon with other species. I am not Dr. Dolittle, so an animal cannot tell me what sort of star it perceives as neutral white.

I just thought of something closer to home timewise than long term evolution. Perhaps our exposure to lots of daylight in infancy was a factor in wiring us to see colors the way we do. If a baby never sees anything but 3200k ambient light during those first critical weeks and months, he or she just might have a perception of star colors that is different from mine. I'm not really disagreeing. There's no question that species have evolved to take advantage of sunlight. The four color cones of birds, for instance, would be interesting if we could see what they do. And it's not just our eyes that have evolved to exploit sunlight; our skin has too. It was serendipity that allowed doctors to learn that sunlight produced significant improvement for jaundice babies simply because sunlight was able to shine on some babies in an English (I think) nursery. I recall designing lighting for our hospital to duplicate this benefit. Perhaps there is a way to test your hypothesis. Grant would be your best bet for this, however.

George
2017-Dec-08, 04:54 PM
I am reasonably certain that whoever plotted that graph bungled it severely. Botched is right! Ug. Thanks for catching it.

Here is the correct Planck curves adjusted to an equal level at 750nm. [The 25,000K values were reduced by 100x, the 15M K values reduces by 90,000x.]

22799

The 15M K distribution give us about 35% more at 450nm (blue) than the 25,000K. Will this make a difference in blue saturation? Perhaps. My attempt originally, several years ago, was to bump the Planck temperature enough to get close to matching a deep blue sky sp. irr. data set I found, but I seem to have lost it. I recall that a saturated blue sky has a very step slope at the blue end and, thus, required a monster amount of temperature to try and match it.

Oddly (perhaps not), Neil Tyson mentioned the core is blue in one of his books that came out not too long after I posted it. [He's here somewhere :shifty:, at least I hope so.]

George
2017-Dec-08, 05:02 PM
I meant to specify as seen from out in space. My own observations in good air quality find that an early F star, about 7500K, is a better neutral white. In really foul air I have seen them look yellowish. This is consistent with Secchi's original star color grouping in establishing our first respectable star types. He had Altair and Vega as example cases of white. Altair seems to fit this temperature, though Vega is around 9600K. I will posit that atmospheric extinctions greatly affected his classifications, though I don't think it takes a heavy dose of extinctions to make subtle color changes. Eta Cas, once again, varies from white to a distinct yellow-gold tint due to atmospheric conditions, at least for me.

Hornblower
2017-Dec-09, 05:06 AM
My hunch is that the inherent yellowing of the limb will be masked by strong atmospheric yellowing near the horizon.

If I understand you, I disagree. With greater and greater atmospheric extinctions as the Sun sinks over the edge, the solar limb light will begin to turn yellow prior to the hotter (bluer) central zone. The greater blue-end flux of the hotter central zone will delay it from appearing yellow as soon as the limb does. I think this is what we are seeing in your picture. This may or may not happen fairly quickly since air mass increases quickly near the horizon, and increase in air mass means an exponential rate for extinctions, blues go first. [We'll ignore the violets.] [It would be very interesting to see this color metamorphosis in pictorial form. hint. ]My bad. When I actually set up a hypothetical combination of solar spectrum and extinction characteristic and did some calculating, I could see that my hunch was wrong. Yes indeed, getting closer to the horizon will make the center pale yellow and the limb somewhat more saturated yellow.

Now I think I see what you meant with your initial remark about extinction. I somehow interpreted it as asserting that the atmospheric effect made a difference between the center and limb colors when there wasn't any before entering the atmosphere. I now figure that you meant that this extinction brings the bluer center to neutral white while bringing the limb to pale yellow.

My image was affected by the combination of low-elevation atmospheric discoloring, the characteristics of the window glass and the binocular and camera lenses, the camera's daylight setting for white balance, and the color balance of the computer monitor. The image initially looked extremely pastel green at the center, and reading the RGB indicator in the software indicated a slight excess of green. I don't know which component was most to blame for that. When I tuned it out and got the software's RGB values equalized, the center really did look neutral white, thus eliminating the monitor as a suspect.

When looking at that large projected image, I think I was having color constancy along with something analogous which I would call brightness constancy. Those swatches I made show that the limb was much darker than it looked to me as part of the broad gradation from center to limb. The whole thing looked neutral white overall, but I think a tiny composite speck would have looked yellowish white, as does a G star, at least to my eyes.

Hornblower
2017-Dec-09, 01:32 PM
Addendum: My educated guess is that the slight green tinge on my raw image was an artifact of the factory setting of the camera's RGB daylight white balance, which generally is aimed at a pleasing rendition of a human face. The camera's spectral sensitivity pattern does not match that of the eye, and a setting that matches a skin tone can distort a neutral gray and vice versa. The monitor has the same issue, and its spectrum may not exactly match that of the camera. This has been an issue for as long as there has been color photography.

I just now looked at a blank white page on my computer screen through the binoculars and also a finder scope. Both instruments made an ever so slight shift to perhaps a greenish tinge which was so slight that I could not be sure of the color. I will try test exposures on a suitable surface later today. Now it appears that there will be an ideal surface in the form of fresh snow under an overcast sky. Another interesting project will be comparing the tint of the snow under different sky conditions.

Hornblower
2017-Dec-09, 06:25 PM
Here is a test image of a piece of white poster board illuminated by the gray sky. The camera is looking "backward" through the binoculars to get a sample of the transmitted light for comparison with the direct light from the board.
2280322804

The first image is directly from the camera and shows a bluish cast. The second image has been neutralized in the editing software, and just above and to the left of the binocular objective is a swatch from the binocular light, brightened to closely match the direct view. It has a slight greenish cast. The light passed through a lot of glass, mostly in the Porro prisms.

Once again, I was not concerned with getting an exact reproduction of the source. I was looking for the brightness and color differences between the center and limb light from the Sun, and this small amount of tinting in the optical system did not have much if any effect on the magnitudes of those differences.

So far there is not enough snow to make a good clean surface for comparison with the poster board. If we get clear weather tomorrow I will take a shot of the poster board under sunshine with blue sky, to see how it compares with the cloudy skylight.

Camera: Fuji Finepix S5200, ISO 100, 1/40 sec, white balance set for daylight.

Hornblower
2017-Dec-09, 06:46 PM
Now there is enough snow on the car for a good comparison of the poster board, the snow and the cloudy sky.
2280522806

George
2017-Dec-09, 07:43 PM
Now I think I see what you meant with your initial remark about extinction. I somehow interpreted it as asserting that the atmospheric effect made a difference between the center and limb colors when there wasn't any before entering the atmosphere. I now figure that you meant that this extinction brings the bluer center to neutral white while bringing the limb to pale yellow.Right. Extinctions are uniformly applied. I think only at the horizon itself will the differences in air mass for that 1/2 degree disk make a difference, and sometimes beautifully so but this is caused by the gradient of air mass itself, not any special properties, of course.


When looking at that large projected image, I think I was having color constancy along with something analogous which I would call brightness constancy. Those swatches I made show that the limb was much darker than it looked to me as part of the broad gradation from center to limb. The whole thing looked neutral white overall, but I think a tiny composite speck would have looked yellowish white, as does a G star, at least to my eyes.Yes, it's surprising how we can be fooled with that much actual contrast. Here is my favorite for this illusion:

22807

[I added the triangles to better see the tansistion.] The apparent difference between the A and B square is remarkable given that they are the same. The solar disk will always exhibit this CLV effect.

George
2017-Dec-09, 08:02 PM
Here is a test image of a piece of white poster board illuminated by the gray sky. The camera is looking "backward" through the binoculars to get a sample of the transmitted light for comparison with the direct light from the board.
2280322804

The first image is directly from the camera and shows a bluish cast. The second image has been neutralized in the editing software, and just above and to the left of the binocular objective is a swatch from the binocular light, brightened to closely match the direct view. It has a slight greenish cast. The light passed through a lot of glass, mostly in the Porro prisms. Yes, the green tint is slightly more obvious, I think, when looking at the thumbnail, but it is too slight of a difference to wonder why. Perhaps the greater use of the blue-free cones of the fovea make a tiny difference. [Ok, so I think when the word "why" is used it makes me throw something at it. :)]

Here is today's SOHO image (from space for those who may not know). I floated the mask from the limb to the center. This is what a 1390K temperature gradient does to luminosity.

22808


So far there is not enough snow to make a good clean surface for comparison with the poster board. If we get clear weather tomorrow I will take a shot of the poster board under sunshine with blue sky, to see how it compares with the cloudy skylight. You might want to also take an image of the snow or card in the shade, where only the blue sky is the light source.

George
2017-Dec-09, 08:08 PM
Now there is enough snow on the car for a good comparison of the poster board, the snow and the cloudy sky.
2280522806

I will guess the the slight difference in brightness is that your background is closer to the horizon. If the brighter zenith region could be taken simultaneously (don't ask me how) then the two may be very close.

Regarding any color issues, snow has a slight variation in spectral reflectivity based on the size of the particles. I posted some differences a good while back, but snow is typically about 90% or better in spectral reflectance in the visible spectrum. It's whiteness is another argument for a non-yellow Sun and the example of yellow snow adds some graphical kick to it when mentioned, not that I would ever do that, of course. :shifty:

Hornblower
2017-Dec-09, 11:17 PM
I will guess the the slight difference in brightness is that your background is closer to the horizon. If the brighter zenith region could be taken simultaneously (don't ask me how) then the two may be very close.

Regarding any color issues, snow has a slight variation in spectral reflectivity based on the size of the particles. I posted some differences a good while back, but snow is typically about 90% or better in spectral reflectance in the visible spectrum. It's whiteness is another argument for a non-yellow Sun and the example of yellow snow adds some graphical kick to it when mentioned, not that I would ever do that, of course. :shifty:

Let me clarify what is in those photos. The left one is the poster board and some adjoining snow on the rear deck of my car. The right one is the sky near the zenith. All I am looking for now is seeing how nearly neutral the snow and the poster board are as reflectors. Then I can evaluate the hue of the combined Sun and blue sky as a light source illuminating the board, as compared with the projected image of the Sun in the darkened room. I can allow for the slight green tint of the binoculars in doing that. While I am at it I will put the board in the shade to get a look at the hue from the blue sky alone. In each case I am manually setting the exposure to get close to the same luminance on each image, for consistency in analyzing the color in the software.

George
2017-Dec-11, 03:23 PM
That makes sense.

It almost looks as if there is a tiny extra tint of blue for the snow. However, I took your left image and floated a mask from just below the bottom edge of the board and placed it upon the board. The juxtaposed snow is within the circle, but a Waldo challenge would be much easier to find. Here it is:

22812

22813

Hornblower
2017-Dec-12, 04:46 AM
Here are some images I have prepared of the Sun as projected in the blacked out room.

1. Projected on white poster board, corrected for greenish tint from binoculars. Time 10:42 EST December 7; altitude 26 degrees.

2. Same image, with background filled with composite daylight at 12 noon on same board, that is, Sun and blue sky. That background almost perfectly matches neutral tone from software. Note how much more apparent the limb darkening is.

3. Same image, but adjusted in computer to match center to board illuminated by Sun at 3:56 EST, altitude 7.5 degrees. Same background as #2. That is probably similar to an M star at the zenith.
228142281522816

If someone had showed me those first two images and I had never heard of the Sun being considered yellow, and they asked me what color I thought it was, I would have said "white" in a heartbeat. Upon looking closely at the limb I might have noticed the brownish tinge.

George
2017-Dec-12, 03:09 PM
Here are some images I have prepared of the Sun as projected in the blacked out room.

1. Projected on white poster board, corrected for greenish tint from binoculars. Time 10:42 EST December 7; altitude 26 degrees. 26 degrees is an air mass of 2.28. I too would call it white, but, looking closer, the dirty yellow is not hard to see especially along the limb. I would have expected, however, a lower elevation for this amount of yellowing. Perhaps the Sunspotter adjusted for low elevations will make a fair comparison.

Any idea if your particle counts are higher than usual?


2. Same image, with background filled with composite daylight at 12 noon on same board, that is, Sun and blue sky. That background almost perfectly matches neutral tone from software. Note how much more apparent the limb darkening is. What I cool-looking image! It makes one see the Sun in daylight and has the 3D touch. Nice!

The dark limb region is not something I would expect, however. Why would the limb be much darker than the light outside of it. [Warning: The IR level is still too intense to stare at it.]
This seems very unlikely since, with scattering, how can "the sum of some of the parts be greater than the whole?"


3. Same image, but adjusted in computer to match center to board illuminated by Sun at 3:56 EST, altitude 7.5 degrees. Same background as #2. That is probably similar to an M star at the zenith. 7.5 deg. gives an air mass of about 7.5 (7.41 deg = AM7.41; Rozenberg formula). This low elevation should give some distinct yellow results. Perhaps your level of attenuation makes the color stand out more than a normal projection. It seems more yellow than it should be, but perhaps not.

When the Sun is very low, the attenuation is often enough to make it easy on the eyes to look at and see the very yellow, or sometimes, orange disk. Imaging at this point would allow visual comparison to see how well the image color fits.

Very interesting. I'm delighted you are doing this. [I am running hard this week but may have time this weekend to do some Sunspotter imaging.]

Hornblower
2017-Dec-12, 04:10 PM
Imaging by this camera obscura method is difficult except around noon because the low Sun is behind trees in this heavily wooded neighborhood. My next project is to play with my eclipse photos through the solar filter which made the Sun look strongly yellow. I will neutralize it in the software and see if I still get the center-to-limb color change. That may give me a baseline for experimenting with images at low elevation. The eclipse images were near the zenith, where the atmospheric yellowing is minimal.

The limb looks so dark against that bright background because it is that dark. When looking at the image on a black background, so there is a smooth gradation from the center, it appears that my visual process has a partial brightness constancy function.

George
2017-Dec-12, 04:47 PM
Imaging by this camera obscura method is difficult except around noon because the low Sun is behind trees in this heavily wooded neighborhood. My next project is to play with my eclipse photos through the solar filter which made the Sun look strongly yellow. I will neutralize it in the software and see if I still get the center-to-limb color change. That may give me a baseline for experimenting with images at low elevation. The eclipse images were near the zenith, where the atmospheric yellowing is minimal. I look forward in seeing your work.


The limb looks so dark against that bright background because it is that dark. But wouldn't the actual surface brightness at the limb exceed that of only scattered light as seen outside the limb? I'm puzzled.

Hornblower
2017-Dec-12, 05:11 PM
I look forward in seeing your work.

But wouldn't the actual surface brightness at the limb exceed that of only scattered light as seen outside the limb? I'm puzzled.

That bright background view is a simulation. I started with the image on the black background and replaced the black with composite daylight in the photo-editing software. There is no scattered light.

Hornblower
2017-Dec-12, 08:05 PM
Let me assure you that my images are not exaggerating the limb darkening. From the published center and limb effective temperatures, my Planck law calculation gives the limb a bolometric luminosity of only about 40% of the center, and visually it will be somewhat less because of being shifted more into the infrared. That is in good agreement with my calibration of the luminance of my monitor over the range of RGB values in the photoediting software. I did that with a professional grade exposure meter.

Hornblower
2017-Dec-13, 05:26 AM
Here are some cleaned up images, eliminating possible excessively dark edges on the Sun when seen on the light background.

22817228182281922820

From left to right:
1. 11 AM, December 7, elevation about 26 degrees, black background.
2. Same image on light background.
3. 3:46 PM, December 11, elevation about 7.5 degrees, black background.
4. Same image on light background.

My attempt at neutralizing the color of the filtered images I took in August were not satisfactory. The yellow tint was just too saturated to deal with, and besides the image scale is much smaller. I will stick with my camera obscura method about 11 AM, when the Sun is clear of the trees. It gives a nice big image, and I can monitor the yellowing at lower altitudes with the illuminated poster board as a reference.

Hornblower
2017-Dec-13, 11:55 PM
More images, with date, time and altitude in degrees:

22826 12/13 7:37 2.5
22827 12/13 7:48 4.3
22828 12.13 8:07 7.2
22829 12/13 8:22 9.4
22830 12/07 10:45 26.1

To be continued in next post.

Hornblower
2017-Dec-14, 12:12 AM
Same images with light backgrounds. Note how much more striking the limb darkening appears this way.

2283122832228332283422835

The sky was clear and as free of particulates as it ever gets around here.

As noted earlier, I have no satisfactory means of imaging the Sun except through that south-facing window for a couple of hours just before noon. I got the early morning colors by photographing the illumination of my white poster board at the stated times, and then adjusting copies of the last image until they matched the board. When I get a chance I will fill in the gap in the altitude range and extend it as the Sun returns north in the next 6 months. It will be interesting to see how much blue shift I get at higher altitudes.

George
2017-Dec-18, 07:48 PM
:clap: Very nice demonstration of the yellowing effect from scattering. Your color steps are excellent. I've been out a lot lately but the sky is solid clouds these days, anyway I still want to attempt some "true" color imaging off the Sunspotter as the Sun sinks. This summer, I should be able to get in the dry SW and maybe get it when it goes orange. It is easy to look at when it is a deep, saturated, yellow or even yellow-orange. This will allow a visual comparison with the imaging.

The CLV differences in your two backgrounds is surprising. I would have expected some of this difference, but not this much. I did a quick floating-crop from you black background to make sure it was there, and it is, of course.