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I’ve been having fun* writing some code to model the performance of my telescope and am getting reasonably accurate signal to noise ratios for night time imaging.
I would like to extend this to daytime imaging but realise I have no magnitudes per arc second brightness value for a cloud free daytime sky. Obviously, this will vary from day to day and location, but does anyone have a representative measured figure? Its a while since we had a clear blue sky here.
Assuming the full Moon is 0.5 degrees across and of magnitude -12.6 I get a sky brightness estimate of 3.4 mags per arc sec but rather suspect 4.4 might be nearer as the full Moon is very obvious in the sky
Has anyone a better figure?
Thanks.
*Yes, I know I’m sad.
What’s a summer blue daytime sky?
Anyway, interesting calculation. The wonderful book “Sunsets, twilights and evening skies” by Aden and Marjorie Meinel contains the attached plot. It indicates a factor of 70 million between a perfect night sky and the noon zenith sky. That is 2.5 * log10(70E6) = 19.6 mags. Assuming a perfect night sky to be 22 mags per square arcsec that would put the noon daytime sky at about 2.4 mags per square arcsec so a bit brighter than you calculated.
The surface brightness of the Full Moon is around 3.4 mags per arcsec so that would imply that it is about 40% the surface brightness of the daytime sky which would be easily detectable with the naked eye. That is something you should be able to demonstrate easily by taking an image and measuring it.
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What’s a summer blue daytime sky?
Anyway, interesting calculation. The wonderful book “Sunsets, twilights and evening skies” by Aden and Marjorie Meinel contains the attached plot. It indicates a factor of 70 million between a perfect night sky and the noon zenith sky. That is 2.5 * log10(70E6) = 19.6 mags. Assuming a perfect night sky to be 22 mags per square arcsec that would put the noon daytime sky at about 2.4 mags per square arcsec so a bit brighter than you calculated.
The surface brightness of the Full Moon is around 3.4 mags per arcsec so that would imply that it is about 40% the surface brightness of the daytime sky which would be easily detectable with the naked eye. That is something you should be able to demonstrate easily by taking an image and measuring it.
The cloudless sky is, of course, not white. Neither is it unpolarized. The use of a polarizing filter can make a big difference in its brightness but a more important method of darkening the sky is to observe through a red or near infrared filter.
I have already posted images of 6th and 7th magnitude Pleiads taken not too long after local noon. With my kit I estimate that I should be able to reach 12th magnitude with a Sloan i’ filter. It will be necessary to take numerous subs where the stars are almost but not quite saturated and then remove the almost as bright sky background in software.
The Meinel plot approximates the response of the human eye which is what I think Grant was interested in. Clearly things would be different if you used filters etc.
Nick: sure.
It is easy, in my experience, to see 2nd magnitude stars through a telescope in daylight. Some decades ago Venus occulted Nunki, or sigma Sgr. From central Oxford the critical moments were clouded out but 20 minutes or so later the star was very easily visible in a 27.5cm Mak-Cas. I guess the limiting visual magnitude on that occasion was around 4 to 4.5.
Thats a useful looking book. Will grab a copy off ebay.
The calcs I am doing are based around the standard CCD S/N calculation mentioned by Steve Howell in his “Handbook of CCD Astronomy” – derived from Mortara&Fowler plus Newberry and others
Something like…
SNR=Nstar*t/sqrt(Nstar*t+npix(Nsky*t+Ndark*t+Nread*Nread))
where:
t – exposure length
Nstar – electrons from the star
npix – number of pixels covered by star
Nsky – electrons from sky in each pixel
Ndark – dark current electrons
Nread – read noiseYeah, polarisation makes a huge difference depending on where you are looking on the sky. Similarly, filtering.
I had a bash at imaging Polaris with an 80mm f/7 refractor a few years back using an H-alpha filter to filter it into the red. Unfortunately, the images kept on saturating as sunrise approached – but I was using a CCD whose shortest exposure was about 0.08sec.
With a modern CMOS sensor I imagine I could do a lot better now.
In about 2000 or 2001 there was a planetary conjunction not far from the Sun (8degs or so I think). Phil Alner of Cody Society and I observed Jupiter, Saturn, some stars and (I think) Mars through a Zeiss 160mm f/15 refractor. While the planets were clear and easy (though the glare from the nearby Sun pretty fierce – don’t try this at home kids) I don’t recall seeing any of the moons of Jupiter which are mag 5. I think we decided the limiting mag was 3ish elsewhere on the sky.
It looks intermittently clear here this afternoon. I may give it a try.
I had a go at imaging Capella this afternoon in a clear, transparent sky after I’d finished with the Sun. I took 1000 frames with an exposure 879 us and gain set to minimum on an ASI1600 using a 90mm, f/6 refr and then took the same number of dark frames with the same exposure. Capella was quite close to the Sun so there is a lot of forward scatter from drifting pollen but, after calibration, and taking the V mag of Capella as 0.08 I get a sky brightness of 2.6 mag/arcsec^2. Remarkably close to what I expected. A video of the calibrated light frames is here:
You had better weather than us – went out to garden twice and it started raining!
Thats a nice video. Love the pollen blowing through. Thats a really helpful figure to have – thanks. I shall adopt that instead of my crude guess.
Yes, a very nice video. Stacking the frames and using something like FABADA to remove the noise and you should end up with a high SNR and, from that, estimate a plausible limiting magnitude.
FWIW, total cloud cover here right now in La Palma but at least it isn’t raining.
OK, you guys, when are you going to start imaging Messier objects? M35, M36 and M37 are well placed right now. 😉
With a modern CMOS sensor I imagine I could do a lot better now.
Or a modern CCD for that matter. A SX 814 works beautifully down to 2ms and was used for my Pleiades imaging.
I think we decided the limiting mag was 3ish elsewhere on the sky.
I came to a similar conclusion (though perhaps half a mag fainter) when attempting to observe Venus occulting sigma Sgr some years back. The actual occultation was clouded out but 20 minutes after the star was very easily seen in a 27.5cm Maksutov Cassegrain.
It was after that episode that I became disillusioned by Asimov’s Nightfall. A superb story but the idea that their astronomers living in a globular cluster couldn’t see stars in the daytime beggars belief. Venus at its brightest is a relatively easy daylight naked eye object here on Earth and some claim to be able to see Sirius.
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