How would I calculate limiting magnitude/star brightness increase based on aperture?

[pipnina]

I will get the chance to find out for real tomorrow night (hopefully!) but I'm trying to work out what the limiting stellar magnitude for my camera+scope will be in live view.

My 105mm f2.8 lens (37mm dia) can manage mag 6.4 just about, so my best estimate is that my 10" dob will manage ~11.6.

And so long as each pixel is larger than dawes/rayleigh limit, stars will become brighter with aperture, right?

Cheers.

[Scooot]

This should give you an idea.

http://www.cruxis.com/scope/limitingmagnitude.htm

[rl]

11.6 might be a little optimistic. 

The light gain will be about 40 times allowing for the central obstruction, assuming the coating losses are the same as he lens transmission losses. By definition a light gain of 100 times is 5 magnitudes, each magnitude up being 2.518 times fainter (5th root of 100). Thus 40 times is almost exactly 4 magnitudes taking you to 10.4...at least that's my back-of-fag-packet guess...

RL 

[vlaiv]

Not an easy calculation at all.

Best you can do is a sort of an estimate.

Aperture difference is rather straight forward to account for. Take aperture ratios and convert to magnitudes, account for central obstruction and transmission / reflection. Problem is that we are talking about very different focal lengths and hence resolutions for same camera / pixel size. If for example pixel size is 3.85um (reading from your signature), with said lens resolution is 7.56"/pixel, while with dob you will have 0.66"/pixel.

In almost all seeing conditions you can expect that star will be spread to up to 4 adjacent pixels on resolution of 7.56"/pixel (majority of light from a single star). On resolution of 0.66"/pixel you can expect majority of light from a star to cover at least 3" or about 5 pixels in width - giving area of roughly 20px minimum. So you will effectively have at least 5 times less light per pixel. But this is very rough guess and calculation, because star profile is not evenly spread over pixels.

Now let's do the math, and see if we even come close

37.5mm diameter would have ~ 980mm squared effective aperture (lens has at least 7-8 elements, each element should be properly coated, so we can give it like 99.something transmission on each surface ....)

254mm Dob, and let's guess some specs like 26% CO, 94% reflectivity per surface. This all comes down to 41746mm squared.

So dob collects 42.6 times more light, but pixels receive 5 times less than that, so we are talking 8.52 times more light per pixel.

End result is 2.33 mag deeper in live view - or ~ 8.7 magnitude stars barely detectable in live view.

Now, as I've said - this is rather wild estimated, but it would be interesting to hear from actual field trials - what was limiting magnitude that you managed to see in live view.

[pipnina]

11 minutes ago, vlaiv said:

Not an easy calculation at all.

Best you can do is a sort of an estimate.

Aperture difference is rather straight forward to account for. Take aperture ratios and convert to magnitudes, account for central obstruction and transmission / reflection. Problem is that we are talking about very different focal lengths and hence resolutions for same camera / pixel size. If for example pixel size is 3.85um (reading from your signature), with said lens resolution is 7.56"/pixel, while with dob you will have 0.66"/pixel.

In almost all seeing conditions you can expect that star will be spread to up to 4 adjacent pixels on resolution of 7.56"/pixel (majority of light from a single star). On resolution of 0.66"/pixel you can expect majority of light from a star to cover at least 3" or about 5 pixels in width - giving area of roughly 20px minimum. So you will effectively have at least 5 times less light per pixel. But this is very rough guess and calculation, because star profile is not evenly spread over pixels.

Now let's do the math, and see if we even come close

37.5mm diameter would have ~ 980mm squared effective aperture (lens has at least 7-8 elements, each element should be properly coated, so we can give it like 99.something transmission on each surface ....)

254mm Dob, and let's guess some specs like 26% CO, 94% reflectivity per surface. This all comes down to 41746mm squared.

So dob collects 42.6 times more light, but pixels receive 5 times less than that, so we are talking 8.52 times more light per pixel.

End result is 2.33 mag deeper in live view - or ~ 8.7 magnitude stars barely detectable in live view.

Now, as I've said - this is rather wild estimated, but it would be interesting to hear from actual field trials - what was limiting magnitude that you managed to see in live view.

1 hour ago, rl said:

11.6 might be a little optimistic. 

The light gain will be about 40 times allowing for the central obstruction, assuming the coating losses are the same as he lens transmission losses. By definition a light gain of 100 times is 5 magnitudes, each magnitude up being 2.518 times fainter (5th root of 100). Thus 40 times is almost exactly 4 magnitudes taking you to 10.4...at least that's my back-of-fag-packet guess...

RL 

I'll be sure to report back with results!

 

 

[Sunshine]

i would first seek out a Flux Capacitor, and a small sample of a dilithium crystal which you can then use to build a magnitude thermodilusive conceptualizer. 

 

[niallk]

Log base 2.5 of the ratio of square of diameter.

Or 5 x {log base 10 (D2/D1) } / {log base 10 (2.5)}