luminance from magnitude calculation

Asked by Dave Blake on 2009-11-13

Can anyone explain the way that Stellarium calculates luminance from magnitude and current fov for a point source (star)? I totally understand the luminance adation calculations of StelToneReproducer, but not how it is used in StelSkyDrawer to determine with what radius to draw each star

StelSkyDrawer::pointSourceMagToLnLuminance returns
 -0.92103f*(mag + 12.12331f) + lnfovFactor

So, rearranging the math, it seems that fovFactor is the luminance of something with magnitude -12.12331, but

lnfovFactor = std::log(1./50.*2025000.f* 60.f*60.f / (fov*fov) / (EYE_RESOLUTION*EYE_RESOLUTION)/powFactor/1.4);

Just where does that equation come from? What has magnitude -12.12331, an almost full moon? Been going nuts trying to figure it out. I know it is not the usual level of user question but I would really like to know what this bit of Stellarium is based on.

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2009-11-13
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2009-11-13
Fabien Chéreau (xalioth) said : #1

Hi,
This formula came after many hours of fiddling around, after starting from physical formulas. So I don't remember the reason of all value here, but the principle is that:

mag = -2.5 log(Flux) + K

so ln (Flux) = -log (e)* (m-K)/2.5

if you combine that with the formula of luminance (http://en.wikipedia.org/wiki/Luminance) you see that fov factor is somewhat there to compute the 1./(dAd*Omega) from the eye resolution and current magnification.

Fabien

PS: why are you trying to do with such formulas?

Dave Blake (barnswood) said : #2

Thanks Fabien, but a shame the fine details are lost in memory. My interest in luminance etc. arises from trying to accurately model the annual heliacal disappearance/reappearance of stars for an archaeoastronomy project. In addition to modelling extinction and all those kinds of issues, I started to look at better ways to represent the dawn/dusk sky on a computer monitor which brings in tone reproduction and luminance adaptation.

I will spend a bit more time seeing if I can see why the results of your fiddling works! I will let you know if I think I have cracked it.

AKAIK the tone reproduction formula requires accurate real world luminance in order to give display luminance (which can them be scaled to a disk radius). To get K in your equations, hence luminance, we need to know the luminance for a specific magnitude, a pair of values to work from. That is where I get stuck. Given a visual magnitude what is the real world luminance?

I any other details do come back to you then I would be most grateful

Dave

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