I tried to verify the results of the "Sky Background calculator" by my own calculation but I get for any input a discrepancy by the factor PI.
My calculation is as follows
- convert [mag/arcsec2] to illuminance [lux]
- convert [lux] to [photons/m2 s]
- calculate photon rate captured by the aperture
- calculate impact of pixelscale [arcsec/pixel]
- calculate impact of quantum efficiency and Mono/Color sensor
that is all.
Any idea what is going wrong in my calculation?
Many Thanks
Sky background calculator
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Re: Sky background calculator
Hi,
I started with the calculations here (in the Photon flux section) - https://web.archive.org/web/20181217054 ... /mags.html
This gives you the photon count from magnitude (and photon count per arcsec squared from mag per arcsec squared) - per meter squared. Then calculate collection area (PI r squared), now multiply by the area of sky captured by each pixel (arcsec squared) - this comes from focal length. When you plug all the numbers in the focal length and radius/diameter can cancel down to the f-ratio.
That's it in outline anyway, I don't have my original notes to hand any more, so would have to work the calculation from scratch to validate my code
cheers,
Robin
I started with the calculations here (in the Photon flux section) - https://web.archive.org/web/20181217054 ... /mags.html
This gives you the photon count from magnitude (and photon count per arcsec squared from mag per arcsec squared) - per meter squared. Then calculate collection area (PI r squared), now multiply by the area of sky captured by each pixel (arcsec squared) - this comes from focal length. When you plug all the numbers in the focal length and radius/diameter can cancel down to the f-ratio.
That's it in outline anyway, I don't have my original notes to hand any more, so would have to work the calculation from scratch to validate my code
cheers,
Robin
Re: Sky background calculator
Hi Robin,
many thanks for your quick reply. I will check my approach with your new inputs and come back afterwards.
regards
Arnold
many thanks for your quick reply. I will check my approach with your new inputs and come back afterwards.
regards
Arnold
Re: Sky background calculator
Hi Robin,
I carefully checked all your inputs but I couldn't reveal the discrepancy. My photon flux calculation is very close to your sources.
A simple example with pixel scale 1: Sky background 20 mag/arcsec^2; focal length 0,4 m; aperture diameter 0,08m; pixel size 1,85 microns (f- ratio = 5, pixels scale = 1 arcsec/pixel) ; colour sensor ; quantum efficiency = 0,5;
photon count per second and meter squared = approximately 100 photons/ s / m^2
photons captured by the aperture = 100 photons /s / m^2 * 0,005 m^2 = 0,5 photons/ s
one arcsec squared is captured by one pixel
impact of quantum efficiency -> 0,25 photons/s
impact of colour sensor -> 0,08 e/pixel/ s
result 0,08 e/pixel/ s
results of Sky Background Calculator 0.23 e/pixel/s
Again the factor pi as discrepancy.
I carefully checked all your inputs but I couldn't reveal the discrepancy. My photon flux calculation is very close to your sources.
A simple example with pixel scale 1: Sky background 20 mag/arcsec^2; focal length 0,4 m; aperture diameter 0,08m; pixel size 1,85 microns (f- ratio = 5, pixels scale = 1 arcsec/pixel) ; colour sensor ; quantum efficiency = 0,5;
photon count per second and meter squared = approximately 100 photons/ s / m^2
photons captured by the aperture = 100 photons /s / m^2 * 0,005 m^2 = 0,5 photons/ s
one arcsec squared is captured by one pixel
impact of quantum efficiency -> 0,25 photons/s
impact of colour sensor -> 0,08 e/pixel/ s
result 0,08 e/pixel/ s
results of Sky Background Calculator 0.23 e/pixel/s
Again the factor pi as discrepancy.
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Re: Sky background calculator
Hi,
I have just reproduced my calculations from scratch to give the same results.
I think you are double counting the reduction due to the colour camera - it looks like your 100 photons/m2/s already accounts for a dlambda/lambda of about 0.16 (typical for the V band), or typical for a single colour channel of R,G or B. Then you are dividing by three again at the end, which is not justified.
cheers,
Robin
I have just reproduced my calculations from scratch to give the same results.
I think you are double counting the reduction due to the colour camera - it looks like your 100 photons/m2/s already accounts for a dlambda/lambda of about 0.16 (typical for the V band), or typical for a single colour channel of R,G or B. Then you are dividing by three again at the end, which is not justified.
cheers,
Robin
Re: Sky background calculator
Hi Robin,
you are right, the fault is my conversion mag -> illumination as I only considered the V-Band and ignored B- and R-Band.
Thank you very much for all your efforts and
best regards
Arnold
you are right, the fault is my conversion mag -> illumination as I only considered the V-Band and ignored B- and R-Band.
Thank you very much for all your efforts and
best regards
Arnold
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Re: Sky background calculator
Hi Arnold,
glad we agree now (I must admit I was also relieved when I managed to reproduce my initial formula!)
cheers,
Robin
glad we agree now (I must admit I was also relieved when I managed to reproduce my initial formula!)
cheers,
Robin