How to Calculate Sky Background Electrons

Required Calibration Convention

The zero point must be the magnitude corresponding to one electron per second. ESO documentation expresses the general photometric relationship as magnitude equals zero point minus 2.5 log10 of count rate.

Use the Sky Background Electron Rate Calculator with a sky brightness and zero point from the same filter and magnitude system.

Surface Brightness to Electron Rate

For sky surface brightness μ and electron-rate zero point ZP:

`rate per arcsec² = 10^((ZP - μ)/2.5)`

Convert to One Pixel

For square pixels with scale s arcsec/pixel:

`pixel area = s²`

`sky rate per pixel = rate per arcsec² × s²`

Exposure Stack

Sky electrons scale with rate, exposure time, aperture pixels, and exposure count.

Dark electrons scale the same way using dark current. Independent read-noise variance is read noise squared times aperture pixels times the number of reads.

Total Background Noise

For independent Poisson sky and dark signals plus Gaussian read noise:

`noise = sqrt(sky electrons + dark electrons + read-noise variance)`

ESO's exposure-time documentation uses the same structure for sky, read noise, and dark-current terms.

Important Calibration Checks

Confirm whether the supplied zero point is in electrons/second or ADU/second, whether extinction is included, and which aperture convention was used.