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| wiki:astronomy:observational_astronomy:observational_astronomy:extinction [2023/11/14 13:02] – Roy Prouty | wiki:astronomy:observational_astronomy:observational_astronomy:extinction [2023/11/14 13:11] (current) – Roy Prouty | ||
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| mb−mt=−2.5log10IbλItλ=−2.5log10[exp(−secz∫tbαλ(x)dx)] | mb−mt=−2.5log10IbλItλ=−2.5log10[exp(−secz∫tbαλ(x)dx)] | ||
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| + | Let's carefully take the log-base-10 of the exponential... | ||
| + | mb−mt=−2.5log10(e)(−secz∫tbαλ(x)dx) | ||
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| + | Finally, recalling that we want to calibrate to the top-of-the-atmosphere, | ||
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| + | mt=mb+2.5log10(e)(−secz∫tbαλ(x)dx) | ||
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| + | So we find that the top-of-the-atmosphere magnitude is our bottom-of-the-atmosphere = top-of-telescope magnitude with some additional magnitude that was " | ||
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| + | Note that the F or I used in the above equations are //not// counts. They must be some unit of power. So radiance, flux, energy per second (power), or even counts-per-second. | ||
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| + | ---- | ||
| + | Sources | ||
| + | - Lifted with minor modification from: https:// | ||