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| Both sides previous revision Previous revision Next revision | Previous revision | ||
| wiki:astronomy:observational_astronomy:data_reduction_toa [2025/01/07 14:56] – Roy Prouty | wiki:astronomy:observational_astronomy:data_reduction_toa [2025/02/05 20:33] (current) – Roy Prouty | ||
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| Line 24: | Line 24: | ||
| Rearrange: | Rearrange: | ||
| - | $$\frac{dI}{I} = d\ln{I} = -\kappa(x)\sec{(z)}dz$$ | + | $$d\ln{I} = -\kappa(x)\sec{(z)}dz$$ |
| Integrate: | Integrate: | ||
| - | $$\int_T^B\frac{dI}{I} = \int_T^Bd\ln{I} = \int_T^B-\kappa(x)\sec{(z)}dx$$ | + | $$\int_T^Bd\ln{I} = \int_T^B-\kappa(x)\sec{(z)}dx$$ |
| We are left with: | We are left with: | ||
| $$\ln{I(x=T)} - \ln{I(x=B)} = -\sec{(z)}\int_T^B\kappa(x)dx$$ | $$\ln{I(x=T)} - \ln{I(x=B)} = -\sec{(z)}\int_T^B\kappa(x)dx$$ | ||
| Line 61: | Line 61: | ||
| - $K$ is the atmosphere-integrated extinction | - $K$ is the atmosphere-integrated extinction | ||
| - | The first two are easy (ish) ! That last one, the atmosphere-integrated extinction is less easy. It must me derived either from measurements of the layer-by-layer extinction coefficient and numerically integrated OR we must find some way to measure the atmosphere-integrated extinction itself. | + | The first two are easy (ish) ! That last one, the atmosphere-integrated extinction is less easy. It must be derived either from measurements of the layer-by-layer extinction coefficient and numerically integrated OR we must find some way to measure the atmosphere-integrated extinction itself. |
| ==== Measuring Atmospheric Extinction ==== | ==== Measuring Atmospheric Extinction ==== | ||
| Line 78: | Line 78: | ||
| ---- | ---- | ||
| - | |||
| - | Sources | ||
| - | |||
| - | - [[https:// | ||
| {{tag> | {{tag> | ||