Total Noise

The total relative noise is estimated for a \(1 \, hr\) time scale observation. Therefore it has units of \(\sqrt{hr}\).

The task dedicated to this job is ComputeTotalNoise.

We start from an empy array of variances :math:` Var_{1 , hr}(lambda)`.

This tasks iterates over the column of the radiometric table looking for noise sources. If a column name contains the word noise then is handled by this task. Assuming that the code founds a column name X_noise. If the column X_noise units are \(ct/s\) then

\[Var_{1 \, hr}(\lambda) = Var_{1 \, hr}(\lambda) + \frac{[\sigma_{X}(\lambda)]^2}{\Delta T_{int}}\]

where \(\Delta T_{int} = 3600 \, s\) for the \(1 \, hr\) integration time.

When the noise from all the columns that has such units has been added, the total variance is converted into relative noise.

Note

To avoid confusion, only the noise from the source and the cumulative foreground are added to the total noise.

Then the relative noise is

\[\sigma_{1 \, hr}(\lambda) = \frac{Var_{1 \, hr}(\lambda)}{S_{source}(\lambda)}\]

where \(S_{source}\) is the source signal in the radiometric table.

Assuming that the code founds also a column name Y_noise and that the column Y_noise has no units. This is a relative noise already. So, the code updates the total noise as

\[\sigma_{1 \, hr}(\lambda) = \sqrt{[\sigma_{1 \, hr}(\lambda)]^2 + [\sigma_{Y}(\lambda)]^2}\]

When also this check is concluded, the total relative noise is added to the radiometric table.

To run the task from script

import exosim.tasks.radiometric as radiometric

computeTotalNoise = radiometric.ComputeTotalNoise()
total_noise = computeTotalNoise(table)