# showapi.calibration¶

This module describes the calibrations applied to the SHOW instrument.

The raw readout signal coming off the SHOW detector is given by

(1)$D_{meas} = B + D_{dark} + D_{light}$

where $$D_{meas}$$ is the measured signal in digital numbers (DN), $$B$$ is a DC bias, $$D_{dark}$$ is the dark current signal and $$D_{light}$$ is the signal due to light incident upon the detector pixel. This can be re-arranged to give the signal due to light.

(2)$D_{light} = D_{meas} - (D_{dark} + B)$

and the error analysis is given by,

(3)$\Delta D_{light} = \sqrt{ \Delta D_{meas}^2 - \Delta (D_{dark} + B)^2}$

### Measurement Error¶

For convenience we can write,

$D_{actual} = D_{dark} + D_{light}$

where $$D_{actual}$$ is the total signal in digital numbers (DN) related to the number of electrons stored in the pixel, alternatively

$D_{actual} = \frac{N_e}{G_e}$

where $$N_e$$ is the total number of electrons in the the pixel and $$G_e$$ is the number of electrons per DN. The error in the number of electrons is given by Poisson counting statistics,

$\Delta N = \sqrt{N_e}$

and this can be converted to equivalent digital noise error as

$\Delta D_{actual} = \frac{ \sqrt{N_e}}{G_e}$

which can be manipulated to give

(4)$\Delta D_{actual} = \sqrt{ \frac{D_{actual}}{G_e} }$