This module describes the calibrations applied to the SHOW instrument.

Readout Noise

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)\[ \Delta D_{actual} = \sqrt{ \frac{D_{actual}}{G_e} }\]