.. _showapi.calibration:

:mod:`showapi.calibration`
==========================

This module describes the calibrations applied to the SHOW instrument.

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

.. math::
   :label: eq_dark1

   D_{meas} = B + D_{dark} + D_{light}

where :math:`D_{meas}` is the measured signal in digital numbers (DN), :math:`B` is a DC bias,  :math:`D_{dark}` is the
dark current signal and :math:`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.

.. math::
   :label: eq_dark2

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


and the error analysis is given by,

.. math::
   :label: eq_dark3

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

Measurement Error
^^^^^^^^^^^^^^^^^
For convenience we can write,

.. math::


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

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

.. math::

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

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

.. math::

    \Delta N = \sqrt{N_e}

and this can be converted to equivalent digital noise error as

.. math::

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

which can be manipulated to give

.. math::
   :label: eq_dark5

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