Analog to Digital conversion#

At this point the NDRs are stored as float64, however, we know that the detector output is reported in integers in \(adu\) units. Here we simulate the Analog to Digital Converter (ADC) thanks to AnalogToDigital, which converts the \(counts\) units of sub-exposures into \(adu\) units of NDRs. This task needs two inputs from the channel configuration file:

  • the number of bits of the output integer (e.g. 16 bits)

  • ADC gain factor

These can be injected as

<channel> channel
    <detector>
        <ADC> True </ADC>
        <ADC_num_bit> 16 </ADC_num_bit>
        <ADC_gain> 0.5 </ADC_gain>
        <ADC_round_method>floor</ADC_round_method>
        <ADC_offset> 1000 </ADC_offset>
    <detector>
</channel>

To enable the conversion set True for the ADC keyword, as in the example. If False, this step will be skipped.

In this example, we want the ADC to convert the NDRs into 16 bits unsigned integers. Because integers can represent numbers up to a maximum value of \(2^{16} -1 = 65535\), we need a conversion factor to rescale our float NDRs to fit in the new data type range. This conversion factor is defined by ADC_gain, such that the float focal plane is multiplied by this gain (\(g_{ADC}\)) before the conversion. If this gain is not known, an estimate is provided by the ADC gain estimator tool.

\[S_{out} = [ ADC_{gain} \cdot( S_{meas} - ADC_{offset}) ]_{int}\]

Note that the offset is subtracted from the NDRs. All the resulting negative values are set to zero. The user can input any integer number of bits up to 32. The AnalogToDigital chooses the minimum Python data type to store the desired output to minimize the size of the output product and to be more representative of the expected result.

ADC_round_method keyword indicates which method the ADC should use to cast the float into integers. Three options are available:

  • floor which uses numpy.floor;

  • ceil which uses numpy.ceil;

  • round which uses numpy.round;

The default is floor.

Automatic ADC#

ExoSim can help you setting this values automatically as

<channel> channel
    <detector>
        <ADC> True </ADC>
        <ADC_num_bit> 16 </ADC_num_bit>
        <ADC_gain> auto </ADC_gain>
        <ADC_offset> auto </ADC_offset>
    <detector>
</channel>

With this configuration, ExoSim will compute the offset (<ADC_offset> auto </ADC_offset>) as the minimum value in all the datacube, and the gain (<ADC_gain> auto </ADC_gain>) as

\[g_{ADC} = \frac{2^{n_{bits}}-1 }{ADC_{max}-offset}\]

The used offset and gain are reported in the output metadata.

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