.. _bands:
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Bands
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The ``Band`` defines all aspects of how detectors on an array will respond to incident radiation, including

* How the detectors respond to different frequencies of radiation.
* The efficiencies of the detectors.
* The noise properties of the detectors.
* The variation in detector gains across the array.

We can create the simplest possible ``Band`` as e.g.

.. plot:: 
   :include-source: True

    import matplotlib.pyplot as plt
    from maria import Band

    my_band = Band(center=150, # in GHz
                   width=30) # in GHz

    my_band.plot()

The ``center`` and ``width`` parameters define the shape of the passband $\\tau(\\nu)$. The convention of $\\tau(\\nu)$ is that of a Rayleigh-Jeans source, so that the power incident on each detector in the band will be

.. math::

   P = \eta k \int_0^\infty T_b(\nu) \tau(\nu) d\nu

where $\\eta$ is the efficiency (from the supplied ``efficiency`` parameter) and $k$ is Boltzmann's constant.