.. _bolometer_etendue: Calculating the Etendue of Bolometer Foils ========================================== In this demonstration we calculate the etendue of each of the bolometer foils in a camera. The camera is produced in the same way as in the :ref:`Camera From Primitives ` demo. A simple analytic formula for the etendue of a foil-aperture system is: .. math:: G = \frac{A_{foil} A_{slit} \cos{\theta_{foil}} \cos{\theta_{slit}}}{d^2} This formula is a good approximation when the distance :math:`d` between the foil and slit is large compared with the foil area :math:`A_{foil}` and the slit area :math:`A_{slit}` (i.e. when the system is well approximated by an infinitesimal pinhole and detector), but as the foil and slit become finite in size it becomes less accurate and a full 3D treatment is required instead. The :class:`BolometerFoil` object has a `calculate_etendue` method which makes this very simple. All that is required is to load the bolometer geometry information and camera body into an otherwise-empty scenegraph and call the `calculate_etendue` method on the foil. .. literalinclude:: ../../../../demos/observers/bolometry/calculate_etendue.py The program outputs the following text, along with a plot of the etendues. Note that the actual values may be slightly different, due to the Monte-Carlo sampling technique used. .. code-block:: console Foil 1 raytraced etendue: 1.851e-07 +- 4e-10 analytic: 1.883e-07 Foil 2 raytraced etendue: 2.341e-07 +- 6e-10 analytic: 2.392e-07 Foil 3 raytraced etendue: 2.338e-07 +- 5e-10 analytic: 2.392e-07 Foil 4 raytraced etendue: 1.854e-07 +- 6e-10 analytic: 1.883e-07 .. figure:: bolometer_etendues.svg :align: center **Caption** The etendue of the foils, calculated analytically and also by ray tracing. There is good agreement between the two methods, with the ray tracing method producing a slightly lower etendue value. The analytic method has been shown to overestimate the etendue when the foil-slit distance is small compared with the aperture size (see the `example `_ in the raysect documentation), which is consistent with this result.