astrohack.utils.zernike_aperture_fitting
========================================

.. py:module:: astrohack.utils.zernike_aperture_fitting


Attributes
----------

.. autoapisummary::

   astrohack.utils.zernike_aperture_fitting.zernike_matrix_functions


Functions
---------

.. autoapisummary::

   astrohack.utils.zernike_aperture_fitting.zernike_order_0
   astrohack.utils.zernike_aperture_fitting.zernike_order_1
   astrohack.utils.zernike_aperture_fitting.zernike_order_2
   astrohack.utils.zernike_aperture_fitting.zernike_order_3
   astrohack.utils.zernike_aperture_fitting.zernike_order_4
   astrohack.utils.zernike_aperture_fitting.zernike_order_5
   astrohack.utils.zernike_aperture_fitting.zernike_order_6
   astrohack.utils.zernike_aperture_fitting.zernike_order_7
   astrohack.utils.zernike_aperture_fitting.zernike_order_8
   astrohack.utils.zernike_aperture_fitting.zernike_order_9
   astrohack.utils.zernike_aperture_fitting.zernike_order_10
   astrohack.utils.zernike_aperture_fitting.create_osa_coordinates
   astrohack.utils.zernike_aperture_fitting.fit_zernike_coefficients


Module Contents
---------------

.. py:function:: zernike_order_0(u_ax, _)

   Zernike 0-eth order polynomial, simple flat disk.
   :param u_ax: Aperture U axis
   :param _: Aperture V axis

   :returns: a [n, 1] Matrix filled with ones.


.. py:function:: zernike_order_1(u_ax, v_ax)

   Zernike first order polynomials, simple linear gradients.
   :param u_ax: Aperture U axis
   :param v_ax: Aperture V axis

   :returns: a [n, 3] Matrix filled with U and V values.


.. py:function:: zernike_order_2(u_ax, v_ax, return_powers=False)

   Zernike second order polynomials, first astigmatisms and linear defocus.
   :param u_ax: Aperture U axis
   :param v_ax: Aperture V axis
   :param return_powers: return list of already compute U and V powers? (saves computing time)

   :returns: a [n, 6] Matrix filled with the first 6 polynomials.


.. py:function:: zernike_order_3(u_ax, v_ax, return_powers=False)

   Zernike third order polynomials, first comas and trefoils.
   :param u_ax: Aperture U axis
   :param v_ax: Aperture V axis
   :param return_powers: return list of already compute U and V powers? (saves computing time)

   :returns: a [n, 10] Matrix filled the first 10 polynomials.


.. py:function:: zernike_order_4(u_ax, v_ax, return_powers=False)

   Zernike forth order polynomials, second astigmatisms, first spherical aberations and tetrafoils.
   :param u_ax: Aperture U axis
   :param v_ax: Aperture V axis
   :param return_powers: return list of already compute U and V powers? (saves computing time)

   :returns: a [n, 15] Matrix filled the first 15 polynomials.


.. py:function:: zernike_order_5(u_ax, v_ax, return_powers=False)

   Zernike fifth order polynomials, pentafoils, second comas.
   :param u_ax: Aperture U axis
   :param v_ax: Aperture V axis
   :param return_powers: return list of already compute U and V powers? (saves computing time)

   :returns: a [n, 21] Matrix filled the first 21 polynomials.


.. py:function:: zernike_order_6(u_ax, v_ax, return_powers=False)

   Zernike sixth order polynomials, second spherical aberations, hexafoils
   :param u_ax: Aperture U axis
   :param v_ax: Aperture V axis
   :param return_powers: return list of already compute U and V powers? (saves computing time)

   :returns: a [n, 28] Matrix filled the first 28 polynomials.


.. py:function:: zernike_order_7(u_ax, v_ax, return_powers=False)

   Zernike seventh order polynomials, heptafoils
   :param u_ax: Aperture U axis
   :param v_ax: Aperture V axis
   :param return_powers: return list of already compute U and V powers? (saves computing time)

   :returns: a [n, 36] Matrix filled the first 36 polynomials.


.. py:function:: zernike_order_8(u_ax, v_ax, return_powers=False)

   Zernike eigth order polynomials, octafoils
   :param u_ax: Aperture U axis
   :param v_ax: Aperture V axis
   :param return_powers: return list of already compute U and V powers? (saves computing time)

   :returns: a [n, 45] Matrix filled the first 45 polynomials.


.. py:function:: zernike_order_9(u_ax, v_ax, return_powers=False)

   Zernike nineth order polynomials, enneafoils
   :param u_ax: Aperture U axis
   :param v_ax: Aperture V axis
   :param return_powers: return list of already compute U and V powers? (saves computing time)

   :returns: a [n, 55] Matrix filled the first 55 polynomials.


.. py:function:: zernike_order_10(u_ax, v_ax, return_powers=False)

   Zernike tenth order polynomials, decafoils
   :param u_ax: Aperture U axis
   :param v_ax: Aperture V axis
   :param return_powers: return list of already compute U and V powers? (saves computing time)

   :returns: a [n, 66] Matrix filled the first 66 polynomials.


.. py:data:: zernike_matrix_functions

.. py:function:: create_osa_coordinates(zernike_order, split_nm=False)

   Create a list of the labels of all the polynomials from the N order given.
   :param zernike_order: The value of the N order.
   :param split_nm: Is result to be given in a 1D list (False, default) or in a 2D [N,M] list.

   :returns: A list containing the OSA ordered Zernike indices labels.


.. py:function:: fit_zernike_coefficients(aperture, u_axis, v_axis, zernike_order, telescope, fitting_engine='numpy', mask_arm_shadows=True)

   Fit zernike polynomial coefficients to an aperture array.
   :param aperture: 5D array containing the correlation apertures ([time, chan, pol, u, v]).
   :param u_axis: U axis for the apertures
   :param v_axis: V axis for the apertures.
   :param zernike_order: The N-eth order to be fitted to the aperture.
   :param telescope: Telescope class object with telescope's optical info.
   :param fitting_engine: Which fittign engine to use, numpy's linear algebra or scipy optimize.
   :param mask_arm_shadows: Mask the shadows of the arms holding the secondary in place (usually only relevant for
   :param cassegrain telescopes):

   :returns: The Zernike coefficients, the model derived from these coefficients, the RMS of the fit and the labeling for
             the zernike coeficients.