calculate_frame_reference_time
=======================================================

.. py:function:: petpal.utils.scan_timing.calculate_frame_reference_time(frame_duration: numpy.ndarray, frame_start: numpy.ndarray, half_life: float) -> numpy.ndarray

   Compute frame reference time as the time at which the average activity occurs.

   Equation comes from the `DICOM standard documentation
   <https://dicom.innolitics.com/ciods/positron-emission-tomography-image/pet-image/00541300>`_

   :math:`T_{ave}=\frac{1}{\lambda}ln\frac{\lambda T}{1-e^{-\lambda T}}`

   where lambda is the decay constant, :math:`\frac{ln2}{T_{1/2}}`, :math:`T_{1/2}` is the half
   life, and :math:`T` is the frame duration.

   :param frame_duration: Duration of each frame in seconds.
   :type frame_duration: np.ndarray
   :param frame_start: Start time of each frame relative to scan start, in seconds.
   :type frame_start: np.ndarray
   :param half_life: Radionuclide half life in seconds.
   :type half_life: float

   :returns: *np.ndarray* -- Frame reference time for each frame in the scan in seconds.