.. _electron-holography-label:

Electron Holography
*******************

HyperSpy provides the user with a signal class which can be used to process
electron holography data:

* :py:class:`~._signals.hologram_image.HologramImage`

It inherits from :py:class:`~._signals.signal2d.Signal2D` class and thus can
use all of its functionality. The usage of the class is explained in the
following sections.


The HologramImage class
=======================

The :py:class:`~._signals.hologram_image.HologramImage` class is designed to
contain images acquired via electron holography.

To transform a :py:class:`~._signals.signal2d.Signal2D` (or subclass) into a
:py:class:`~._signals.hologram_image.HologramImage` use:

.. code-block:: python

    >>> im.set_signal_type('hologram')


Reconstruction of holograms
---------------------------
The detailed description of electron holography and reconstruction of holograms
can be found in literature :ref:`[Gabor1948] <Gabor1948>`,
:ref:`[Tonomura1999] <Tonomura1999>`,
:ref:`[McCartney2007] <McCartney2007>`,
and :ref:`[Joy1993] <Joy1993>`.
Fourier based reconstruction of off-axis holograms (includes
finding a side band in FFT, isolating and filtering it, recenter and
calculate inverse Fourier transform) can be performed using the
:meth:`~._signals.hologram_image.HologramImage.reconstruct_phase` method
which returns a :py:class:`~._signals.complex_signal2d.Complex2D` class,
containing the reconstructed electron wave.
The :meth:`~._signals.hologram_image.HologramImage.reconstruct_phase` method
takes sideband position and size as parameters:

.. code-block:: python

    >>> import hyperspy.api as hs
    >>> im =  hs.datasets.example_signals.object_hologram()
    >>> wave_image = im.reconstruct_phase(sb_position=(<y>, <x>),
    ...                                   sb_size=sb_radius)

The parameters can be found automatically by calling following methods:

.. code-block:: python

    >>> sb_position = im.estimate_sideband_position(ap_cb_radius=None,
    ...                                             sb='lower')
    >>> sb_size = im.estimate_sideband_size(sb_position)

:meth:`~._signals.hologram_image.HologramImage.estimate_sideband_position`
method searches for maximum of intensity in upper or lower part of FFT pattern
(parameter ``sb``) excluding the middle area defined by ``ap_cb_radius``.
:meth:`~._signals.hologram_image.HologramImage.estimate_sideband_size` method
calculates the radius of the sideband filter as half of the distance to the
central band which is commonly used for strong phase objects. Alternatively,
the sideband filter radius can be recalculate as 1/3 of the distance
(often used for weak phase objects) for example:

.. code-block:: python

    >>> sb_size = sb_size * 2 / 3


To reconstruct the hologram with a vacuum reference wave, the reference
hologram should be provided to the method either as Hyperspy's
:py:class:`~._signals.hologram_image.HologramImage` or as a nparray:

.. code-block:: python

    >>> reference_hologram = hs.datasets.example_signals.reference_hologram()
    >>> wave_image = im.reconstruct_phase(reference_hologram,
    ...                                   sb_position=sb_position,
    ...                                   sb_size=sb_sb_size)

Using the reconstructed wave, one can access its amplitude and phase (also
unwrapped phase) using
``amplitude`` and ``phase`` properties
(also the :meth:`~._signals.complex_signal.ComplexSignal_mixin.unwrapped_phase`
method):

.. code-block:: python

    >>> wave_image.unwrapped_phase().plot()

.. figure:: images/holography_unwrapped_phase.png
  :align: center

  Unwrapped phase image.

Additionally, it is possible to change the smoothness of the sideband filter
edge (which is by default set to 5% of the filter radius) using parameter
``sb_smoothness``.

Both ``sb_size`` and ``sb_smoothness`` can be provided in desired units rather
than pixels (by default) by setting ``sb_unit`` value either to ``mrad`` or
``nm`` for milliradians or inverse nanometers respectively. For example:

.. code-block:: python

    >>> wave_image = im.reconstruct_phase(reference_hologram,
    ...                                   sb_position=sb_position, sb_size=30,
    ...                                   sb_smoothness=0.05*30,sb_unit='mrad')

Also the :py:meth:`~._signals.hologram_image.HologramImage.reconstruct_phase`
method can output wave images with desired size (shape). By default the shape
of the original hologram is preserved. Though this leads to oversampling of the
output wave images, since the information is limited by the size of the
sideband filter. To avoid oversampling the output shape can be set to the
diameter of the sideband as follows:

.. code-block:: python

    >>> wave_image = im.reconstruct_phase(reference_hologram,
    ...                                   sb_position=sb_position,
    ...                                   sb_size=sb_sb_size,
    ...                                   output_shape=(2*sb_size, 2*sb_size))

Note that the
:py:meth:`~._signals.hologram_image.HologramImage.reconstruct_phase`
method can be called without parameters, which will cause their automatic
assignment by
:py:meth:`~._signals.hologram_image.HologramImage.estimate_sideband_position`
and :py:meth:`~._signals.hologram_image.HologramImage.estimate_sideband_size`
methods. This, however, is not recommended for not experienced users.