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fixing manual
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@emilyruzich
emilyruzich committed May 12, 2011
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52 changes: 12 additions & 40 deletions doc/source/manual/forward.rst
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Expand Up @@ -792,36 +792,8 @@ The columns of the tables contain the following data:
.. note:: The coil geometry information is stored in the file $MNE_ROOT/share/mne/coil_def.dat, which is automatically created by the utility mne_list_coil_def , see :ref:`BJEHHJIJ`.


.. tabularcolumns:: |p{0.1\linewidth}|p{0.3\linewidth}|p{0.1\linewidth}|p{0.3\linewidth}|p{0.2\linewidth}|
.. _BGBBHGEC:
.. table:: Normal coil descriptions. Note: If a plus-minus sign occurs in several coordinates, all possible combinations have to be included.

======= ================================================================ ==== =============================================================== ===============================================================
Id Description n r/mm w
======= ================================================================ ==== =============================================================== ===============================================================
2 Neuromag-122 planar gradiometer 2 :math:`\pm (8.1, 0, 0)`mm INLINE_EQUATION
2000 A point magnetometer 1 :math:`(0, 0, 0)`mm INLINE_EQUATION
3012 Vectorview type 1 planar gradiometer 2 :math:`(\pm 8.4, 0, 0.3)`mm INLINE_EQUATION
3013 Vectorview type 2 planar gradiometer 2 :math:`(\pm 8.4, 0, 0.3)`mm INLINE_EQUATION
3022 Vectorview type 1 magnetometer 4 :math:`(\pm 6.45, \pm 6.45, 0.3)`mm INLINE_EQUATION
3023 Vectorview type 2 magnetometer 4 :math:`(\pm 6.45, \pm 6.45, 0.3)`mm INLINE_EQUATION
3024 Vectorview type 3 magnetometer 4 :math:`(\pm 5.25, \pm 5.25, 0.3)`mm INLINE_EQUATION
2000 An ideal point magnetometer 1 :math:`(0,0,0)`mm
4001 Magnes WH magnetometer 4 :math:`(\pm 5.75, \pm 5.75, 0)`mm INLINE_EQUATION
4002 Magnes WH 3600 axial gradiometer 8 :math:`(\pm 4.5, \pm 4.5, 0)`mm :math:`(\pm 4.5, \pm 4.5, 50)`mm INLINE_EQUATION
4003 Magnes reference magnetometer 4 :math:`(\pm 7.5, \pm 7.5, 0)`mm INLINE_EQUATION
4004 Magnes reference gradiometer measuring diagonal gradients 8 INLINE_EQUATION INLINE_EQUATION INLINE_EQUATION
4005 Magnes reference gradiometer measuring off-diagonal gradients 8 INLINE_EQUATION INLINE_EQUATION INLINE_EQUATION INLINE_EQUATION INLINE_EQUATION INLINE_EQUATION INLINE_EQUATION INLINE_EQUATION
5001 CTF 275 axial gradiometer 8 INLINE_EQUATION INLINE_EQUATION INLINE_EQUATION INLINE_EQUATION
5002 CTF reference magnetometer 4 INLINE_EQUATION INLINE_EQUATION
5003 CTF reference gradiometer measuring diagonal gradients 8 INLINE_EQUATION INLINE_EQUATION INLINE_EQUATION INLINE_EQUATION
5004 CTF reference gradiometer measuring off-diagonal gradients 8 INLINE_EQUATION INLINE_EQUATION INLINE_EQUATION INLINE_EQUATION INLINE_EQUATION INLINE_EQUATION INLINE_EQUATION INLINE_EQUATION
6001 MIT KIT system axial gradiometer 8 INLINE_EQUATION INLINE_EQUATION INLINE_EQUATION INLINE_EQUATION
======= ================================================================ ==== =============================================================== ===============================================================


.. XXX : incomplete

.. tabularcolumns:: |p{0.1\linewidth}|p{0.3\linewidth}|p{0.1\linewidth}|p{0.25\linewidth}|p{0.2\linewidth}|
.. _CHDBDFJE:
.. table:: Accurate coil descriptions
Expand Down Expand Up @@ -1180,7 +1152,7 @@ The EEG sphere model definition file

For the computation of the electric potential distribution
on the surface of the head (EEG) it is necessary to define the conductivities
(INLINE_EQUATION) and radiuses of the spherically
(:math:`\sigma`) and radiuses of the spherically
symmetric layers. Different sphere models can be specified with
the ``--eegmodels`` option.

Expand All @@ -1202,7 +1174,7 @@ always provided. This model has the structure given in :ref:`BABEBGDA`
.. table:: Structure of the default EEG model

======== ======================= =======================
Layer Relative outer radius INLINE_EQUATION (S/m)
Layer Relative outer radius :math:`\sigma` (S/m)
======== ======================= =======================
Head 1.0 0.33
Skull 0.97 0.04
Expand All @@ -1222,8 +1194,8 @@ and amplitudes are determined by minimizing the cost function:

.. math:: S(r_1,\dotsc,r_m\ ,\ \mu_1,\dotsc,\mu_m) = \int_{scalp} {(V_{true} - V_{approx})}\,dS

where INLINE_EQUATION and INLINE_EQUATION are
the locations and amplitudes of the approximating dipoles and INLINE_EQUATION and INLINE_EQUATION are
where :math:`r_1,\dotsc,r_m` and :math:`\mu_1,\dotsc,\mu_m` are
the locations and amplitudes of the approximating dipoles and :math:`V_{true}` and :math:`V_{approx}` are
the potential distributions given by the true and approximative
formulas, respectively. It can be shown that this integral can be
expressed in closed form using an expansion of the potentials in
Expand All @@ -1242,26 +1214,26 @@ location coordinates to the output file. Let

.. math:: G_k = [g_{xk} g_{yk} g_{zk}]

be the INLINE_EQUATION matrix containing
the signals produced by three orthogonal dipoles at location INLINE_EQUATION making
up INLINE_EQUATIONthe gain matrix
be the :math:`N_{chan} \times 3` matrix containing
the signals produced by three orthogonal dipoles at location :math:`r_k` making
up :math:`N_{chan} \times 3N_{source}` the gain matrix

.. math:: G = [G_1 \dotso G_{N_{source}}]\ .

With the ``--grad`` option, the output from mne_forward_solution also
contains the INLINE_EQUATION derivative matrix
contains the :math:`N_{chan} \times 9N_{source}` derivative matrix

.. math:: D = [D_1 \dotso D_{N_{source}}]\ ,

where

.. math:: D_k = [\frac{\delta g_{xk}}{\delta x_k} \frac{\delta g_{xk}}{\delta y_k} \frac{\delta g_{xk}}{\delta z_k} \frac{\delta g_{yk}}{\delta x_k} \frac{\delta g_{yk}}{\delta y_k} \frac{\delta g_{yk}}{\delta z_k} \frac{\delta g_{zk}}{\delta x_k} \frac{\delta g_{zk}}{\delta y_k} \frac{\delta g_{zk}}{\delta z_k}]\ ,

where INLINE_EQUATION are the location
coordinates of the INLINE_EQUATION dipole. If
where :math:`x_k`, :math:`y_k`, and :math:`z_k` are the location
coordinates of the :math:`k^{th}` dipole. If
the dipole orientations are to the cortical normal with the ``--fixed``
option, the dimensions of INLINE_EQUATION and INLINE_EQUATION are INLINE_EQUATION and INLINE_EQUATION,
respectively. Both INLINE_EQUATION and INLINE_EQUATION can
option, the dimensions of :math:`G` and :math:`D` are :math:`N_{chan} \times N_{source}` and :math:`N_{chan} \times 3N_{source}`,
respectively. Both :math:`G` and :math:`D` can
be read with the mne_read_forward_solution Matlab
function, see Table 10.1.

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