r'''FOV module for IMA
:class:`SimpleFOV` provides the simplest fov geometry, namely
the equally separted solid angle. This is independent of
the energy. So that in the low energy part it does not
provide good vector.
*IMA Frame*
There is always a confusion. In SPICE, there are two (not identical)
frames: ``MEX_ASPERA_IMA`` and ``MEX_ASPERA_IMAS``.
In this module, ``MEX_ASPERA_IMAS`` to be the IMA frame,
since most of the internal document looks to follow the definition of IMAS.
Anyway both are rigidly fixed, but the axis is different (also focul point).
From the MEX_V11.TF, the following is the definition.
::
-Z s/c side view ("main engine" side):
--------------------------------------
+Xsc
-Y Solar Array ^ +Y Solar Array
._________________ .______|______. .________________.
| \ | | | / |
| \ | | | / |
| | | |+Zsc | | |
| +Zimas |+Yimas x------->o| |
| +Xima |+Zima +Ysc . |
| <----o +Zimau | \ |
._________________/ <----o__________. \_________________.
+Ximau | |' `.
V /|________\
+Ximas V HGA
+Yima +Yimau
+Zsc is into the page
+Zima, +Zimau, and +Yimas
are out of the page
-Z s/c side view ("main engine" side) -- zoom in:
-------------------------------------------------
-- ^ +Xsc
| \ |
| \__ |
| \_________ |
| \ |
| \ x------->
IMA |._____________. \ +Zsc +Ysc
Aperture || o o | \
.___________________. | \____
+Zimas | | +Yimas | | \
+Xima | | +Zima | | \
<-------o | | | \
| | | | | | IMA |
| | | | | | Mounting \
.___|_______________. | plate |
| || o <-------o | |
+Ximas V |. +Ximau ___|_. /
+Yima | | | "Main Engine"
.____________|_______________/ Deck
|
+Yimau V
In addition, the instrument numbering is as follows::
This diagram illustrates in-plane (azimuthal) IMA sector layout:
+Yimas
^ +Zima
| A# indicate the azimuthal
V5 | V4 sector "#" position in
V6 ....|.... V3 the sensor assembly.
.' A13 | A12 `.
V7 .' A14 | A11`. V2 V# indicate the "#" sector
. A15 | A10. view direction.
V8 . | . V1
.A0 | A9. +Ximas For example, for
. o--------------> +Yima Sector "11" the view
.A1 / +Zimas A8. direction is the vector
V9 . / +Xima . V0 emanating from the
.A2 / A7. aperture center through
V10 . / A6 . V15 the point designated
`. / A4 A5 .' by "V11".
V11 ......... ' V14
/ V12 V13
V
Azimuthal sector "11"
view direction
This diagram illustrates cross-plane (polar) IMA sector layout:
+Yimas
+Zima Polar Sector "3"
^ ^ view dir. A# indicate the polar
V8 | V7 / sector "#" position in
.----|----. V3 the sensor assembly.
V15 ,-' P8|P7 `/. V0
.' | P3 `.
`.P15 | / P0.' V# indicate the "#" sector
`. | / .' view direction.
`. | / .'
`. | / .' For example, for polar
`. |/+Ximas Sector "3" the view
<-------------`o'+Yima direction is the vector
+Zimas .' `. emanating from the
+Xima .' `. aperture center through
.' `. the point designated
.' `. by "V2".
.'P15 P0`.
`. .'
V15 `-. P8 P7 ,-' V0
`---------'
V8 V7
See also http://aspera-3.irf.se/Members/futaana/illustration/FovAspera3.png
'''
import irfpy.util.exception as ex
import numpy as np
import numpy as _np
spiceframename = "MEX_ASPERA_IMAS"
[docs]def get_azimuth_angle(azim_nr, direction='look'):
""" Return the azimuthal angle.
The origin is -x direction of s/c frame. Increase toward -z s/c.
Note that the definition is 180-degrees opposite from the definition of IMA Bible.
:param azim_nr: Azimuthal number, extended to floating point without bounds.
:param direction: The direction of azimuth angle.
:return: Angle.
"""
phi = -11.25 + 22.5 * np.array(azim_nr)
return phi
[docs]class SimpleFOV:
''' Field of view for equally spaced solid angle.
The FOV class reporesents the simplest geometric FOV for MEX/IMA.
The IMAS frame, according to SPICE, is used.
The benefit of using geometric FOV is the simplest handling,
intuitive understanding, no dependence on energy or mode,
allowance of floating-point elevation steps, quick implementation
and easily vectorized.
In addition, inverse solution (from vector knowing sensor ID) can be
uniquely determined.
The drawback is that the FOV does not (necessarily) represent the
actual IMA FOV. Particularly for low energy steps, the elevation
scan did not apply, so that the diverge is not accepatble for
serious science. In this case, one have to use :class:`TableFOV`.
'''
def __init__(self):
pass
[docs] def viewvector_imasframe(self, azim_nr, elev_nr):
r''' Return the viewing vector for IMAS frame
For azimuth, viewing channel 0 is -11.25 deg from +Ximas toward +Yimas
(so that -Y direction in principle). Direction 1 is +11.25 deg.
Thus azimuth angle is :math:`-11.25 + 22.5 \times az`
For elevation, the viewing angle for 0 is -42.1875 deg
from X,Yimas plane toward +Zimas
Increasing number will increase by 5.625 deg.
Thus, elevation angle is :math:`-42.1875 + 5.625 \times el`.
>>> fov = SimpleFOV()
The azimuth 0.5 and elevation 7.5 specifies the x direction looking.
>>> print(fov.viewvector_imasframe(0.5, 7.5)) # doctest: +NORMALIZE_WHITESPACE
[1. 0. 0.]
If you change the azimuth to 4.5, this is y axis.
>>> viewdir = fov.viewvector_imasframe(4.5, 7.5)
>>> print('{0[0]:.2f} {0[1]:.2f} {0[2]:.2f}'.format(viewdir))
0.00 1.00 0.00
The view vector for the elevation -0.5 is
the loweredge, namely, -45 degrees in azimuth.
>>> viewdir = fov.viewvector_imasframe(0.5, -0.5)
>>> print('{0[0]:.2f} {0[1]:.2f} {0[2]:.2f}'.format(viewdir))
0.71 0.00 -0.71
If the elevation step -10 is given, this is out of the
elevation range. Masked array is returned.
>>> viewdir = fov.viewvector_imasframe(0.5, -10)
>>> print(viewdir)
[-- -- --]
The last sample shows the masked array, when the elevtion number is out of range.
The azimuthal number is periodic.
>>> viewdir = fov.viewvector_imasframe(16.5, 7.5) # Should be the same as (0.5, 7.5), ie, x axis
>>> print('{0[0]:.2f} {0[1]:.2f} {0[2]:.2f}'.format(viewdir))
1.00 -0.00 0.00
One can get the velocity vector from :meth:`velocityvector_imasframe`, which is just a negated array of
:meth:`viewvector_imasframe`.
>>> viewdir = fov.viewvector_imasframe(1, -0.5)
>>> print('{0[0]:.2f} {0[1]:.2f} {0[2]:.2f}'.format(viewdir))
0.69 0.14 -0.71
>>> veldir = fov.velocityvector_imasframe(1, -0.5)
>>> print('{0[0]:.2f} {0[1]:.2f} {0[2]:.2f}'.format(veldir))
-0.69 -0.14 0.71
If the shapes for the arguments are the same, you can use arrays as input.
'''
anr = np.array(azim_nr)
enr = np.array(elev_nr)
if anr.shape != enr.shape:
raise ValueError('Dimension of azim_nr {0.shape} and elev_nr {1.shape} should be the same'.format(anr, enr))
phi = -11.25 + 22.5 * anr
theta = -42.1875 + 5.625 * enr
phi = np.deg2rad(phi)
theta = np.deg2rad(np.ma.masked_outside(theta, -90, 90))
cp = np.cos(phi)
sp = np.sin(phi)
ct = np.ma.cos(theta)
st = np.ma.sin(theta)
x = ct * cp
y = ct * sp
z = st
return np.ma.masked_array([x, y, z])
[docs] def elevation_angle(self, elev_nr, direction='look'):
''' Return the elevation angle.
'''
if direction == 'look':
theta = -42.1875 + 5.625 * np.array(elev_nr)
elif direction == 'velocity':
theta = -(-42.1875 + 5.625 * np.array(elev_nr))
else:
raise ValueError('``direction`` must be ``look`` r ``velocity``')
return theta
[docs] def azimuth_angle(self, azim_nr, direction='look'):
if direction == 'look':
phi = -11.25 + 22.5 * np.array(azim_nr)
elif direction == 'velocity':
phi = -11.25 + 22.5 * np.array(azim_nr) + 180.
else:
raise ValueError('``direction`` must be ``look`` r ``velocity``')
return phi
[docs] def velocityvector_imasframe(self, azim_nr, elev_nr):
''' Return the velocity vector for IMAS frame
Mathematically identical to minus of :meth:`viewvector_imasframe`.
'''
return -self.viewvector_imasframe(azim_nr, elev_nr)
[docs] def numbering_imasframe(self, viewvector):
''' Return the (az, el) tuple corresponding view vector.
The viewvecotr in IMAS frame is converted to the numbering of
az and el.
Here, ``az`` should range from -0.5 to 15.5.
``el`` should range from -8.5 to 23.5, while -0.5 to 15.5 is only detectable.
>>> fov = SimpleFOV()
>>> viewvec = [1, 0, 0]
>>> print(fov.numbering_imasframe(viewvec)) # doctest: +NORMALIZE_WHITESPACE
[0.5 7.5]
>>> viewvec = [np.sqrt(0.5), 0, -np.sqrt(0.5)]
>>> print(fov.numbering_imasframe(viewvec)) # doctest: +NORMALIZE_WHITESPACE
[ 0.5 -0.5]
>>> viewvec = [0, 1, 0]
>>> print(fov.numbering_imasframe(viewvec)) # doctest: +NORMALIZE_WHITESPACE
[4.5 7.5]
>>> viewvec = [0, 0, 1]
>>> print(fov.numbering_imasframe(viewvec)[1])
23.5
You may give (3, N) shaped array. Then, you may get
(2, N) shaped array, with (az, el) for axis 0.
>>> viewvec = [[1, 0, 1, 0], [0, 1, 0, -1], [-1, -1, 1, 1]]
>>> print(fov.numbering_imasframe(viewvec))# doctest: +NORMALIZE_WHITESPACE
[[ 0.5 4.5 0.5 12.5]
[-0.5 -0.5 15.5 15.5]]
'''
# First, viewvector should be converted to the angle.
vv = np.array(viewvector)
lvv = np.sqrt((vv * vv).sum(axis=0))
vv = vv / lvv
enr = np.array((np.rad2deg(np.arcsin(vv[2])) + 42.1875) / 5.625)
anr = (np.rad2deg(np.arctan2(vv[1], vv[0])) + 11.25) / 22.5 # -8.5 to 7.5
anr = np.where(anr >= -0.5, anr, anr + 16)
return np.array((anr, enr))
[docs] def shadow_mask(self):
""" Return the pre-defined angular mask.
:returns: (A16, P16) shaped boolean array. True for channel with mask, False for free mask.
Discussion in Futaana et al., 2010. Phobos paper.
>>> mask_table = SimpleFOV().shadow_mask()
>>> mask_table.shape
(16, 16)
>>> mask_table[0, 0] # Azimuth=0, elevation=0 is shadowed by SC
True
>>> mask_table[2, 10] # Azimuth=2, elevation=10 is free
False
>>> mask_table[12, :].all() # For azimuth=12, all elevation is blocked.
True
"""
mask = np.zeros([16, 16], dtype=bool)
mask[0, 0:7] = True
mask[1, 2:7] = True
mask[8, 0:2] = True
mask[9:16, 0:8] = True
mask[15, 8:10] = True
mask[11, 11:] = True
mask[12, :] = True
mask[13, 11:] = True
return mask
[docs] def shadow_mask_corners(self, phase=0):
''' Return corner index as a (N, 2)-shaped array.
The corner index, in the (N, 2)-shaped array.
By connecting the element of array, you may get the
envelope of the shadow mask.
:keyword phase: The phase of the index. If the phase is
0 (default), the azimuthal index varies from (-8.5 to 1.5).
If the phase 1 1, the azimuthal index varies from (7.5 to 17.5).
This is prepared since the envelope crosses the boundary between
the channels of 15 and 0.
>>> fov = SimpleFOV()
>>> corners = fov.shadow_mask_corners()
>>> print(corners.shape)
(21, 2)
>>> print(corners[0]) # The start point of the envelope, which is azimuth -8.5 and elevation -0.5.
[-8.5 -0.5]
'''
corners = _np.array([[8, 0], [8, 2], [9, 2], [9, 8], [12, 8], [12, 11], [11, 11], [11, 16], [14, 16], [14, 11], [13, 11], [13, 8], [15, 8], [15, 10], [16, 10], [16, 7], [18, 7], [18, 2], [17, 2], [17, 0], [8, 0]]) - 0.5
corners[:, 0] += 16 * (phase - 1)
return corners
[docs]class TableFOV:
""" FOV information from the table provided from Andrei
The information is from ima_info.nc file provided from Andrei in Nov 2014.
The FOV information is in ImaElev variable, with the size of
(ImaNTables=4, ImaEnerDim=96, ImaElevDim=16).
Therefore, the :meth:`viewvector_imasframe` or other method should take
table_id argument.
- table_id=0, Default table in PROM
- table_id=1, updated in 2006. in EEPROM=0
- table id=2, updated in 2009. in EEPROM=15
- table id=3, for fast scan. EEPROM=13
In addition, energy and elevation steps should be given by the integer with
the range 0--95 and 0--15 respectively. It is allowed to have float values
for azimuthal directions.
>>> fov = TableFOV() # Create table based FOV.
>>> simplefov = SimpleFOV() # Create geometric based FOV for comparison.
For table=0, azimuth=0.5, elevation=10, and energy step = 15, the looking direction
in IMA frame is obtained by as follows.
>>> print(fov.viewvector_imasframe(0, 0.5, 10, 15)) # doctest:+ELLIPSIS +NORMALIZE_WHITESPACE
[0.977415... 0. 0.21132... ]
You can compare with the results from the simple FOV.
>>> print(simplefov.viewvector_imasframe(0.5, 10)) # doctest:+ELLIPSIS +NORMALIZE_WHITESPACE
[0.97003... 0. 0.24298...]
If the view angle does not make sense, [nan, nan, nan] array will be returend.
>>> print(fov.viewvector_imasframe(0, 0.5, 3, 80)) # doctest: +NORMALIZE_WHITESPACE
[nan nan nan]
>>> viewdir = fov.viewvector_imasframe(1, 4.5, 0, 21) # This is the lower edge of el=0, ie, around -45 deg.
>>> print('{0[0]:.2f} {0[1]:.2f} {0[2]:.2f}'.format(viewdir))
0.00 0.74 -0.67
One can get the velocity vector from :meth:`velocityvector_imasframe`, which is just a negated array of
:meth:`viewvector_imasframe`.
>>> veldir = fov.velocityvector_imasframe(1, 4.5, 0, 21)
>>> print('{0[0]:.2f} {0[1]:.2f} {0[2]:.2f}'.format(veldir))
-0.00 -0.74 0.67
"""
promsection_to_tableid = {0: 0, 'PROM': 0,
1: 1, 'EEPROM_00': 1,
16: 2, 'EEPROM_15': 2,
15: 2, 'EEPROM_14': 2,
14: 3, 'EEPROM_13': 3, }
""" Dictionary showing the PROM section index to the table ID.
PROM-section is the booting software section. It defines the energy / direction table.
MEX/IMA has 1 PROM and 16 EEPROM (0 to 15).
PROM is representedted by 0, while EEPROM is represented with increment by 1
(PROM is 0, EEPROM_00 is 1, EEPROM_01 is 2, and so on).
On the other hand, some ground software uses "table_id", where ``irfpy`` follows this custom.
.. todo::
A new implementation directly handle the table according to the data (ImaPacket) is needed.
Similar implementation in ``irfpy.mima.energy``
"""
[docs] def viewvector_imasframe(self, table_id, azim_nr, elev_nr, ene_nr):
""" View vector in IMAS frame is returned.
:param table_id: Table number. So far 0 to 3 is supported.
:param azim_nr: Azimuthal step
:param elev_nr: Elevation step
:param ene_nr: Energy step
:return: View vector in IMAS frame. If no viewing direction is defined,
[nan, nan, nan] is returned.
Vectorization is not supported.
"""
anr = azim_nr
enr = elev_nr
ennr = ene_nr
phi = self.azimuth_angle(anr)
theta = self.elevation_angle(table_id, enr, ennr, direction="look")
phi = np.deg2rad(phi)
theta = np.deg2rad(theta)
cp = np.ma.cos(phi)
sp = np.ma.sin(phi)
ct = np.ma.cos(theta)
st = np.ma.sin(theta)
x = ct * cp
y = ct * sp
z = st
return np.array([x, y, z])
[docs] def elevation_angle(self, table_id, elev_nr, ene_nr, direction='look'):
return self.elev_table[table_id, ene_nr, elev_nr]
[docs] def azimuth_angle(self, azim_nr, direction='look'):
if direction == 'look':
phi = -11.25 + 22.5 * azim_nr
elif direction == 'velocity':
phi = -11.25 + 22.5 * azim_nr + 180.
else:
raise ValueError('``direction`` must be ``look`` r ``velocity``')
return phi
[docs] def velocityvector_imasframe(self, table_id, azim_nr, elev_nr, ene_nr):
return -self.viewvector_imasframe(table_id, azim_nr, elev_nr, ene_nr)
[docs] def numbering_imasframe(self, viewvector):
""" Numbering in IMAS frame will be returned.
"""
raise NotImplementedError("numbering_imasframe is not supported for TableFOV object.")
[docs] def shadow_mask(self):
""" This method is not implemented. Use :meth:`shadow_mask3d`.
"""
raise NotImplementedError("shadow_mask() is not implemented for TableFOV. Use shadow_mask3d()")
[docs] def shadow_mask3d(self, table_id):
""" Return a table, with a shape of (A16, E96, P16), where the shadow_mask is embedded.
:param table_id: The table ID
:returns: (A16, E96, P16) boolean array showing the shadow mask. True is masked.
>>> tableFov = TableFOV()
>>> mask0 = tableFov.shadow_mask3d(0)
>>> print(mask0.shape)
(16, 96, 16)
>>> print(mask0[10, 32, 5]) # Azimuth=10, energy=32, elevation=5
True
>>> print(mask0[7, 32, 5]) # Azimuth=7, energy=32, elevation=5
False
"""
simpleFov = SimpleFOV()
simpleShadow = simpleFov.shadow_mask()
tableShadow = np.zeros([16, 96, 16], dtype=bool)
for ia in range(16):
for ie in range(96):
for ip in range(16):
vv = self.viewvector_imasframe(table_id, ia, ip, ie)
saz, spol = simpleFov.numbering_imasframe(vv)
try:
saz = int(np.round(saz))
spol = int(np.round(spol))
tableShadow[ia, ie, ip] = simpleShadow[saz, spol]
except (ValueError, IndexError) as e:
tableShadow[ia, ie, ip] = True # Error means shadowed! ValueError is for underfined angle, and IndexError for out of 45 deg bounds.
return tableShadow
__table_str = """ 0.4632961, 0.5299193, -0.4524347, -0.3762243, -0.2957081, -0.2130304,
-0.1287956, -0.04361939, 0.04013179, 0.1253332, 0.2096186, 0.2940403,
0.3746066, 0.4524347, 0.5239859, -0.4663866,
0.5548445, -0.5254717, -0.4539905, -0.3762243, -0.2957081, -0.2130304,
-0.1287956, -0.04361939, 0.04013179, 0.1253332, 0.2096186, 0.2940403,
0.3746066, 0.4524347, 0.5239859, -0.5577452,
-0.5906057, -0.5254717, -0.4539905, -0.3778408, -0.2957081, -0.2130304,
-0.1287956, -0.04536299, 0.04013179, 0.1253332, 0.2096186, 0.2940403,
0.3762243, 0.4539905, 0.5239859, 0.5877852,
-0.5906057, -0.5269558, -0.4555449, -0.3778408, -0.2973749, -0.2147353,
-0.1305262, -0.04536299, 0.04013179, 0.1253332, 0.2096186, 0.2940403,
0.3762243, 0.4539905, 0.5254717, 0.5891963,
-0.5920132, -0.5269558, -0.4555449, -0.3778408, -0.2973749, -0.2147353,
-0.1305262, -0.04536299, 0.04013179, 0.1253332, 0.2113248, 0.2940403,
0.3762243, 0.4539905, 0.5254717, 0.5891963,
-0.5934189, -0.5284384, -0.4570979, -0.3794562, -0.2990408, -0.2147353,
-0.1305262, -0.04536299, 0.04013179, 0.1253332, 0.2096186, 0.2940403,
0.3762243, 0.4539905, 0.5254717, 0.5891963,
-0.5934189, -0.5299193, -0.4570979, -0.3794562, -0.2990408, -0.2147353,
-0.1305262, -0.04536299, 0.04013179, 0.1253332, 0.2113248, 0.2940403,
0.3762243, 0.4539905, 0.5269558, 0.5906057,
-0.5948228, -0.5299193, -0.4586495, -0.3810704, -0.2990408, -0.2164396,
-0.1305262, -0.04536299, 0.04013179, 0.1253332, 0.2113248, 0.2957081,
0.3778408, 0.4555449, 0.5269558, 0.5906057,
-0.5962248, -0.5313986, -0.4601998, -0.3810704, -0.3007058, -0.2164396,
-0.1322564, -0.04710646, 0.04013179, 0.1253332, 0.2113248, 0.2957081,
0.3778408, 0.4555449, 0.5269558, 0.5920132,
-0.5976252, -0.5328763, -0.4601998, -0.3826835, -0.3007058, -0.2181432,
-0.1322564, -0.04710646, 0.04013179, 0.1253332, 0.2113248, 0.2957081,
0.3778408, 0.4555449, 0.5284384, 0.5920132,
-0.5990236, -0.5343524, -0.4617486, -0.3842953, -0.3023699, -0.2181432,
-0.1322564, -0.04710646, 0.03838781, 0.1253332, 0.2113248, 0.2957081,
0.3778408, 0.4570979, 0.5284384, 0.5934189,
-0.6004203, -0.5358269, -0.4632961, -0.3842953, -0.3023699, -0.2181432,
-0.1339862, -0.04710646, 0.03838781, 0.1253332, 0.2113248, 0.2957081,
0.3778408, 0.4570979, 0.5299193, 0.5948228,
-0.601815, -0.5372996, -0.4648421, -0.3859061, -0.3040331, -0.2198462,
-0.1339862, -0.04884977, 0.03838781, 0.1253332, 0.2113248, 0.2973749,
0.3794562, 0.4586495, 0.5299193, 0.5948228,
-0.6045992, -0.5387707, -0.4663866, -0.3875156, -0.3056953, -0.2198462,
-0.1339862, -0.04884977, 0.03838781, 0.1253332, 0.2113248, 0.2957081,
0.3794562, 0.4586495, 0.5313986, 0.5962248,
-0.6059884, -0.5402403, -0.4679298, -0.3891239, -0.3073566, -0.2215485,
-0.1357156, -0.04884977, 0.03838781, 0.1253332, 0.2113248, 0.2973749,
0.3794562, 0.4586495, 0.5328763, 0.5976252,
-0.6087614, -0.5431745, -0.4694716, -0.3907312, -0.309017, -0.2232501,
-0.1374445, -0.05059294, 0.03838781, 0.1253332, 0.2113248, 0.2973749,
0.3810704, 0.4601998, 0.5343524, 0.5990236,
-0.611527, -0.5461019, -0.4725508, -0.3923371, -0.309017, -0.2232501,
-0.1374445, -0.05059294, 0.03664371, 0.1253332, 0.2113248, 0.2973749,
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"""
def __init__(self):
tbl = np.fromstring(TableFOV.__table_str, sep=',').reshape(4, 96, 16)
tbl = np.ma.masked_outside(tbl, -1, 1)
self.elev_table = np.degrees(np.ma.arcsin(tbl)) # (96, 16) shaped masked array
""" Elevation table in np.array format.
The elevation table read from the ima_info.nc.
The shape is (ntalbe=4, enestep=96, elevstep=16)
"""
import unittest
import doctest
[docs]def doctests():
return unittest.TestSuite((
doctest.DocTestSuite(),
))
if __name__ == '__main__':
unittest.main(defaultTest='doctests')