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Content
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Problem
Meng sees a problem with interpretation of data. She observes in data large sample of events which have 2-peaks in the qH around two most probable positions 1.1 and 1.7 1/Å. In contrast, our model of lattice does not show these peaks simultaneously.
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A few crosschecks are presented below in order to address this issue.
Lattice
Triclinic crystal cell primitive vectors
We use a few methods from pyimgalgos.FiberIndexing to generate lattice:
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# 3-d space primitive vectors: # a1 = ( 18.550000, 0.000000, 0.000000) # a2 = ( -5.435624, 26.645524, 0.000000) # a3 = ( 0.000000, 0.000000, 4.860100) |
Reciprocal space primitive vectors
b1, b2, b3 = reciprocal_from_bravias(a1, a2, a3) - converts 3-d primitive vectors to reciprocal space primitive vectors.
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# reciprocal space primitive vectors: # b1 = ( 0.053908, 0.010997, -0.000000) # b2 = ( 0.000000, 0.037530, 0.000000) # b3 = ( 0.000000, -0.000000, 0.205757) |
Lattice generator and test
Then, call to method
x, y, z, r, h, k, l = lattice(b1, b2, b3, hmax, kmax, lmax, cdtype)
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h.shape: (13, 9) row: -4 -3 -2 -1 0 1 2 3 4 row: -4 -3 -2 -1 0 1 2 3 4 row: -4 -3 -2 -1 0 1 2 3 4 row: -4 -3 -2 -1 0 1 2 3 4 row: -4 -3 -2 -1 0 1 2 3 4 row: -4 -3 -2 -1 0 1 2 3 4 row: -4 -3 -2 -1 0 1 2 3 4 row: -4 -3 -2 -1 0 1 2 3 4 row: -4 -3 -2 -1 0 1 2 3 4 row: -4 -3 -2 -1 0 1 2 3 4 row: -4 -3 -2 -1 0 1 2 3 4 row: -4 -3 -2 -1 0 1 2 3 4 row: -4 -3 -2 -1 0 1 2 3 4 k.shape: (13, 9) row: -6 -6 -6 -6 -6 -6 -6 -6 -6 row: -5 -5 -5 -5 -5 -5 -5 -5 -5 row: -4 -4 -4 -4 -4 -4 -4 -4 -4 row: -3 -3 -3 -3 -3 -3 -3 -3 -3 row: -2 -2 -2 -2 -2 -2 -2 -2 -2 row: -1 -1 -1 -1 -1 -1 -1 -1 -1 row: 0 0 0 0 0 0 0 0 0 row: 1 1 1 1 1 1 1 1 1 row: 2 2 2 2 2 2 2 2 2 row: 3 3 3 3 3 3 3 3 3 row: 4 4 4 4 4 4 4 4 4 row: 5 5 5 5 5 5 5 5 5 row: 6 6 6 6 6 6 6 6 6 l.shape: (13, 9) row: 0 0 0 0 0 0 0 0 0 row: 0 0 0 0 0 0 0 0 0 row: 0 0 0 0 0 0 0 0 0 row: 0 0 0 0 0 0 0 0 0 row: 0 0 0 0 0 0 0 0 0 row: 0 0 0 0 0 0 0 0 0 row: 0 0 0 0 0 0 0 0 0 row: 0 0 0 0 0 0 0 0 0 row: 0 0 0 0 0 0 0 0 0 row: 0 0 0 0 0 0 0 0 0 row: 0 0 0 0 0 0 0 0 0 row: 0 0 0 0 0 0 0 0 0 row: 0 0 0 0 0 0 0 0 0 x coords.shape: (13, 9) row: -0.2156 -0.1617 -0.1078 -0.0539 0.0000 0.0539 0.1078 0.1617 0.2156 row: -0.2156 -0.1617 -0.1078 -0.0539 0.0000 0.0539 0.1078 0.1617 0.2156 row: -0.2156 -0.1617 -0.1078 -0.0539 0.0000 0.0539 0.1078 0.1617 0.2156 row: -0.2156 -0.1617 -0.1078 -0.0539 0.0000 0.0539 0.1078 0.1617 0.2156 row: -0.2156 -0.1617 -0.1078 -0.0539 0.0000 0.0539 0.1078 0.1617 0.2156 row: -0.2156 -0.1617 -0.1078 -0.0539 0.0000 0.0539 0.1078 0.1617 0.2156 row: -0.2156 -0.1617 -0.1078 -0.0539 0.0000 0.0539 0.1078 0.1617 0.2156 row: -0.2156 -0.1617 -0.1078 -0.0539 0.0000 0.0539 0.1078 0.1617 0.2156 row: -0.2156 -0.1617 -0.1078 -0.0539 0.0000 0.0539 0.1078 0.1617 0.2156 row: -0.2156 -0.1617 -0.1078 -0.0539 0.0000 0.0539 0.1078 0.1617 0.2156 row: -0.2156 -0.1617 -0.1078 -0.0539 0.0000 0.0539 0.1078 0.1617 0.2156 row: -0.2156 -0.1617 -0.1078 -0.0539 0.0000 0.0539 0.1078 0.1617 0.2156 row: -0.2156 -0.1617 -0.1078 -0.0539 0.0000 0.0539 0.1078 0.1617 0.2156 y coords.shape: (13, 9) row: -0.2692 -0.2582 -0.2472 -0.2362 -0.2252 -0.2142 -0.2032 -0.1922 -0.1812 row: -0.2316 -0.2206 -0.2096 -0.1986 -0.1876 -0.1767 -0.1657 -0.1547 -0.1437 row: -0.1941 -0.1831 -0.1721 -0.1611 -0.1501 -0.1391 -0.1281 -0.1171 -0.1061 row: -0.1566 -0.1456 -0.1346 -0.1236 -0.1126 -0.1016 -0.0906 -0.0796 -0.0686 row: -0.1190 -0.1081 -0.0971 -0.0861 -0.0751 -0.0641 -0.0531 -0.0421 -0.0311 row: -0.0815 -0.0705 -0.0595 -0.0485 -0.0375 -0.0265 -0.0155 -0.0045 0.0065 row: -0.0440 -0.0330 -0.0220 -0.0110 0.0000 0.0110 0.0220 0.0330 0.0440 row: -0.0065 0.0045 0.0155 0.0265 0.0375 0.0485 0.0595 0.0705 0.0815 row: 0.0311 0.0421 0.0531 0.0641 0.0751 0.0861 0.0971 0.1081 0.1190 row: 0.0686 0.0796 0.0906 0.1016 0.1126 0.1236 0.1346 0.1456 0.1566 row: 0.1061 0.1171 0.1281 0.1391 0.1501 0.1611 0.1721 0.1831 0.1941 row: 0.1437 0.1547 0.1657 0.1767 0.1876 0.1986 0.2096 0.2206 0.2316 row: 0.1812 0.1922 0.2032 0.2142 0.2252 0.2362 0.2472 0.2582 0.2692 z coords.shape: (13, 9) row: 0.0000 0.0000 0.0000 0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 row: 0.0000 0.0000 0.0000 0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 row: 0.0000 0.0000 0.0000 0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 row: 0.0000 0.0000 0.0000 0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 row: 0.0000 0.0000 0.0000 0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 row: 0.0000 0.0000 0.0000 0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 row: 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 row: 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 row: 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 row: 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 row: 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 row: 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 row: 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 r of lattice nodes.shape: (13, 9) row: 0.3449 0.3046 0.2697 0.2423 0.2252 0.2209 0.2300 0.2512 0.2817 row: 0.3165 0.2736 0.2357 0.2058 0.1876 0.1847 0.1977 0.2238 0.2591 row: 0.2901 0.2443 0.2031 0.1699 0.1501 0.1492 0.1675 0.1997 0.2403 row: 0.2665 0.2176 0.1724 0.1348 0.1126 0.1150 0.1408 0.1803 0.2263 row: 0.2463 0.1945 0.1451 0.1015 0.0751 0.0837 0.1202 0.1671 0.2179 row: 0.2305 0.1764 0.1232 0.0725 0.0375 0.0601 0.1089 0.1618 0.2157 row: 0.2201 0.1651 0.1100 0.0550 0.0000 0.0550 0.1100 0.1651 0.2201 row: 0.2157 0.1618 0.1089 0.0601 0.0375 0.0725 0.1232 0.1764 0.2305 row: 0.2179 0.1671 0.1202 0.0837 0.0751 0.1015 0.1451 0.1945 0.2463 row: 0.2263 0.1803 0.1408 0.1150 0.1126 0.1348 0.1724 0.2176 0.2665 row: 0.2403 0.1997 0.1675 0.1492 0.1501 0.1699 0.2031 0.2443 0.2901 row: 0.2591 0.2238 0.1977 0.1847 0.1876 0.2058 0.2357 0.2736 0.3165 row: 0.2817 0.2512 0.2300 0.2209 0.2252 0.2423 0.2697 0.3046 0.3449 |
Table of lattice node parameters sorted by radius
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( h, k) R(h,k)[1/A] ( 0, 0) 0.0000 ( 0, 1) 0.0375 ( 1, 0) 0.0550 (-1, 1) 0.0601 ( 1, 1) 0.0725 ( 0, 2) 0.0751 (-1, 2) 0.0837 ( 1, 2) 0.1015 (-2, 1) 0.1089 ( 2, 0) 0.1100 ( 0, 3) 0.1126 (-1, 3) 0.1150 (-2, 2) 0.1202 ( 2, 1) 0.1232 ( 1, 3) 0.1348 (-2, 3) 0.1408 ( 2, 2) 0.1451 (-1, 4) 0.1492 ( 0, 4) 0.1501 (-3, 1) 0.1618 ( 3, 0) 0.1651 (-3, 2) 0.1671 (-2, 4) 0.1675 ( 1, 4) 0.1699 ( 2, 3) 0.1724 ( 3, 1) 0.1764 (-3, 3) 0.1803 (-1, 5) 0.1847 ( 0, 5) 0.1876 ( 3, 2) 0.1945 (-2, 5) 0.1977 (-3, 4) 0.1997 ( 2, 4) 0.2031 ( 1, 5) 0.2058 (-4, 1) 0.2157 ( 3, 3) 0.2176 (-4, 2) 0.2179 ( 4, 0) 0.2201 (-1, 6) 0.2209 (-3, 5) 0.2238 ( 0, 6) 0.2252 (-4, 3) 0.2263 (-2, 6) 0.2300 ( 4, 1) 0.2305 ( 2, 5) 0.2357 (-4, 4) 0.2403 ( 1, 6) 0.2423 ( 3, 4) 0.2443 ( 4, 2) 0.2463 (-3, 6) 0.2512 (-4, 5) 0.2591 ( 4, 3) 0.2665 ( 2, 6) 0.2697 ( 3, 5) 0.2736 (-4, 6) 0.2817 ( 4, 4) 0.2901 ( 3, 6) 0.3046 ( 4, 5) 0.3165 ( 4, 6) 0.3449 |
Rotation of the crystal lattice
Both in test_lattice and make_lookup_table methods crystal lattice in reciprocal space is rotated around Z and Y axes by omega_deg and beta_deg, respectively using calls:
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Rotation in test_lattice for omega_deg = 0; beta_deg = 9 produces the plot
Other movies Movies with frame delay 0.4s, 0.4s, 0.8s:50, 100, 200, 400ms:
Look-up table
Look-up table is generated in method make_lookup_table_v2 called as
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generates 2-d array, which presents look-up table in 2-d plot and its projection:
Look-up table is generated for bpomega = BinPars((0., 180.), 360,...)
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# file name: ./v02-lut-cxif5315-r0169-2016-02-03T15:10:48.txt
# photon energy = 6003.1936 eV
# wavelength = 2.0653 A
# wave number/Evald radius k = 1/lambda = 0.484187 1/A
# sigma_ql = 0.001453 1/A (approximately = k * <pixel size>/
# sigma_qt = 0.000484 1/A (approximately = k * <pixel size>/<sample-to-detector distance> = k*100um/100mm)
# 3*sigma_ql = 0.004358 1/A
# 3*sigma_qt = 0.001453 1/A
# Triclinic crystal cell parameters:
# a = 18.55 A
# b = 27.19 A
# c = 4.86 A
# alpha = 90.00 deg
# beta = 90.00 deg
# gamma = 78.47 deg
# 3-d space primitive vectors:
# a1 = ( 18.550000, 0.000000, 0.000000)
# a2 = ( -5.435624, 26.645524, 0.000000)
# a3 = ( 0.000000, 0.000000, 4.860100)
# reciprocal space primitive vectors:
# b1 = ( 0.053908, 0.010997, -0.000000)
# b2 = ( 0.000000, 0.037530, 0.000000)
# b3 = ( 0.000000, -0.000000, 0.205757)
# _________________________________________________________________________________________
# beta 0.00 omega 0.00 degree
# index beta omega h k l dr[1/A] R(h,k,l) qv[1/A] qh[1/A] P(omega)
1 0.00 0.00 0 -1 0 0.001452 0.037530 0.000000 -0.037446 0.606641
1 0.00 0.00 0 1 0 0.001452 0.037530 0.000000 0.037446 0.606641
1 0.00 0.00 -1 6 0 -0.003549 0.220861 0.000000 0.221647 0.050590
# beta 0.00 omega 0.50 degree
# index beta omega h k l dr[1/A] R(h,k,l) qv[1/A] qh[1/A] P(omega)
2 0.00 0.50 0 -1 0 0.001779 0.037530 0.000000 -0.037419 0.472496
2 0.00 0.50 0 1 0 0.001126 0.037530 0.000000 0.037469 0.740615
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Check for look-up table
Method cxif5315/plot-lattice-from-data.py generates two plots from look-up table;
- intensities for omega vs. qh
- reconstructed lattice from measured omega and qh
- the same image convolved with 2-d gaussian weight matrix arr_2d_gauss(2, 1.5)
Mask
Mask is regenerated for equatorial region as
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Wedge 871.5 878 450 383 148 196 1 k False False
Wedge 871.5 878 450 383 -27 21 1 k False False
where parameters
t = pars[0] # figure type, ex. 'Wedge'
x = float(pars[1]) # x coordinate of the wedge center
y = float(pars[2]) # y coordinate of the wedge center
r = float(pars[3]) # 1-st radius of the wedge
w = float(pars[4]) # radial width of the wedge
t1 = float(pars[5]) # 1-st angle
t2 = float(pars[6]) # 2-nd angle
lw = int(pars[7]) # line width
col = str(pars[8]) # color
s = self.dicBool[pars[9].lower()] # isSelected boolean parameter
rem = self.dicBool[pars[10].lower()] # isRemoved - helper parameter |
Lattice reconstructed by Meng
Lattice reconstructed by Meng
Original and convoluted images
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