Open Philip-Go opened 2 years ago
Thanks for letting us know. I will update the code to include the Oxford HDF5 format... It would help if I could have access to a small example HDF5 file.
Regards, Marc.
On 10/21/22 6:34 AM, Philip-Go wrote:
Hi everybody,
I'm using EMsoft 5.0 in a nightly-build copiled package and was using it with OxfordBinaries .ebsp from AZtec versions 3.1 to 4.3. In that combo, the DI went smoothly and resulted great mappings of nano-crystalline metals and deformed microstructures.
However, recently one of our EBSD systems got an update of the AZtec software, from 3.1 to AZtec 6.0. With this update some changes in the OxfordBinary file must have occured, because EMEBSDDIpreview can't access the .ebsp any more. This can be related to the HDF5 file, because now the OxfordHDF5 file format .h5oina contains the uncompressed Kikuchi patternswhich are nicely accessible, for example in Python via h5py and matplotlib. The path to access them is '1/EBSD/Data/Processed Patterns'. Unfortunately, the EMsoft inputtype OxfordHDF leads to an hard coded break. From the code I could find out that as of 2019 the OxfordHDF5 did not contain any Kikuchi patterns, so no routine was implemented.
However, now the Kikuchi patterns are there. I'm not that familiar with HDF5 yet, but I asumed that it's advantage is data accessability independent of the hardware manufacturer. So I tried to run EMEBSDDIpreview on the OxfordHDF with inputtype BrukerHDF, which failed, and TSLHDF, which then was succesfull! Of course I tried the dictionary indexing EMEBSDDI on the OxfordHDF with the TSLHDF, which started out nicely. But eventually, the programm failed during Pattern Preprocessing inbetween row 260 and 265 of 500 rows with the error:
|Completed row 260 of 500 rows| |Error code : -1| |returned by routine HDF_readHyperslabIntegerArray3D:h5dread_f:Processed Patterns|
Interestingly, when I define a ROI from 1st to 250th column, the DI programm runs smoothly and returns a proper .ctf file:
|Completed row 250 of 250 rows| |-> experimental patterns preprocessed| |Number of experimental patterns processed per second : 34883.7| |-> computing Average Dot Product map (ADP)| |-> Number of threads set to 8| |Oct 21 2022 11:56:12.770 AM| |min./max. dot product = 0.768612 / 0.867969; 1.2% complete| |min./max. dot product = 0.768987 / 0.870098; 2.4% complete| etc...
The dataset contains 375000 datapoint/kikuchi patterns in 750 columns and 500 rows, Kikuchi patterns have a size of 168x128 px.
My question is know, if someone has implemented but not released a routine for reading OxfordHDF files containing Kikuchi patterns or maybe has an idea, why the TSLHDF set only works until a specific row. I am neither experienced with HDF5 nor Fortran. But following the error-code, the error occurs in the h5read_f line in the HDF_readHyperslabIntegerArray3D procedure.
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Hi Phillip and Marc,
we recently added a reader for Oxfords H5OINA files in kikuchipy (Python) as well (soon to be released). I only tested it on files which were not cropped to a region of interest. I assume our reader will not read a file with an ROI either, so I too would be interested in a small example H5OINA file with an ROI.
The H5OINA format specification might be helpful, including the definition of the ROI.
Hello Marc and Hakon,
thanks for your quick reply! The following link gives you an .h5oina file of a 75 x75 EBSD mapping of an Aluminum sample: https://faubox.rrze.uni-erlangen.de/getlink/fiTbeDDgQ8ZfSz7ocD87vh/Al_SLBM%2010kV_8x8_small.h5oina
The Kikuchi-Pattern from the center point of that map is here:
The Oxford Detector Parameters are:
Collected: 21.10.2022 16:15:13 Accelerating Voltage: 10.00 kV Working Distance: 16.0 mm Detector Insertion Distance: 174.9 mm Tilt Axis: Parallel to X Specimen Tilt (degrees): 70.0° EBSD Camera Binning Mode: 8x8 (168x128 pixels) EBSD Camera Exposure Time: 29.24 ms EBSD Camera Gain: 0 Frame Averaging: 1 frames Static Background Correction: On Auto Background Correction: On Pattern Center: (0.563, 0.570) Detector Distance: 0.506 = 16.04 mm Hough Resolution: 60 Band Detection Mode: Centers Number of Bands Detected: 6 Indexing Mode: Refined Accuracy
The Oxford Detector Parameters translate to the following EMsoft parameters (d = 25µm, binnig = 8, tilt = 5°): xPC = -10.584 yPC = 31.76 L = 17001.6
I haven't tested this file with the inputtype='TSLHDF' flag, but asume from the behavior of the big map, that it should work - but I'll try it.
@hakonanes: the map behind the link should also be a ROI as defined in the H5OINA spec., meaning, that the EBSD mapping was performed on a smaller area than the respective electron image. However the ROI I was referring to in the opening post was the ROI defined in the EMEBSDDI.namelist file, so a rectangular subspace within the EBSD map.
Regards, Philip
Thank you, Philip, with your file I could confirm that the mentioned reader in kikuchipy reads your file without issue.
I tried feeding the patterns and PC values automatically read from the file directly to PyEBSDIndex for Hough indexing (PC values converted via kikuchipy's EBSD detector to Bruker's PC convention used internally), which produced results as expected (map colors according to IPF-Z):
That might be off topic regarding EMsoft, but the resulting IPf map looks well indexed. Does PyEBSDIndex achieve such a high indexation rate by hough indexing alone or was the map subjected to some cleaning and filtering afterwards? I'm wondering, since with online indexing during the measurement AZtec yields only ~60% indexation rate. I should definately take a closer look at that, thanks showing that!
I'm going to use Dictionary Indexing to reproduce this IPF map. I don't really know the camera details here... can you confirm that the camera is tilted by 6.6° from vertical with the top of the detector moving away from the sample ?
I can confirm that EMsoft programs can read this file using the TSLHDF input mode; we'll need to figure out why it didn't properly work with the larger data set. For starters, let's make sure that the conventions are correct: ipf_ht and ipd_wd are the height and width of the complete acquired data set; they should remain the same if an ROI is defined.
Thanks, Marc.
On 10/21/22 11:13 AM, Håkon Wiik Ånes wrote:
Thank you, Philip, with your file I could confirm that the mentioned reader in kikuchipy reads your file without issue.
I tried feeding the patterns and PC values automatically read from the file directly to PyEBSDIndex for Hough indexing (PC values converted via kikuchipy's EBSD detector to Bruker's PC convention used internally), which produced results as expected (map colors according to IPF-Z):
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Hi Marc, the detector geometry values we measured and obtained from Oxford are (as stated above):
tilt: 5°-6°, but could be 6.5°, I haven't obtained it more accurately, but this can be within the measurment error detector pixel size: 25 µm binning (in this mapping): 8x
The PC detector parameters from Oxford are: xPC(Ox) = 0.563 yPC(Ox) = 0.570 zPC(Ox) = 0.503
translating this into EMsoft definition I would get: xPC = -10.584 yPC = 31.76 L = 17001.6 mm
If it is of any help, I could upload the large dataset as well. However this will be 7-8 Gb large.
Regards, Philip
Hi Philip,
Here is a preliminary result from the EMsoft Dictionary Indexing program; I did a pattern center refinement starting from the values you listed, and the refined values are (EMsoft convention)
xPC = -13.4377 yPC = 32.4216 L = 16772.985
I used a detector tilt of 6.5°; my pixel size was 200 microns, but I set the binning to 1, so that produces the same result.
Here are the reference pattern and the best fit:
And the IPFZ map:
Note that some grains have different colors from the Kikuchipy solution... I'm attaching the .ang file so we can start comparing. The orientations in the .ang file have been reduced to the cubic fundamental zone.
It would be a good idea to also test the full size data set if you don't mind making that available.
Regards, Marc.
On 10/21/22 5:00 PM, Philip-Go wrote:
Hi Marc, the detector geometry values we measured and obtained from Oxford are (as stated above):
tilt: 5°-6°, but could be 6.5°, I haven't obtained it more accurately, but this can be within the measurment error detector pixel size: 25 µm binning (in this mapping): 8x
The PC detector parameters from Oxford are: xPC(Ox) = 0.563 yPC(Ox) = 0.570 zPC(Ox) = 0.5037888
translating this into EMsoft definition I would get: xPC = -10.584 yPC = 31.76 L = 17001.6 mm
If it is of any help, I could upload the large dataset as well. However this will be 7-8 Gb large.
Regards, Philip
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Ph: (412) 268-8527 Fx: (412) 268-7596 @.*** web:http://materials.cmu.edu/degraef
Admin. Asst.: Marygrace Antkowski Phone: (412) 268-7240
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0.886 1 2.68188 0.63360 2.86833 2.70300 0.31800 52.7 0.885 1 2.68188 0.63360 2.86833 2.86200 0.31800 41.3 0.857 1 5.13591 0.05103 1.63905 3.02100 0.31800 39.7 0.853 1 4.32320 0.38896 1.57104 3.18000 0.31800 41.1 0.844 1 4.32320 0.38896 1.57104 3.33900 0.31800 48.5 0.872 1 4.32320 0.38896 1.57104 3.49800 0.31800 52.5 0.878 1 4.32320 0.38896 1.57104 3.65700 0.31800 52.8 0.873 1 4.32320 0.38896 1.57104 3.81600 0.31800 49.7 0.869 1 4.32320 0.38896 1.57104 3.97500 0.31800 44.0 0.858 1 1.49197 0.71388 4.50751 4.13400 0.31800 39.6 0.830 1 1.49197 0.71388 4.50751 4.29300 0.31800 43.4 0.843 1 1.47615 0.72097 4.54259 4.45200 0.31800 44.2 0.848 1 1.47615 0.72097 4.54259 4.61100 0.31800 44.7 0.852 1 1.47615 0.72097 4.54259 4.77000 0.31800 45.9 0.846 1 1.47615 0.72097 4.54259 4.92900 0.31800 46.2 0.847 1 1.47615 0.72097 4.54259 5.08800 0.31800 42.4 0.843 1 3.07599 0.44085 3.57996 5.24700 0.31800 34.5 0.834 1 3.07599 0.44085 3.57996 5.40600 0.31800 38.1 0.850 1 3.07599 0.44085 3.57996 5.56500 0.31800 41.7 0.851 1 0.46577 0.56118 6.03948 5.72400 0.31800 42.6 0.851 1 0.46577 0.56118 6.03948 5.88300 0.31800 44.8 0.867 1 0.46577 0.56118 6.03948 6.04200 0.31800 45.0 0.867 1 0.46577 0.56118 6.03948 6.20100 0.31800 42.8 0.845 1 1.64265 0.80097 3.95287 6.36000 0.31800 37.9 0.838 1 2.05977 0.89813 4.11889 6.51900 0.31800 40.6 0.841 1 1.05209 0.05078 4.54895 6.67800 0.31800 43.6 0.862 1 0.72125 0.05436 4.88006 6.83700 0.31800 50.7 0.876 1 0.72125 0.05436 4.88006 6.99600 0.31800 51.0 0.877 1 0.72125 0.05436 4.88006 7.15500 0.31800 49.2 0.867 1 1.64265 0.80097 3.95287 7.31400 0.31800 47.0 0.862 1 1.64265 0.80097 3.95287 7.47300 0.31800 47.3 0.866 1 0.72125 0.05436 4.88006 7.63200 0.31800 46.9 0.855 1 1.05209 0.05078 4.54895 7.79100 0.31800 50.3 0.871 1 0.72125 0.05436 4.88006 7.95000 0.31800 50.8 0.881 1 0.72125 0.05436 4.88006 8.10900 0.31800 46.0 0.876 1 1.05209 0.05078 4.54895 8.26800 0.31800 39.0 0.849 1 0.65819 0.57285 6.14060 8.42700 0.31800 39.5 0.831 1 4.77620 0.76090 1.89186 8.58600 0.31800 40.7 0.841 1 4.77620 0.76090 1.89186 8.74500 0.31800 44.2 0.859 1 4.77620 0.76090 1.89186 8.90400 0.31800 47.0 0.862 1 4.77620 0.76090 1.89186 9.06300 0.31800 44.1 0.847 1 2.05669 0.31954 4.32161 9.22200 0.31800 43.6 0.867 1 2.05449 0.31446 4.33958 9.38100 0.31800 45.4 0.878 1 2.05669 0.31954 4.32161 9.54000 0.31800 44.1 0.865 1 5.58293 0.21292 1.14725 9.69900 0.31800 45.8 0.866 1 5.58293 0.21292 1.14725 9.85800 0.31800 55.6 0.885 1 5.58293 0.21292 1.14725 10.01700 0.31800 58.8 0.887 1 5.58293 0.21292 1.14725 10.17600 0.31800 56.9 0.885 1 5.58293 0.21292 1.14725 10.33500 0.31800 57.7 0.885 1 5.58293 0.21292 1.14725 10.49400 0.31800 58.5 0.884 1 5.58293 0.21292 1.14725 10.65300 0.31800 53.6 0.881 1 5.58293 0.21292 1.14725 10.81200 0.31800 44.4 0.862 1 3.62078 0.41924 2.11797 10.97100 0.31800 39.2 0.833 1 3.62078 0.41924 2.11797 11.13000 0.31800 44.4 0.856 1 3.62078 0.41924 2.11797 11.28900 0.31800 46.6 0.854 1 3.98334 0.50735 2.91653 11.44800 0.31800 47.2 0.842 1 3.98334 0.50735 2.91653 11.60700 0.31800 51.3 0.874 1 3.98334 0.50735 2.91653 11.76600 0.31800 56.3 0.880 1 3.98334 0.50735 2.91653 11.92500 0.31800 56.6 0.881 1 1.61763 0.39478 4.36605 0.00000 0.47700 51.1 0.881 1 1.58422 0.41803 4.43312 0.15900 0.47700 48.7 0.876 1 1.58422 0.41803 4.43312 0.31800 0.47700 38.9 0.847 1 2.06935 0.39189 4.55985 0.47700 0.47700 40.3 0.849 1 2.06935 0.39189 4.55985 0.63600 0.47700 43.1 0.865 1 2.06935 0.39189 4.55985 0.79500 0.47700 40.6 0.862 1 0.68179 0.79560 5.16067 0.95400 0.47700 40.6 0.848 1 0.68179 0.79560 5.16067 1.11300 0.47700 50.3 0.875 1 0.68179 0.79560 5.16067 1.27200 0.47700 51.7 0.878 1 0.68179 0.79560 5.16067 1.43100 0.47700 47.8 0.873 1 0.68179 0.79560 5.16067 1.59000 0.47700 42.4 0.857 1 0.68179 0.79560 5.16067 1.74900 0.47700 37.2 0.836 1 1.58737 0.41359 4.68701 1.90800 0.47700 35.5 0.848 1 1.58737 0.41359 4.68701 2.06700 0.47700 36.9 0.840 1 2.68188 0.63360 2.86833 2.22600 0.47700 45.3 0.865 1 2.68188 0.63360 2.86833 2.38500 0.47700 55.0 0.883 1 2.68188 0.63360 2.86833 2.54400 0.47700 54.4 0.884 1 2.68188 0.63360 2.86833 2.70300 0.47700 51.3 0.882 1 2.68188 0.63360 2.86833 2.86200 0.47700 42.1 0.864 1 5.08433 0.07103 1.68819 3.02100 0.47700 39.7 0.845 1 4.28172 0.39075 1.61433 3.18000 0.47700 41.0 0.841 1 4.32320 0.38896 1.57104 3.33900 0.47700 47.7 0.871 1 4.32320 0.38896 1.57104 3.49800 0.47700 52.8 0.875 1 4.32320 0.38896 1.57104 3.65700 0.47700 53.7 0.875 1 4.32320 0.38896 1.57104 3.81600 0.47700 51.3 0.872 1 4.32320 0.38896 1.57104 3.97500 0.47700 47.7 0.866 1 4.32320 0.38896 1.57104 4.13400 0.47700 41.3 0.850 1 3.88951 0.26964 2.31872 4.29300 0.47700 38.8 0.836 1 4.00123 0.25179 2.25620 4.45200 0.47700 41.2 0.845 1 3.07599 0.44085 3.57996 4.61100 0.47700 40.5 0.829 1 3.07599 0.44085 3.57996 4.77000 0.47700 46.4 0.859 1 3.07599 0.44085 3.57996 4.92900 0.47700 47.6 0.865 1 3.07599 0.44085 3.57996 5.08800 0.47700 44.6 0.862 1 3.07599 0.44085 3.57996 5.24700 0.47700 44.7 0.865 1 3.07599 0.44085 3.57996 5.40600 0.47700 45.7 0.869 1 3.07599 0.44085 3.57996 5.56500 0.47700 47.3 0.864 1 3.07599 0.44085 3.57996 5.72400 0.47700 41.6 0.854 1 3.07599 0.44085 3.57996 5.88300 0.47700 39.8 0.832 1 1.64265 0.80097 3.95287 6.04200 0.47700 41.6 0.843 1 1.64265 0.80097 3.95287 6.20100 0.47700 47.1 0.870 1 1.64265 0.80097 3.95287 6.36000 0.47700 43.7 0.870 1 1.64265 0.80097 3.95287 6.51900 0.47700 40.3 0.844 1 1.05209 0.05078 4.54895 6.67800 0.47700 46.9 0.872 1 0.72125 0.05436 4.88006 6.83700 0.47700 49.6 0.874 1 0.72125 0.05436 4.88006 6.99600 0.47700 50.7 0.873 1 0.72125 0.05436 4.88006 7.15500 0.47700 45.9 0.851 1 1.64265 0.80097 3.95287 7.31400 0.47700 50.6 0.874 1 1.64265 0.80097 3.95287 7.47300 0.47700 52.5 0.880 1 1.64265 0.80097 3.95287 7.63200 0.47700 51.3 0.874 1 1.64265 0.80097 3.95287 7.79100 0.47700 45.6 0.850 1 0.72125 0.05436 4.88006 7.95000 0.47700 49.5 0.872 1 1.05209 0.05078 4.54895 8.10900 0.47700 51.5 0.880 1 1.05209 0.05078 4.54895 8.26800 0.47700 46.4 0.872 1 0.72125 0.05436 4.88006 8.42700 0.47700 39.6 0.840 1 0.65819 0.57285 6.14060 8.58600 0.47700 38.7 0.846 1 4.77620 0.76090 1.89186 8.74500 0.47700 37.8 0.834 1 2.05669 0.31954 4.32161 8.90400 0.47700 42.5 0.842 1 2.05669 0.31954 4.32161 9.06300 0.47700 44.6 0.869 1 2.05669 0.31954 4.32161 9.22200 0.47700 47.8 0.877 1 2.05669 0.31954 4.32161 9.38100 0.47700 46.4 0.871 1 2.05669 0.31954 4.32161 9.54000 0.47700 41.9 0.846 1 5.58293 0.21292 1.14725 9.69900 0.47700 47.7 0.872 1 5.58293 0.21292 1.14725 9.85800 0.47700 54.6 0.883 1 5.58293 0.21292 1.14725 10.01700 0.47700 57.4 0.886 1 5.58293 0.21292 1.14725 10.17600 0.47700 57.7 0.886 1 5.58293 0.21292 1.14725 10.33500 0.47700 58.4 0.887 1 5.58293 0.21292 1.14725 10.49400 0.47700 58.1 0.885 1 5.58293 0.21292 1.14725 10.65300 0.47700 54.9 0.882 1 5.58293 0.21292 1.14725 10.81200 0.47700 48.4 0.873 1 5.58293 0.21292 1.14725 10.97100 0.47700 38.5 0.839 1 3.62078 0.41924 2.11797 11.13000 0.47700 39.8 0.839 1 3.98334 0.50735 2.91653 11.28900 0.47700 44.9 0.840 1 3.98334 0.50735 2.91653 11.44800 0.47700 49.1 0.864 1 3.98334 0.50735 2.91653 11.60700 0.47700 55.3 0.878 1 3.98334 0.50735 2.91653 11.76600 0.47700 56.9 0.880 1 3.98334 0.50735 2.91653 11.92500 0.47700 58.2 0.881 1 1.61763 0.39478 4.36605 0.00000 0.63600 58.9 0.886 1 1.58422 0.41803 4.43312 0.15900 0.63600 52.9 0.882 1 1.58422 0.41803 4.43312 0.31800 0.63600 44.7 0.856 1 2.06935 0.39189 4.55985 0.47700 0.63600 44.8 0.871 1 2.06935 0.39189 4.55985 0.63600 0.63600 49.1 0.880 1 2.06935 0.39189 4.55985 0.79500 0.63600 47.3 0.880 1 2.06935 0.39189 4.55985 0.95400 0.63600 41.4 0.852 1 0.68179 0.79560 5.16067 1.11300 0.63600 44.5 0.865 1 0.68179 0.79560 5.16067 1.27200 0.63600 51.1 0.872 1 0.68179 0.79560 5.16067 1.43100 0.63600 49.4 0.872 1 0.68179 0.79560 5.16067 1.59000 0.63600 42.3 0.866 1 0.68179 0.79560 5.16067 1.74900 0.63600 38.3 0.839 1 1.58737 0.41359 4.68701 1.90800 0.63600 40.2 0.863 1 1.58737 0.41359 4.68701 2.06700 0.63600 41.1 0.859 1 2.68188 0.63360 2.86833 2.22600 0.63600 38.2 0.845 1 2.68188 0.63360 2.86833 2.38500 0.63600 49.8 0.879 1 2.68188 0.63360 2.86833 2.54400 0.63600 50.5 0.879 1 2.68188 0.63360 2.86833 2.70300 0.63600 50.4 0.879 1 2.68188 0.63360 2.86833 2.86200 0.63600 43.2 0.870 1 2.68188 0.63360 2.86833 3.02100 0.63600 36.7 0.841 1 4.28172 0.39075 1.61433 3.18000 0.63600 37.8 0.848 1 4.32320 0.38896 1.57104 3.33900 0.63600 47.6 0.869 1 4.32320 0.38896 1.57104 3.49800 0.63600 49.9 0.871 1 4.32320 0.38896 1.57104 3.65700 0.63600 51.7 0.871 1 4.32320 0.38896 1.57104 3.81600 0.63600 51.2 0.871 1 4.32320 0.38896 1.57104 3.97500 0.63600 48.4 0.867 1 4.32320 0.38896 1.57104 4.13400 0.63600 45.1 0.854 1 3.88951 0.26964 2.31872 4.29300 0.63600 42.8 0.844 1 3.88951 0.26964 2.31872 4.45200 0.63600 46.8 0.857 1 3.07599 0.44085 3.57996 4.61100 0.63600 39.9 0.835 1 3.07599 0.44085 3.57996 4.77000 0.63600 50.7 0.873 1 3.07599 0.44085 3.57996 4.92900 0.63600 53.9 0.874 1 3.07599 0.44085 3.57996 5.08800 0.63600 51.5 0.873 1 3.07599 0.44085 3.57996 5.24700 0.63600 51.1 0.871 1 3.07599 0.44085 3.57996 5.40600 0.63600 49.5 0.869 1 3.07599 0.44085 3.57996 5.56500 0.63600 50.0 0.865 1 3.07599 0.44085 3.57996 5.72400 0.63600 45.3 0.857 1 3.07599 0.44085 3.57996 5.88300 0.63600 37.6 0.839 1 1.64265 0.80097 3.95287 6.04200 0.63600 41.0 0.864 1 1.64265 0.80097 3.95287 6.20100 0.63600 52.7 0.884 1 1.64265 0.80097 3.95287 6.36000 0.63600 52.3 0.882 1 1.64265 0.80097 3.95287 6.51900 0.63600 45.3 0.865 1 1.05209 0.05078 4.54895 6.67800 0.63600 46.7 0.864 1 0.72125 0.05436 4.88006 6.83700 0.63600 47.7 0.866 1 0.72125 0.05436 4.88006 6.99600 0.63600 48.5 0.862 1 1.64265 0.80097 3.95287 7.15500 0.63600 46.8 0.859 1 1.64265 0.80097 3.95287 7.31400 0.63600 52.9 0.880 1 1.64265 0.80097 3.95287 7.47300 0.63600 58.0 0.883 1 1.64265 0.80097 3.95287 7.63200 0.63600 56.9 0.883 1 1.64265 0.80097 3.95287 7.79100 0.63600 51.4 0.877 1 0.72125 0.05436 4.88006 7.95000 0.63600 46.7 0.848 1 0.72125 0.05436 4.88006 8.10900 0.63600 48.9 0.873 1 1.05209 0.05078 4.54895 8.26800 0.63600 48.8 0.872 1 0.72125 0.05436 4.88006 8.42700 0.63600 42.0 0.860 1 0.65819 0.57285 6.14060 8.58600 0.63600 35.6 0.832 1 0.65819 0.57285 6.14060 8.74500 0.63600 32.2 0.824 1 2.05669 0.31954 4.32161 8.90400 0.63600 41.8 0.864 1 2.05669 0.31954 4.32161 9.06300 0.63600 48.1 0.875 1 2.05669 0.31954 4.32161 9.22200 0.63600 49.8 0.871 1 5.07193 0.76649 0.57283 9.38100 0.63600 47.7 0.852 1 5.07193 0.76649 0.57283 9.54000 0.63600 42.8 0.857 1 5.58293 0.21292 1.14725 9.69900 0.63600 44.9 0.861 1 5.58293 0.21292 1.14725 9.85800 0.63600 53.5 0.879 1 5.58293 0.21292 1.14725 10.01700 0.63600 55.0 0.882 1 5.58293 0.21292 1.14725 10.17600 0.63600 56.7 0.886 1 5.58293 0.21292 1.14725 10.33500 0.63600 59.1 0.886 1 5.58293 0.21292 1.14725 10.49400 0.63600 55.5 0.885 1 5.58293 0.21292 1.14725 10.65300 0.63600 54.5 0.880 1 5.58293 0.21292 1.14725 10.81200 0.63600 50.7 0.874 1 5.58293 0.21292 1.14725 10.97100 0.63600 40.5 0.856 1 3.98334 0.50735 2.91653 11.13000 0.63600 36.7 0.831 1 3.98334 0.50735 2.91653 11.28900 0.63600 48.3 0.866 1 3.98334 0.50735 2.91653 11.44800 0.63600 52.6 0.873 1 3.98334 0.50735 2.91653 11.60700 0.63600 55.3 0.875 1 3.98334 0.50735 2.91653 11.76600 0.63600 56.0 0.878 1 3.98334 0.50735 2.91653 11.92500 0.63600 57.8 0.880 1 1.61763 0.39478 4.36605 0.00000 0.79500 56.6 0.884 1 1.58422 0.41803 4.43312 0.15900 0.79500 54.8 0.882 1 1.58422 0.41803 4.43312 0.31800 0.79500 44.2 0.858 1 2.10897 0.39460 4.51979 0.47700 0.79500 46.6 0.874 1 2.10897 0.39460 4.51979 0.63600 0.79500 51.0 0.879 1 2.06935 0.39189 4.55985 0.79500 0.79500 50.2 0.881 1 2.06935 0.39189 4.55985 0.95400 0.79500 42.6 0.868 1 0.68179 0.79560 5.16067 1.11300 0.79500 38.9 0.839 1 0.68179 0.79560 5.16067 1.27200 0.79500 44.0 0.863 1 0.68179 0.79560 5.16067 1.43100 0.79500 45.1 0.865 1 0.68179 0.79560 5.16067 1.59000 0.79500 41.5 0.860 1 0.68179 0.79560 5.16067 1.74900 0.79500 35.9 0.832 1 1.58737 0.41359 4.68701 1.90800 0.79500 44.2 0.868 1 1.58737 0.41359 4.68701 2.06700 0.79500 41.8 0.864 1 1.58737 0.41359 4.68701 2.22600 0.79500 32.7 0.826 1 2.68188 0.63360 2.86833 2.38500 0.79500 44.0 0.863 1 2.68188 0.63360 2.86833 2.54400 0.79500 45.7 0.871 1 2.68188 0.63360 2.86833 2.70300 0.79500 45.7 0.870 1 2.68188 0.63360 2.86833 2.86200 0.79500 41.8 0.867 1 2.68188 0.63360 2.86833 3.02100 0.79500 34.2 0.840 1 4.28172 0.39075 1.61433 3.18000 0.79500 38.4 0.856 1 4.32320 0.38896 1.57104 3.33900 0.79500 47.8 0.868 1 4.32320 0.38896 1.57104 3.49800 0.79500 49.6 0.868 1 4.32320 0.38896 1.57104 3.65700 0.79500 49.6 0.868 1 4.32320 0.38896 1.57104 3.81600 0.79500 50.0 0.868 1 4.32320 0.38896 1.57104 3.97500 0.79500 46.8 0.862 1 4.32320 0.38896 1.57104 4.13400 0.79500 44.6 0.853 1 3.88951 0.26964 2.31872 4.29300 0.79500 44.5 0.850 1 3.88951 0.26964 2.31872 4.45200 0.79500 50.9 0.862 1 3.88951 0.26964 2.31872 4.61100 0.79500 43.5 0.837 1 3.07599 0.44085 3.57996 4.77000 0.79500 52.8 0.873 1 3.07599 0.44085 3.57996 4.92900 0.79500 57.0 0.876 1 3.07599 0.44085 3.57996 5.08800 0.79500 55.6 0.875 1 3.07599 0.44085 3.57996 5.24700 0.79500 53.2 0.869 1 3.07599 0.44085 3.57996 5.40600 0.79500 49.6 0.864 1 3.07599 0.44085 3.57996 5.56500 0.79500 45.6 0.860 1 3.07599 0.44085 3.57996 5.72400 0.79500 40.9 0.852 1 1.64265 0.80097 3.95287 5.88300 0.79500 36.7 0.842 1 1.64265 0.80097 3.95287 6.04200 0.79500 46.2 0.872 1 1.64265 0.80097 3.95287 6.20100 0.79500 54.2 0.881 1 1.64265 0.80097 3.95287 6.36000 0.79500 55.3 0.883 1 1.64265 0.80097 3.95287 6.51900 0.79500 48.6 0.873 1 1.64265 0.80097 3.95287 6.67800 0.79500 48.0 0.853 1 1.64265 0.80097 3.95287 6.83700 0.79500 46.4 0.858 1 1.64265 0.80097 3.95287 6.99600 0.79500 47.2 0.862 1 1.64265 0.80097 3.95287 7.15500 0.79500 50.7 0.876 1 1.64265 0.80097 3.95287 7.31400 0.79500 56.7 0.883 1 1.64265 0.80097 3.95287 7.47300 0.79500 58.1 0.882 1 1.64265 0.80097 3.95287 7.63200 0.79500 59.1 0.886 1 1.64265 0.80097 3.95287 7.79100 0.79500 54.0 0.881 1 1.64265 0.80097 3.95287 7.95000 0.79500 47.0 0.866 1 0.72125 0.05436 4.88006 8.10900 0.79500 47.7 0.861 1 1.05209 0.05078 4.54895 8.26800 0.79500 49.9 0.873 1 0.72125 0.05436 4.88006 8.42700 0.79500 44.1 0.861 1 1.27079 0.71457 5.74983 8.58600 0.79500 36.6 0.840 1 1.27079 0.71457 5.74983 8.74500 0.79500 31.2 0.827 1 2.05669 0.31954 4.32161 8.90400 0.79500 38.6 0.850 1 2.05669 0.31954 4.32161 9.06300 0.79500 47.1 0.857 1 5.07193 0.76649 0.57283 9.22200 0.79500 47.5 0.857 1 5.07193 0.76649 0.57283 9.38100 0.79500 50.1 0.873 1 5.07193 0.76649 0.57283 9.54000 0.79500 50.3 0.875 1 5.07193 0.76649 0.57283 9.69900 0.79500 45.9 0.853 1 5.58293 0.21292 1.14725 9.85800 0.79500 51.0 0.870 1 5.58293 0.21292 1.14725 10.01700 0.79500 53.1 0.881 1 5.58293 0.21292 1.14725 10.17600 0.79500 56.6 0.885 1 5.58293 0.21292 1.14725 10.33500 0.79500 56.4 0.883 1 5.58293 0.21292 1.14725 10.49400 0.79500 56.9 0.884 1 5.58293 0.21292 1.14725 10.65300 0.79500 53.8 0.879 1 5.58293 0.21292 1.14725 10.81200 0.79500 50.3 0.869 1 5.58293 0.21292 1.14725 10.97100 0.79500 43.7 0.859 1 3.98334 0.50735 2.91653 11.13000 0.79500 39.2 0.836 1 3.98334 0.50735 2.91653 11.28900 0.79500 49.7 0.870 1 3.98334 0.50735 2.91653 11.44800 0.79500 54.7 0.875 1 3.98334 0.50735 2.91653 11.60700 0.79500 57.2 0.875 1 3.98334 0.50735 2.91653 11.76600 0.79500 56.4 0.874 1 3.98334 0.50735 2.91653 11.92500 0.79500 57.9 0.876 1 1.61763 0.39478 4.36605 0.00000 0.95400 55.5 0.881 1 1.58422 0.41803 4.43312 0.15900 0.95400 54.1 0.880 1 1.58422 0.41803 4.43312 0.31800 0.95400 46.0 0.865 1 2.10897 0.39460 4.51979 0.47700 0.95400 43.9 0.857 1 2.10897 0.39460 4.51979 0.63600 0.95400 48.5 0.875 1 2.06935 0.39189 4.55985 0.79500 0.95400 48.1 0.876 1 2.06935 0.39189 4.55985 0.95400 0.95400 43.8 0.866 1 2.06935 0.39189 4.55985 1.11300 0.95400 34.9 0.831 1 0.68179 0.79560 5.16067 1.27200 0.95400 37.1 0.830 1 0.68179 0.79560 5.16067 1.43100 0.95400 38.6 0.840 1 0.68179 0.79560 5.16067 1.59000 0.95400 35.6 0.837 1 1.58737 0.41359 4.68701 1.74900 0.95400 31.8 0.823 1 1.58737 0.41359 4.68701 1.90800 0.95400 40.1 0.861 1 1.58737 0.41359 4.68701 2.06700 0.95400 39.2 0.857 1 1.58737 0.41359 4.68701 2.22600 0.95400 32.6 0.825 1 2.68188 0.63360 2.86833 2.38500 0.95400 36.2 0.830 1 2.68188 0.63360 2.86833 2.54400 0.95400 40.2 0.843 1 2.93499 0.22944 2.70244 2.70300 0.95400 39.9 0.840 1 2.93499 0.22944 2.70244 2.86200 0.95400 37.3 0.838 1 2.93499 0.22944 2.70244 3.02100 0.95400 33.3 0.829 1 4.32320 0.38896 1.57104 3.18000 0.95400 39.5 0.853 1 4.32320 0.38896 1.57104 3.33900 0.95400 42.9 0.861 1 4.32320 0.38896 1.57104 3.49800 0.95400 46.3 0.864 1 4.32320 0.38896 1.57104 3.65700 0.95400 47.6 0.862 1 4.32320 0.38896 1.57104 3.81600 0.95400 45.5 0.859 1 4.32320 0.38896 1.57104 3.97500 0.95400 43.9 0.853 1 3.88951 0.26964 2.31872 4.13400 0.95400 44.0 0.843 1 3.88951 0.26964 2.31872 4.29300 0.95400 49.6 0.859 1 3.88951 0.26964 2.31872 4.45200 0.95400 53.1 0.863 1 3.98523 0.27654 2.25517 4.61100 0.95400 46.3 0.846 1 3.07599 0.44085 3.57996 4.77000 0.95400 50.8 0.870 1 3.07599 0.44085 3.57996 4.92900 0.95400 56.4 0.875 1 3.07599 0.44085 3.57996 5.08800 0.95400 56.2 0.872 1 3.07599 0.44085 3.57996 5.24700 0.95400 53.3 0.865 1 3.07599 0.44085 3.57996 5.40600 0.95400 45.0 0.851 1 3.07599 0.44085 3.57996 5.56500 0.95400 39.9 0.835 1 3.07599 0.44085 3.57996 5.72400 0.95400 35.0 0.825 1 1.64265 0.80097 3.95287 5.88300 0.95400 36.5 0.837 1 1.64265 0.80097 3.95287 6.04200 0.95400 47.6 0.859 1 1.64265 0.80097 3.95287 6.20100 0.95400 50.5 0.871 1 1.64265 0.80097 3.95287 6.36000 0.95400 56.0 0.879 1 1.64265 0.80097 3.95287 6.51900 0.95400 53.2 0.880 1 1.64265 0.80097 3.95287 6.67800 0.95400 53.2 0.879 1 1.64265 0.80097 3.95287 6.83700 0.95400 54.1 0.882 1 1.64265 0.80097 3.95287 6.99600 0.95400 54.7 0.883 1 1.64265 0.80097 3.95287 7.15500 0.95400 57.3 0.885 1 1.64265 0.80097 3.95287 7.31400 0.95400 58.6 0.885 1 1.64265 0.80097 3.95287 7.47300 0.95400 59.6 0.885 1 1.64265 0.80097 3.95287 7.63200 0.95400 60.4 0.885 1 1.64265 0.80097 3.95287 7.79100 0.95400 57.8 0.882 1 1.64265 0.80097 3.95287 7.95000 0.95400 51.4 0.875 1 1.64265 0.80097 3.95287 8.10900 0.95400 43.4 0.849 1 0.72125 0.05436 4.88006 8.26800 0.95400 44.1 0.859 1 0.72125 0.05436 4.88006 8.42700 0.95400 46.0 0.849 1 1.27079 0.71457 5.74983 8.58600 0.95400 43.8 0.870 1 1.27079 0.71457 5.74983 8.74500 0.95400 39.8 0.863 1 5.07193 0.76649 0.57283 8.90400 0.95400 40.7 0.851 1 5.07193 0.76649 0.57283 9.06300 0.95400 50.0 0.872 1 5.07193 0.76649 0.57283 9.22200 0.95400 53.0 0.879 1 5.07193 0.76649 0.57283 9.38100 0.95400 57.4 0.882 1 5.07193 0.76649 0.57283 9.54000 0.95400 56.6 0.881 1 5.07193 0.76649 0.57283 9.69900 0.95400 51.1 0.874 1 5.07193 0.76649 0.57283 9.85800 0.95400 48.5 0.849 1 5.58293 0.21292 1.14725 10.01700 0.95400 50.1 0.871 1 5.58293 0.21292 1.14725 10.17600 0.95400 53.1 0.880 1 5.58293 0.21292 1.14725 10.33500 0.95400 53.5 0.881 1 5.58293 0.21292 1.14725 10.49400 0.95400 53.9 0.882 1 5.58293 0.21292 1.14725 10.65300 0.95400 51.4 0.875 1 5.58293 0.21292 1.14725 10.81200 0.95400 46.6 0.855 1 3.49805 0.65667 2.77578 10.97100 0.95400 41.6 0.847 1 3.49805 0.65667 2.77578 11.13000 0.95400 36.2 0.830 1 3.98334 0.50735 2.91653 11.28900 0.95400 47.0 0.865 1 3.98334 0.50735 2.91653 11.44800 0.95400 54.7 0.876 1 3.98334 0.50735 2.91653 11.60700 0.95400 56.2 0.875 1 3.98334 0.50735 2.91653 11.76600 0.95400 54.5 0.875 1 3.98334 0.50735 2.91653 11.92500 0.95400 55.0 0.873 1 1.61763 0.39478 4.36605 0.00000 1.11300 53.3 0.877 1 1.61763 0.39478 4.36605 0.15900 1.11300 52.4 0.877 1 1.58422 0.41803 4.43312 0.31800 1.11300 47.6 0.873 1 1.58422 0.41803 4.43312 0.47700 1.11300 41.9 0.853 1 2.10897 0.39460 4.51979 0.63600 1.11300 42.1 0.852 1 2.10897 0.39460 4.51979 0.79500 1.11300 45.8 0.864 1 2.06935 0.39189 4.55985 0.95400 1.11300 38.5 0.849 1 1.15579 0.92185 5.56912 1.11300 1.11300 35.5 0.839 1 1.15579 0.92185 5.56912 1.27200 1.11300 37.2 0.847 1 1.15579 0.92185 5.56912 1.43100 1.11300 37.2 0.849 1 1.15579 0.92185 5.56912 1.59000 1.11300 36.6 0.845 1 1.38827 0.41128 4.85003 1.74900 1.11300 32.9 0.824 1 1.57752 0.41258 4.67515 1.90800 1.11300 34.5 0.831 1 1.58737 0.41359 4.68701 2.06700 1.11300 32.9 0.829 1 2.87009 0.81712 3.98364 2.22600 1.11300 31.4 0.840 1 2.87009 0.81712 3.98364 2.38500 1.11300 30.5 0.822 1 2.93499 0.22944 2.70244 2.54400 1.11300 39.4 0.857 1 2.93499 0.22944 2.70244 2.70300 1.11300 40.9 0.863 1 2.93499 0.22944 2.70244 2.86200 1.11300 39.9 0.866 1 2.93499 0.22944 2.70244 3.02100 1.11300 37.2 0.859 1 4.32320 0.38896 1.57104 3.18000 1.11300 33.3 0.828 1 4.32320 0.38896 1.57104 3.33900 1.11300 35.0 0.846 1 4.32320 0.38896 1.57104 3.49800 1.11300 39.6 0.846 1 4.32320 0.38896 1.57104 3.65700 1.11300 40.3 0.846 1 4.32320 0.38896 1.57104 3.81600 1.11300 39.4 0.841 1 4.32320 0.38896 1.57104 3.97500 1.11300 39.0 0.830 1 3.88951 0.26964 2.31872 4.13400 1.11300 47.3 0.856 1 3.88951 0.26964 2.31872 4.29300 1.11300 52.9 0.865 1 3.88951 0.26964 2.31872 4.45200 1.11300 54.7 0.862 1 3.88951 0.26964 2.31872 4.61100 1.11300 47.6 0.851 1 3.07599 0.44085 3.57996 4.77000 1.11300 48.4 0.862 1 3.07599 0.44085 3.57996 4.92900 1.11300 56.3 0.871 1 3.07599 0.44085 3.57996 5.08800 1.11300 54.8 0.873 1 3.07599 0.44085 3.57996 5.24700 1.11300 51.3 0.866 1 3.07599 0.44085 3.57996 5.40600 1.11300 43.4 0.847 1 5.65635 0.71202 6.25275 5.56500 1.11300 37.9 0.830 1 5.65635 0.71202 6.25275 5.72400 1.11300 34.4 0.844 1 5.65635 0.71202 6.25275 5.88300 1.11300 36.0 0.847 1 5.65635 0.71202 6.25275 6.04200 1.11300 43.7 0.848 1 1.64265 0.80097 3.95287 6.20100 1.11300 46.6 0.844 1 1.64265 0.80097 3.95287 6.36000 1.11300 51.9 0.872 1 1.64265 0.80097 3.95287 6.51900 1.11300 54.4 0.878 1 1.64265 0.80097 3.95287 6.67800 1.11300 58.0 0.882 1 1.64265 0.80097 3.95287 6.83700 1.11300 60.3 0.884 1 1.64265 0.80097 3.95287 6.99600 1.11300 60.5 0.886 1 1.64265 0.80097 3.95287 7.15500 1.11300 61.6 0.885 1 1.64265 0.80097 3.95287 7.31400 1.11300 62.2 0.885 1 1.64265 0.80097 3.95287 7.47300 1.11300 61.5 0.885 1 1.64265 0.80097 3.95287 7.63200 1.11300 60.5 0.882 1 1.64265 0.80097 3.95287 7.79100 1.11300 59.0 0.879 1 1.64265 0.80097 3.95287 7.95000 1.11300 54.1 0.875 1 1.64265 0.80097 3.95287 8.10900 1.11300 44.7 0.857 1 1.27079 0.71457 5.74983 8.26800 1.11300 40.1 0.840 1 1.27079 0.71457 5.74983 8.42700 1.11300 47.4 0.866 1 1.27079 0.71457 5.74983 8.58600 1.11300 51.5 0.883 1 1.27079 0.71457 5.74983 8.74500 1.11300 53.4 0.884 1 5.07193 0.76649 0.57283 8.90400 1.11300 42.8 0.853 1 5.07193 0.76649 0.57283 9.06300 1.11300 53.0 0.880 1 5.07193 0.76649 0.57283 9.22200 1.11300 58.9 0.885 1 5.07193 0.76649 0.57283 9.38100 1.11300 60.1 0.886 1 5.07193 0.76649 0.57283 9.54000 1.11300 61.0 0.885 1 5.07193 0.76649 0.57283 9.69900 1.11300 57.6 0.880 1 5.07193 0.76649 0.57283 9.85800 1.11300 50.9 0.868 1 5.07193 0.76649 0.57283 10.01700 1.11300 48.2 0.845 1 5.58293 0.21292 1.14725 10.17600 1.11300 50.9 0.869 1 5.58293 0.21292 1.14725 10.33500 1.11300 50.7 0.877 1 5.58293 0.21292 1.14725 10.49400 1.11300 52.2 0.876 1 5.58293 0.21292 1.14725 10.65300 1.11300 49.7 0.868 1 3.49805 0.65667 2.77578 10.81200 1.11300 46.4 0.849 1 3.49805 0.65667 2.77578 10.97100 1.11300 43.9 0.854 1 5.58293 0.21292 1.14725 11.13000 1.11300 36.6 0.828 1 3.98334 0.50735 2.91653 11.28900 1.11300 44.2 0.863 1 3.98334 0.50735 2.91653 11.44800 1.11300 53.2 0.872 1 3.98334 0.50735 2.91653 11.60700 1.11300 53.9 0.871 1 3.95808 0.52278 2.92888 11.76600 1.11300 53.3 0.873 1 3.98334 0.50735 2.91653 11.92500 1.11300 52.8 0.870 1 1.61763 0.39478 4.36605 0.00000 1.27200 49.1 0.870 1 1.61763 0.39478 4.36605 0.15900 1.27200 50.7 0.873 1 1.58422 0.41803 4.43312 0.31800 1.27200 47.8 0.873 1 1.58422 0.41803 4.43312 0.47700 1.27200 42.4 0.864 1 1.58422 0.41803 4.43312 0.63600 1.27200 37.1 0.838 1 2.10897 0.39460 4.51979 0.79500 1.27200 39.8 0.835 1 1.48594 0.78484 4.91650 0.95400 1.27200 36.0 0.830 1 1.15579 0.92185 5.56912 1.11300 1.27200 39.6 0.840 1 1.15579 0.92185 5.56912 1.27200 1.27200 38.2 0.841 1 1.15579 0.92185 5.56912 1.43100 1.27200 33.9 0.843 1 1.15579 0.92185 5.56912 1.59000 1.27200 34.0 0.842 1 1.38827 0.41128 4.85003 1.74900 1.27200 37.6 0.846 1 1.38827 0.41128 4.85003 1.90800 1.27200 35.8 0.844 1 2.81548 0.75216 4.16669 2.06700 1.27200 29.9 0.821 1 2.89117 0.81339 3.96803 2.22600 1.27200 34.3 0.825 1 2.93499 0.22944 2.70244 2.38500 1.27200 30.1 0.820 1 2.93499 0.22944 2.70244 2.54400 1.27200 40.6 0.858 1 2.93499 0.22944 2.70244 2.70300 1.27200 43.9 0.862 1 2.93499 0.22944 2.70244 2.86200 1.27200 43.7 0.863 1 2.93499 0.22944 2.70244 3.02100 1.27200 41.4 0.863 1 2.93499 0.22944 2.70244 3.18000 1.27200 32.4 0.843 1 1.12430 0.36383 5.83669 3.33900 1.27200 28.8 0.828 1 4.28746 0.60883 1.39533 3.49800 1.27200 33.9 0.826 1 4.28746 0.60883 1.39533 3.65700 1.27200 39.5 0.843 1 4.28746 0.60883 1.39533 3.81600 1.27200 40.9 0.846 1 4.28746 0.60883 1.39533 3.97500 1.27200 39.8 0.836 1 3.99287 0.27862 2.26454 4.13400 1.27200 45.9 0.854 1 3.88951 0.26964 2.31872 4.29300 1.27200 55.8 0.863 1 3.88951 0.26964 2.31872 4.45200 1.27200 54.6 0.865 1 3.88951 0.26964 2.31872 4.61100 1.27200 49.3 0.856 1 3.07599 0.44085 3.57996 4.77000 1.27200 47.1 0.851 1 3.07599 0.44085 3.57996 4.92900 1.27200 55.4 0.869 1 3.07599 0.44085 3.57996 5.08800 1.27200 53.9 0.867 1 3.07599 0.44085 3.57996 5.24700 1.27200 50.3 0.861 1 3.07599 0.44085 3.57996 5.40600 1.27200 44.5 0.852 1 5.65635 0.71202 6.25275 5.56500 1.27200 40.4 0.848 1 5.65635 0.71202 6.25275 5.72400 1.27200 44.5 0.866 1 5.65635 0.71202 6.25275 5.88300 1.27200 45.1 0.867 1 5.65635 0.71202 6.25275 6.04200 1.27200 50.0 0.868 1 5.65635 0.71202 6.25275 6.20100 1.27200 46.3 0.856 1 1.64265 0.80097 3.95287 6.36000 1.27200 48.2 0.850 1 1.64265 0.80097 3.95287 6.51900 1.27200 52.5 0.870 1 1.64265 0.80097 3.95287 6.67800 1.27200 55.7 0.878 1 1.64265 0.80097 3.95287 6.83700 1.27200 60.4 0.882 1 1.64265 0.80097 3.95287 6.99600 1.27200 61.7 0.881 1 1.64265 0.80097 3.95287 7.15500 1.27200 61.8 0.883 1 1.64265 0.80097 3.95287 7.31400 1.27200 63.3 0.884 1 1.64265 0.80097 3.95287 7.47300 1.27200 61.4 0.881 1 1.64265 0.80097 3.95287 7.63200 1.27200 57.9 0.877 1 1.64265 0.80097 3.95287 7.79100 1.27200 56.5 0.877 1 1.64265 0.80097 3.95287 7.95000 1.27200 52.9 0.870 1 1.64265 0.80097 3.95287 8.10900 1.27200 46.3 0.849 1 1.27079 0.71457 5.74983 8.26800 1.27200 45.5 0.862 1 1.27079 0.71457 5.74983 8.42700 1.27200 52.5 0.882 1 1.27079 0.71457 5.74983 8.58600 1.27200 57.3 0.888 1 1.27079 0.71457 5.74983 8.74500 1.27200 51.2 0.882 1 5.07193 0.76649 0.57283 8.90400 1.27200 47.8 0.855 1 5.07193 0.76649 0.57283 9.06300 1.27200 55.9 0.884 1 5.07193 0.76649 0.57283 9.22200 1.27200 60.6 0.886 1 5.07193 0.76649 0.57283 9.38100 1.27200 63.0 0.887 1 5.07193 0.76649 0.57283 9.54000 1.27200 60.5 0.886 1 5.07193 0.76649 0.57283 9.69900 1.27200 60.6 0.883 1 5.07193 0.76649 0.57283 9.85800 1.27200 57.5 0.879 1 5.07193 0.76649 0.57283 10.01700 1.27200 51.3 0.868 1 5.07193 0.76649 0.57283 10.17600 1.27200 46.5 0.845 1 5.58293 0.21292 1.14725 10.33500 1.27200 47.8 0.865 1 5.58293 0.21292 1.14725 10.49400 1.27200 48.6 0.864 1 5.58293 0.21292 1.14725 10.65300 1.27200 48.8 0.858 1 3.49805 0.65667 2.77578 10.81200 1.27200 46.2 0.848 1 5.58293 0.21292 1.14725 10.97100 1.27200 43.5 0.848 1 5.58293 0.21292 1.14725 11.13000 1.27200 36.7 0.834 1 3.98334 0.50735 2.91653 11.28900 1.27200 46.5 0.864 1 3.98334 0.50735 2.91653 11.44800 1.27200 51.6 0.869 1 3.95808 0.52278 2.92888 11.60700 1.27200 51.6 0.866 1 3.98334 0.50735 2.91653 11.76600 1.27200 49.8 0.863 1 3.95808 0.52278 2.92888 11.92500 1.27200 51.1 0.862 1 1.61763 0.39478 4.36605 0.00000 1.43100 44.2 0.860 1 1.61763 0.39478 4.36605 0.15900 1.43100 45.4 0.863 1 1.58422 0.41803 4.43312 0.31800 1.43100 46.2 0.868 1 1.58422 0.41803 4.43312 0.47700 1.43100 44.5 0.862 1 1.58422 0.41803 4.43312 0.63600 1.43100 36.2 0.838 1 1.48594 0.78484 4.91650 0.79500 1.43100 36.4 0.845 1 1.48594 0.78484 4.91650 0.95400 1.43100 41.3 0.858 1 1.48594 0.78484 4.91650 1.11300 1.43100 44.7 0.859 1 1.48594 0.78484 4.91650 1.27200 1.43100 38.0 0.847 1 1.47226 0.78203 4.94823 1.43100 1.43100 31.3 0.829 1 1.38827 0.41128 4.85003 1.59000 1.43100 31.0 0.828 1 1.38827 0.41128 4.85003 1.74900 1.43100 40.8 0.857 1 1.38827 0.41128 4.85003 1.90800 1.43100 38.2 0.847 1 2.81548 0.75216 4.16669 2.06700 1.43100 32.9 0.842 1 2.81548 0.75216 4.16669 2.22600 1.43100 35.7 0.852 1 2.81548 0.75216 4.16669 2.38500 1.43100 32.8 0.829 1 2.92303 0.41946 2.96341 2.54400 1.43100 38.9 0.836 1 2.93499 0.22944 2.70244 2.70300 1.43100 43.6 0.841 1 2.93499 0.22944 2.70244 2.86200 1.43100 44.4 0.846 1 2.93499 0.22944 2.70244 3.02100 1.43100 40.8 0.850 1 2.93499 0.22944 2.70244 3.18000 1.43100 31.9 0.833 1 1.12430 0.36383 5.83669 3.33900 1.43100 32.3 0.852 1 4.28746 0.60883 1.39533 3.49800 1.43100 33.5 0.828 1 4.28746 0.60883 1.39533 3.65700 1.43100 39.4 0.849 1 4.28746 0.60883 1.39533 3.81600 1.43100 42.3 0.854 1 4.28746 0.60883 1.39533 3.97500 1.43100 40.1 0.845 1 3.99287 0.27862 2.26454 4.13400 1.43100 43.8 0.847 1 3.99287 0.27862 2.26454 4.29300 1.43100 52.8 0.865 1 3.99287 0.27862 2.26454 4.45200 1.43100 57.4 0.866 1 3.88951 0.26964 2.31872 4.61100 1.43100 51.0 0.861 1 3.98523 0.27654 2.25517 4.77000 1.43100 44.3 0.840 1 3.07599 0.44085 3.57996 4.92900 1.43100 48.2 0.859 1 3.07599 0.44085 3.57996 5.08800 1.43100 50.2 0.863 1 3.07599 0.44085 3.57996 5.24700 1.43100 47.9 0.855 1 3.07599 0.44085 3.57996 5.40600 1.43100 45.7 0.844 1 5.65635 0.71202 6.25275 5.56500 1.43100 45.1 0.861 1 5.65635 0.71202 6.25275 5.72400 1.43100 51.0 0.873 1 5.65635 0.71202 6.25275 5.88300 1.43100 53.4 0.876 1 5.65635 0.71202 6.25275 6.04200 1.43100 54.2 0.876 1 5.65635 0.71202 6.25275 6.20100 1.43100 53.3 0.872 1 5.65635 0.71202 6.25275 6.36000 1.43100 48.4 0.855 1 5.65635 0.71202 6.25275 6.51900 1.43100 45.1 0.842 1 1.64212 0.77980 3.97340 6.67800 1.43100 46.7 0.844 1 1.64265 0.80097 3.95287 6.83700 1.43100 57.1 0.874 1 1.64265 0.80097 3.95287 6.99600 1.43100 60.0 0.880 1 1.64265 0.80097 3.95287 7.15500 1.43100 62.3 0.882 1 1.64265 0.80097 3.95287 7.31400 1.43100 61.6 0.882 1 1.64265 0.80097 3.95287 7.47300 1.43100 60.0 0.882 1 1.64265 0.80097 3.95287 7.63200 1.43100 57.2 0.878 1 1.64265 0.80097 3.95287 7.79100 1.43100 54.4 0.872 1 1.64265 0.80097 3.95287 7.95000 1.43100 50.7 0.860 1 1.27079 0.71457 5.74983 8.10900 1.43100 46.3 0.855 1 1.27079 0.71457 5.74983 8.26800 1.43100 51.6 0.877 1 1.27079 0.71457 5.74983 8.42700 1.43100 56.1 0.886 1 1.27079 0.71457 5.74983 8.58600 1.43100 58.5 0.890 1 1.27079 0.71457 5.74983 8.74500 1.43100 55.6 0.885 1 1.27079 0.71457 5.74983 8.90400 1.43100 48.6 0.848 1 5.07193 0.76649 0.57283 9.06300 1.43100 57.6 0.883 1 5.07193 0.76649 0.57283 9.22200 1.43100 61.1 0.886 1 5.07193 0.76649 0.57283 9.38100 1.43100 61.5 0.887 1 5.07193 0.76649 0.57283 9.54000 1.43100 61.2 0.887 1 5.07193 0.76649 0.57283 9.69900 1.43100 64.2 0.884 1 5.07193 0.76649 0.57283 9.85800 1.43100 58.9 0.882 1 5.07193 0.76649 0.57283 10.01700 1.43100 57.1 0.876 1 5.07193 0.76649 0.57283 10.17600 1.43100 49.6 0.865 1 5.07193 0.76649 0.57283 10.33500 1.43100 42.4 0.837 1 3.49805 0.65667 2.77578 10.49400 1.43100 43.8 0.850 1 3.49805 0.65667 2.77578 10.65300 1.43100 46.5 0.866 1 3.49805 0.65667 2.77578 10.81200 1.43100 46.0 0.866 1 3.49805 0.65667 2.77578 10.97100 1.43100 44.8 0.850 1 5.58293 0.21292 1.14725 11.13000 1.43100 33.4 0.831 1 3.95808 0.52278 2.92888 11.28900 1.43100 40.1 0.848 1 3.98334 0.50735 2.91653 11.44800 1.43100 46.5 0.855 1 3.95808 0.52278 2.92888 11.60700 1.43100 46.5 0.852 1 4.52565 0.71646 2.27301 11.76600 1.43100 45.0 0.851 1 4.54991 0.71331 2.25320 11.92500 1.43100 47.0 0.856 1 0.44612 0.66973 6.08110 0.00000 1.59000 38.2 0.845 1 0.44612 0.66973 6.08110 0.15900 1.59000 40.8 0.840 1 1.58422 0.41803 4.43312 0.31800 1.59000 39.4 0.856 1 1.58422 0.41803 4.43312 0.47700 1.59000 38.0 0.844 1 1.48594 0.78484 4.91650 0.63600 1.59000 39.4 0.848 1 1.48594 0.78484 4.91650 0.79500 1.59000 45.7 0.869 1 1.48594 0.78484 4.91650 0.95400 1.59000 51.1 0.873 1 1.47226 0.78203 4.94823 1.11300 1.59000 51.7 0.875 1 1.47226 0.78203 4.94823 1.27200 1.59000 49.3 0.872 1 1.47226 0.78203 4.94823 1.43100 1.59000 41.0 0.863 1 1.47226 0.78203 4.94823 1.59000 1.59000 33.0 0.831 1 1.38827 0.41128 4.85003 1.74900 1.59000 40.0 0.844 1 2.77813 0.42500 4.07972 1.90800 1.59000 37.1 0.829 1 2.81548 0.75216 4.16669 2.06700 1.59000 36.3 0.843 1 2.81548 0.75216 4.16669 2.22600 1.59000 38.1 0.857 1 2.92303 0.41946 2.96341 2.38500 1.59000 35.1 0.834 1 2.92303 0.41946 2.96341 2.54400 1.59000 43.4 0.861 1 2.92303 0.41946 2.96341 2.70300 1.59000 47.4 0.864 1 2.92303 0.41946 2.96341 2.86200 1.59000 46.9 0.860 1 2.92303 0.41946 2.96341 3.02100 1.59000 43.3 0.851 1 1.12430 0.36383 5.83669 3.18000 1.59000 33.7 0.826 1 1.12430 0.36383 5.83669 3.33900 1.59000 34.7 0.856 1 1.12430 0.36383 5.83669 3.49800 1.59000 32.4 0.832 1 4.28746 0.60883 1.39533 3.65700 1.59000 34.7 0.837 1 4.48140 0.64548 2.27141 3.81600 1.59000 39.3 0.834 1 4.48140 0.64548 2.27141 3.97500 1.59000 38.1 0.831 1 3.99287 0.27862 2.26454 4.13400 1.59000 40.7 0.846 1 3.99287 0.27862 2.26454 4.29300 1.59000 52.7 0.865 1 3.99287 0.27862 2.26454 4.45200 1.59000 56.8 0.869 1 3.99287 0.27862 2.26454 4.61100 1.59000 53.5 0.864 1 3.98523 0.27654 2.25517 4.77000 1.59000 46.7 0.852 1 3.07599 0.44085 3.57996 4.92900 1.59000 43.3 0.846 1 3.07599 0.44085 3.57996 5.08800 1.59000 46.4 0.856 1 5.65635 0.71202 6.25275 5.24700 1.59000 43.0 0.840 1 5.65635 0.71202 6.25275 5.40600 1.59000 45.0 0.864 1 5.65635 0.71202 6.25275 5.56500 1.59000 52.4 0.873 1 5.65635 0.71202 6.25275 5.72400 1.59000 56.2 0.878 1 5.65635 0.71202 6.25275 5.88300 1.59000 59.1 0.881 1 5.65635 0.71202 6.25275 6.04200 1.59000 57.9 0.879 1 5.65635 0.71202 6.25275 6.20100 1.59000 58.4 0.879 1 5.65635 0.71202 6.25275 6.36000 1.59000 56.7 0.875 1 5.65635 0.71202 6.25275 6.51900 1.59000 47.6 0.855 1 1.64212 0.77980 3.97340 6.67800 1.59000 46.9 0.847 1 1.64265 0.80097 3.95287 6.83700 1.59000 55.4 0.871 1 1.64265 0.80097 3.95287 6.99600 1.59000 59.5 0.878 1 1.64265 0.80097 3.95287 7.15500 1.59000 61.6 0.880 1 1.64265 0.80097 3.95287 7.31400 1.59000 61.4 0.880 1 1.64265 0.80097 3.95287 7.47300 1.59000 60.2 0.879 1 1.64265 0.80097 3.95287 7.63200 1.59000 56.6 0.876 1 1.64265 0.80097 3.95287 7.79100 1.59000 52.9 0.868 1 1.64265 0.80097 3.95287 7.95000 1.59000 47.5 0.848 1 1.27079 0.71457 5.74983 8.10900 1.59000 50.6 0.869 1 1.27079 0.71457 5.74983 8.26800 1.59000 56.8 0.883 1 1.27079 0.71457 5.74983 8.42700 1.59000 59.7 0.886 1 1.27079 0.71457 5.74983 8.58600 1.59000 60.9 0.889 1 1.27079 0.71457 5.74983 8.74500 1.59000 58.1 0.888 1 1.27079 0.71457 5.74983 8.90400 1.59000 50.6 0.858 1 5.07193 0.76649 0.57283 9.06300 1.59000 53.8 0.877 1 5.07193 0.76649 0.57283 9.22200 1.59000 58.1 0.884 1 5.07193 0.76649 0.57283 9.38100 1.59000 62.6 0.886 1 5.07193 0.76649 0.57283 9.54000 1.59000 63.3 0.888 1 5.07193 0.76649 0.57283 9.69900 1.59000 63.4 0.885 1 5.07193 0.76649 0.57283 9.85800 1.59000 61.6 0.885 1 5.07193 0.76649 0.57283 10.01700 1.59000 59.1 0.879 1 5.07193 0.76649 0.57283 10.17600 1.59000 54.2 0.873 1 5.07193 0.76649 0.57283 10.33500 1.59000 44.2 0.852 1 3.49805 0.65667 2.77578 10.49400 1.59000 46.1 0.875 1 3.49805 0.65667 2.77578 10.65300 1.59000 52.2 0.885 1 3.49805 0.65667 2.77578 10.81200 1.59000 51.7 0.883 1 3.49805 0.65667 2.77578 10.97100 1.59000 48.1 0.876 1 3.49805 0.65667 2.77578 11.13000 1.59000 39.5 0.858 1 4.54991 0.71331 2.25320 11.28900 1.59000 35.6 0.839 1 4.54991 0.71331 2.25320 11.44800 1.59000 44.7 0.866 1 4.54991 0.71331 2.25320 11.60700 1.59000 48.6 0.872 1 4.54991 0.71331 2.25320 11.76600 1.59000 49.9 0.880 1 4.54991 0.71331 2.25320 11.92500 1.59000 50.6 0.880 1 0.44612 0.66973 6.08110 0.00000 1.74900 41.8 0.862 1 0.44612 0.66973 6.08110 0.15900 1.74900 39.1 0.858 1 0.44612 0.66973 6.08110 0.31800 1.74900 33.8 0.832 1 0.45933 0.41889 0.25191 0.47700 1.74900 36.1 0.833 1 1.47226 0.78203 4.94823 0.63600 1.74900 41.0 0.856 1 1.48594 0.78484 4.91650 0.79500 1.74900 52.5 0.875 1 1.47226 0.78203 4.94823 0.95400 1.74900 57.5 0.878 1 1.47226 0.78203 4.94823 1.11300 1.74900 57.7 0.879 1 1.47226 0.78203 4.94823 1.27200 1.74900 56.9 0.879 1 1.47226 0.78203 4.94823 1.43100 1.74900 54.5 0.881 1 1.47226 0.78203 4.94823 1.59000 1.74900 43.6 0.865 1 2.79951 0.44040 4.04675 1.74900 1.74900 39.1 0.840 1 2.79951 0.44040 4.04675 1.90800 1.74900 43.6 0.863 1 2.77813 0.42500 4.07972 2.06700 1.74900 44.1 0.857 1 2.77813 0.42500 4.07972 2.22600 1.74900 37.4 0.833 1 2.92303 0.41946 2.96341 2.38500 1.74900 37.7 0.840 1 2.92303 0.41946 2.96341 2.54400 1.74900 47.4 0.868 1 2.92303 0.41946 2.96341 2.70300 1.74900 51.2 0.873 1 2.92303 0.41946 2.96341 2.86200 1.74900 51.3 0.872 1 2.92303 0.41946 2.96341 3.02100 1.74900 46.0 0.866 1 2.92303 0.41946 2.96341 3.18000 1.74900 36.5 0.841 1 1.34131 0.61640 5.24311 3.33900 1.74900 35.2 0.850 1 1.34131 0.61640 5.24311 3.49800 1.74900 33.6 0.851 1 1.34131 0.61640 5.24311 3.65700 1.74900 34.2 0.822 1 4.48140 0.64548 2.27141 3.81600 1.74900 41.2 0.852 1 4.48140 0.64548 2.27141 3.97500 1.74900 40.1 0.851 1 3.99287 0.27862 2.26454 4.13400 1.74900 37.8 0.837 1 3.99287 0.27862 2.26454 4.29300 1.74900 50.8 0.864 1 3.99287 0.27862 2.26454 4.45200 1.74900 53.4 0.867 1 3.99287 0.27862 2.26454 4.61100 1.74900 54.4 0.865 1 3.98523 0.27654 2.25517 4.77000 1.74900 49.6 0.859 1 3.07599 0.44085 3.57996 4.92900 1.74900 41.3 0.837 1 3.07599 0.44085 3.57996 5.08800 1.74900 42.2 0.844 1 5.65635 0.71202 6.25275 5.24700 1.74900 43.8 0.861 1 5.65635 0.71202 6.25275 5.40600 1.74900 52.6 0.877 1 5.65635 0.71202 6.25275 5.56500 1.74900 57.1 0.881 1 5.65635 0.71202 6.25275 5.72400 1.74900 58.9 0.880 1 5.65635 0.71202 6.25275 5.88300 1.74900 59.8 0.880 1 5.65635 0.71202 6.25275 6.04200 1.74900 60.5 0.879 1 5.65635 0.71202 6.25275 6.20100 1.74900 60.6 0.878 1 5.65635 0.71202 6.25275 6.36000 1.74900 60.0 0.877 1 5.65635 0.71202 6.25275 6.51900 1.74900 56.4 0.872 1 5.65635 0.71202 6.25275 6.67800 1.74900 50.4 0.866 1 1.64212 0.77980 3.97340 6.83700 1.74900 46.3 0.848 1 1.64212 0.77980 3.97340 6.99600 1.74900 57.4 0.872 1 1.64212 0.77980 3.97340 7.15500 1.74900 60.4 0.873 1 1.64212 0.77980 3.97340 7.31400 1.74900 59.4 0.877 1 1.64265 0.80097 3.95287 7.47300 1.74900 59.6 0.877 1 1.64265 0.80097 3.95287 7.63200 1.74900 53.9 0.872 1 1.64212 0.77980 3.97340 7.79100 1.74900 50.7 0.854 1 1.27079 0.71457 5.74983 7.95000 1.74900 51.1 0.861 1 1.27079 0.71457 5.74983 8.10900 1.74900 54.3 0.881 1 1.27079 0.71457 5.74983 8.26800 1.74900 58.5 0.886 1 1.27079 0.71457 5.74983 8.42700 1.74900 59.8 0.884 1 1.27079 0.71457 5.74983 8.58600 1.74900 61.1 0.889 1 1.27079 0.71457 5.74983 8.74500 1.74900 59.0 0.889 1 1.27079 0.71457 5.74983 8.90400 1.74900 52.8 0.876 1 5.07193 0.76649 0.57283 9.06300 1.74900 50.5 0.862 1 5.07193 0.76649 0.57283 9.22200 1.74900 56.7 0.881 1 5.07193 0.76649 0.57283 9.38100 1.74900 61.6 0.884 1 5.07193 0.76649 0.57283 9.54000 1.74900 61.1 0.884 1 5.07193 0.76649 0.57283 9.69900 1.74900 61.4 0.885 1 5.07193 0.76649 0.57283 9.85800 1.74900 62.7 0.884 1 5.07193 0.76649 0.57283 10.01700 1.74900 62.1 0.883 1 5.07193 0.76649 0.57283 10.17600 1.74900 57.7 0.876 1 5.07193 0.76649 0.57283 10.33500 1.74900 46.8 0.859 1 3.49805 0.65667 2.77578 10.49400 1.74900 49.7 0.876 1 3.49805 0.65667 2.77578 10.65300 1.74900 53.6 0.886 1 3.49805 0.65667 2.77578 10.81200 1.74900 53.3 0.885 1 3.49805 0.65667 2.77578 10.97100 1.74900 53.1 0.885 1 3.49805 0.65667 2.77578 11.13000 1.74900 47.2 0.876 1 4.54991 0.71331 2.25320 11.28900 1.74900 39.5 0.840 1 4.54991 0.71331 2.25320 11.44800 1.74900 49.1 0.882 1 4.54991 0.71331 2.25320 11.60700 1.74900 53.0 0.885 1 4.54991 0.71331 2.25320 11.76600 1.74900 54.6 0.885 1 4.54991 0.71331 2.25320 11.92500 1.74900 55.0 0.886 1 0.44612 0.66973 6.08110 0.00000 1.90800 44.3 0.865 1 0.44612 0.66973 6.08110 0.15900 1.90800 41.8 0.856 1 5.34240 0.40884 1.56023 0.31800 1.90800 35.4 0.832 1 0.41816 0.41808 0.29354 0.47700 1.90800 34.8 0.825 1 1.48594 0.78484 4.91650 0.63600 1.90800 46.9 0.865 1 1.48594 0.78484 4.91650 0.79500 1.90800 55.5 0.877 1 1.47226 0.78203 4.94823 0.95400 1.90800 58.2 0.879 1 1.47226 0.78203 4.94823 1.11300 1.90800 59.5 0.881 1 1.47226 0.78203 4.94823 1.27200 1.90800 58.5 0.881 1 1.47226 0.78203 4.94823 1.43100 1.90800 49.2 0.871 1 1.47226 0.78203 4.94823 1.59000 1.90800 43.2 0.848 1 2.79951 0.44040 4.04675 1.74900 1.90800 47.6 0.867 1 2.79951 0.44040 4.04675 1.90800 1.90800 51.0 0.875 1 2.79951 0.44040 4.04675 2.06700 1.90800 50.6 0.873 1 2.77813 0.42500 4.07972 2.22600 1.90800 43.3 0.863 1 2.77813 0.42500 4.07972 2.38500 1.90800 41.0 0.845 1 2.92303 0.41946 2.96341 2.54400 1.90800 47.2 0.862 1 2.92303 0.41946 2.96341 2.70300 1.90800 53.5 0.873 1 2.92303 0.41946 2.96341 2.86200 1.90800 54.1 0.873 1 2.92303 0.41946 2.96341 3.02100 1.90800 51.7 0.869 1 2.92303 0.41946 2.96341 3.18000 1.90800 39.7 0.843 1 1.34131 0.61640 5.24311 3.33900 1.90800 41.3 0.866 1 1.34131 0.61640 5.24311 3.49800 1.90800 36.8 0.863 1 1.34131 0.61640 5.24311 3.65700 1.90800 35.6 0.838 1 4.48140 0.64548 2.27141 3.81600 1.90800 41.6 0.844 1 4.48140 0.64548 2.27141 3.97500 1.90800 42.5 0.853 1 3.99287 0.27862 2.26454 4.13400 1.90800 39.3 0.830 1 3.99287 0.27862 2.26454 4.29300 1.90800 49.9 0.860 1 3.99287 0.27862 2.26454 4.45200 1.90800 52.3 0.867 1 3.99287 0.27862 2.26454 4.61100 1.90800 54.3 0.868 1 3.98523 0.27654 2.25517 4.77000 1.90800 49.2 0.860 1 3.98523 0.27654 2.25517 4.92900 1.90800 39.7 0.833 1 5.65635 0.71202 6.25275 5.08800 1.90800 41.8 0.841 1 5.65635 0.71202 6.25275 5.24700 1.90800 47.0 0.871 1 5.65635 0.71202 6.25275 5.40600 1.90800 56.2 0.880 1 5.65635 0.71202 6.25275 5.56500 1.90800 57.8 0.881 1 5.65635 0.71202 6.25275 5.72400 1.90800 59.3 0.879 1 5.65635 0.71202 6.25275 5.88300 1.90800 61.7 0.881 1 5.65635 0.71202 6.25275 6.04200 1.90800 60.5 0.881 1 5.65635 0.71202 6.25275 6.20100 1.90800 61.6 0.876 1 5.65635 0.71202 6.25275 6.36000 1.90800 61.2 0.876 1 5.65635 0.71202 6.25275 6.51900 1.90800 59.1 0.877 1 5.65635 0.71202 6.25275 6.67800 1.90800 54.0 0.870 1 5.65635 0.71202 6.25275 6.83700 1.90800 46.9 0.841 1 1.64212 0.77980 3.97340 6.99600 1.90800 53.8 0.866 1 1.64212 0.77980 3.97340 7.15500 1.90800 56.6 0.871 1 1.64212 0.77980 3.97340 7.31400 1.90800 57.8 0.872 1 1.64212 0.77980 3.97340 7.47300 1.90800 57.6 0.874 1 1.64265 0.80097 3.95287 7.63200 1.90800 52.5 0.865 1 1.27079 0.71457 5.74983 7.79100 1.90800 50.0 0.852 1 1.27079 0.71457 5.74983 7.95000 1.90800 53.1 0.878 1 1.27079 0.71457 5.74983 8.10900 1.90800 55.2 0.885 1 1.27079 0.71457 5.74983 8.26800 1.90800 58.2 0.886 1 1.27079 0.71457 5.74983 8.42700 1.90800 58.4 0.884 1 1.27079 0.71457 5.74983 8.58600 1.90800 61.8 0.886 1 1.27079 0.71457 5.74983 8.74500 1.90800 60.6 0.890 1 1.27079 0.71457 5.74983 8.90400 1.90800 57.4 0.886 1 1.27079 0.71457 5.74983 9.06300 1.90800 50.2 0.856 1 5.07193 0.76649 0.57283 9.22200 1.90800 52.7 0.872 1 5.07193 0.76649 0.57283 9.38100 1.90800 56.2 0.880 1 5.07193 0.76649 0.57283 9.54000 1.90800 60.6 0.884 1 5.07193 0.76649 0.57283 9.69900 1.90800 61.3 0.884 1 5.07193 0.76649 0.57283 9.85800 1.90800 61.8 0.883 1 5.07193 0.76649 0.57283 10.01700 1.90800 61.2 0.882 1 5.07193 0.76649 0.57283 10.17600 1.90800 59.0 0.879 1 5.07193 0.76649 0.57283 10.33500 1.90800 53.8 0.869 1 3.49805 0.65667 2.77578 10.49400 1.90800 48.0 0.855 1 3.49805 0.65667 2.77578 10.65300 1.90800 53.3 0.882 1 3.49805 0.65667 2.77578 10.81200 1.90800 55.3 0.886 1 3.49805 0.65667 2.77578 10.97100 1.90800 56.3 0.884 1 3.49805 0.65667 2.77578 11.13000 1.90800 52.8 0.883 1 3.49805 0.65667 2.77578 11.28900 1.90800 43.2 0.858 1 4.54991 0.71331 2.25320 11.44800 1.90800 49.2 0.876 1 4.54991 0.71331 2.25320 11.60700 1.90800 53.9 0.884 1 4.54991 0.71331 2.25320 11.76600 1.90800 56.2 0.886 1 4.54991 0.71331 2.25320 11.92500 1.90800 55.5 0.885 1 0.44612 0.66973 6.08110 0.00000 2.06700 44.3 0.857 1 5.34240 0.40884 1.56023 0.15900 2.06700 42.1 0.847 1 5.34240 0.40884 1.56023 0.31800 2.06700 38.9 0.861 1 5.34240 0.40884 1.56023 0.47700 2.06700 39.1 0.853 1 1.47226 0.78203 4.94823 0.63600 2.06700 46.0 0.859 1 1.48594 0.78484 4.91650 0.79500 2.06700 55.0 0.875 1 1.47226 0.78203 4.94823 0.95400 2.06700 56.5 0.878 1 1.47226 0.78203 4.94823 1.11300 2.06700 57.2 0.879 1 1.47226 0.78203 4.94823 1.27200 2.06700 56.7 0.880 1 1.47226 0.78203 4.94823 1.43100 2.06700 52.6 0.873 1 2.79951 0.44040 4.04675 1.59000 2.06700 45.9 0.850 1 2.79951 0.44040 4.04675 1.74900 2.06700 53.1 0.877 1 2.79951 0.44040 4.04675 1.90800 2.06700 56.2 0.880 1 2.79951 0.44040 4.04675 2.06700 2.06700 56.0 0.878 1 2.77813 0.42500 4.07972 2.22600 2.06700 52.4 0.873 1 2.77813 0.42500 4.07972 2.38500 2.06700 48.7 0.869 1 2.77813 0.42500 4.07972 2.54400 2.06700 45.5 0.850 1 2.92303 0.41946 2.96341 2.70300 2.06700 48.8 0.861 1 2.92303 0.41946 2.96341 2.86200 2.06700 54.5 0.870 1 2.92303 0.41946 2.96341 3.02100 2.06700 50.9 0.870 1 2.92303 0.41946 2.96341 3.18000 2.06700 41.6 0.846 1 1.34131 0.61640 5.24311 3.33900 2.06700 38.7 0.861 1 1.34131 0.61640 5.24311 3.49800 2.06700 39.4 0.855 1 3.86364 0.57476 2.44602 3.65700 2.06700 36.4 0.840 1 3.86364 0.57476 2.44602 3.81600 2.06700 38.8 0.835 1 4.48140 0.64548 2.27141 3.97500 2.06700 42.7 0.835 1 3.86364 0.57476 2.44602 4.13400 2.06700 36.6 0.841 1 3.99287 0.27862 2.26454 4.29300 2.06700 44.8 0.849 1 3.99287 0.27862 2.26454 4.45200 2.06700 51.0 0.862 1 3.99287 0.27862 2.26454 4.61100 2.06700 52.9 0.867 1 3.99287 0.27862 2.26454 4.77000 2.06700 47.9 0.861 1 3.98523 0.27654 2.25517 4.92900 2.06700 37.9 0.836 1 5.65635 0.71202 6.25275 5.08800 2.06700 40.2 0.853 1 5.65635 0.71202 6.25275 5.24700 2.06700 53.5 0.878 1 5.65635 0.71202 6.25275 5.40600 2.06700 56.8 0.881 1 5.65635 0.71202 6.25275 5.56500 2.06700 58.6 0.879 1 5.65635 0.71202 6.25275 5.72400 2.06700 57.8 0.879 1 5.65635 0.71202 6.25275 5.88300 2.06700 58.4 0.878 1 5.65635 0.71202 6.25275 6.04200 2.06700 60.0 0.880 1 5.65635 0.71202 6.25275 6.20100 2.06700 59.9 0.877 1 5.65635 0.71202 6.25275 6.36000 2.06700 58.3 0.878 1 5.65635 0.71202 6.25275 6.51900 2.06700 60.7 0.878 1 5.65635 0.71202 6.25275 6.67800 2.06700 58.7 0.875 1 5.65635 0.71202 6.25275 6.83700 2.06700 55.1 0.872 1 1.64212 0.77980 3.97340 6.99600 2.06700 49.4 0.854 1 1.64212 0.77980 3.97340 7.15500 2.06700 54.9 0.867 1 1.64212 0.77980 3.97340 7.31400 2.06700 54.9 0.869 1 1.64212 0.77980 3.97340 7.47300 2.06700 55.2 0.870 1 1.64212 0.77980 3.97340 7.63200 2.06700 48.4 0.856 1 1.27079 0.71457 5.74983 7.79100 2.06700 49.4 0.867 1 1.27079 0.71457 5.74983 7.95000 2.06700 56.1 0.883 1 1.27079 0.71457 5.74983 8.10900 2.06700 59.4 0.889 1 1.27079 0.71457 5.74983 8.26800 2.06700 59.9 0.886 1 1.27079 0.71457 5.74983 8.42700 2.06700 60.5 0.885 1 1.27079 0.71457 5.74983 8.58600 2.06700 60.7 0.885 1 1.27079 0.71457 5.74983 8.74500 2.06700 61.8 0.888 1 1.27079 0.71457 5.74983 8.90400 2.06700 61.0 0.892 1 1.27079 0.71457 5.74983 9.06300 2.06700 54.1 0.879 1 1.27079 0.71457 5.74983 9.22200 2.06700 49.2 0.847 1 5.07193 0.76649 0.57283 9.38100 2.06700 52.6 0.872 1 5.07193 0.76649 0.57283 9.54000 2.06700 59.4 0.882 1 5.07193 0.76649 0.57283 9.69900 2.06700 61.1 0.882 1 5.07193 0.76649 0.57283 9.85800 2.06700 62.3 0.884 1 5.07193 0.76649 0.57283 10.01700 2.06700 60.8 0.884 1 5.07193 0.76649 0.57283 10.17600 2.06700 60.8 0.880 1 5.07193 0.76649 0.57283 10.33500 2.06700 55.5 0.875 1 5.07193 0.76649 0.57283 10.49400 2.06700 48.8 0.853 1 3.49805 0.65667 2.77578 10.65300 2.06700 49.9 0.873 1 3.49805 0.65667 2.77578 10.81200 2.06700 54.7 0.884 1 3.49805 0.65667 2.77578 10.97100 2.06700 55.1 0.885 1 3.49805 0.65667 2.77578 11.13000 2.06700 54.2 0.884 1 3.49805 0.65667 2.77578 11.28900 2.06700 47.7 0.871 1 4.54991 0.71331 2.25320 11.44800 2.06700 45.8 0.860 1 4.54991 0.71331 2.25320 11.60700 2.06700 54.5 0.882 1 4.54991 0.71331 2.25320 11.76600 2.06700 54.9 0.883 1 4.54991 0.71331 2.25320 11.92500 2.06700 56.4 0.883 1 5.34240 0.40884 1.56023 0.00000 2.22600 45.0 0.856 1 5.34240 0.40884 1.56023 0.15900 2.22600 47.7 0.876 1 5.34240 0.40884 1.56023 0.31800 2.22600 48.7 0.875 1 5.34240 0.40884 1.56023 0.47700 2.22600 46.2 0.870 1 5.34240 0.40884 1.56023 0.63600 2.22600 44.5 0.841 1 1.47226 0.78203 4.94823 0.79500 2.22600 53.5 0.872 1 1.47226 0.78203 4.94823 0.95400 2.22600 57.7 0.876 1 1.47226 0.78203 4.94823 1.11300 2.22600 58.0 0.878 1 1.47226 0.78203 4.94823 1.27200 2.22600 56.2 0.877 1 1.47226 0.78203 4.94823 1.43100 2.22600 51.6 0.873 1 2.79951 0.44040 4.04675 1.59000 2.22600 45.1 0.849 1 2.79951 0.44040 4.04675 1.74900 2.22600 54.0 0.881 1 2.79951 0.44040 4.04675 1.90800 2.22600 58.0 0.882 1 2.79951 0.44040 4.04675 2.06700 2.22600 57.8 0.882 1 2.79951 0.44040 4.04675 2.22600 2.22600 57.2 0.880 1 2.77813 0.42500 4.07972 2.38500 2.22600 55.9 0.876 1 2.77813 0.42500 4.07972 2.54400 2.22600 50.0 0.868 1 2.92303 0.41946 2.96341 2.70300 2.22600 43.5 0.845 1 2.92303 0.41946 2.96341 2.86200 2.22600 53.6 0.870 1 2.92303 0.41946 2.96341 3.02100 2.22600 50.7 0.868 1 2.92303 0.41946 2.96341 3.18000 2.22600 40.9 0.848 1 1.34131 0.61640 5.24311 3.33900 2.22600 37.2 0.852 1 3.86364 0.57476 2.44602 3.49800 2.22600 41.4 0.844 1 3.86364 0.57476 2.44602 3.65700 2.22600 41.9 0.864 1 3.86364 0.57476 2.44602 3.81600 2.22600 42.1 0.865 1 3.86364 0.57476 2.44602 3.97500 2.22600 43.9 0.865 1 3.86364 0.57476 2.44602 4.13400 2.22600 44.1 0.870 1 3.86364 0.57476 2.44602 4.29300 2.22600 45.2 0.854 1 3.99287 0.27862 2.26454 4.45200 2.22600 46.6 0.854 1 3.99287 0.27862 2.26454 4.61100 2.22600 48.9 0.864 1 3.99287 0.27862 2.26454 4.77000 2.22600 45.7 0.862 1 3.98523 0.27654 2.25517 4.92900 2.22600 38.1 0.837 1 5.65635 0.71202 6.25275 5.08800 2.22600 42.7 0.860 1 5.65635 0.71202 6.25275 5.24700 2.22600 53.3 0.878 1 5.65635 0.71202 6.25275 5.40600 2.22600 56.3 0.880 1 5.65635 0.71202 6.25275 5.56500 2.22600 56.2 0.879 1 5.65635 0.71202 6.25275 5.72400 2.22600 59.0 0.879 1 5.65635 0.71202 6.25275 5.88300 2.22600 58.2 0.879 1 5.65635 0.71202 6.25275 6.04200 2.22600 58.4 0.879 1 5.65635 0.71202 6.25275 6.20100 2.22600 59.4 0.876 1 5.65635 0.71202 6.25275 6.36000 2.22600 61.0 0.877 1 5.65635 0.71202 6.25275 6.51900 2.22600 60.2 0.877 1 5.65635 0.71202 6.25275 6.67800 2.22600 58.4 0.878 1 5.65635 0.71202 6.25275 6.83700 2.22600 54.3 0.868 1 5.65635 0.71202 6.25275 6.99600 2.22600 47.0 0.842 1 1.64212 0.77980 3.97340 7.15500 2.22600 50.6 0.859 1 1.64212 0.77980 3.97340 7.31400 2.22600 51.9 0.865 1 1.64212 0.77980 3.97340 7.47300 2.22600 51.9 0.864 1 1.64483 0.79398 3.98790 7.63200 2.22600 47.3 0.851 1 1.27079 0.71457 5.74983 7.79100 2.22600 50.8 0.870 1 1.27079 0.71457 5.74983 7.95000 2.22600 58.0 0.885 1 1.27079 0.71457 5.74983 8.10900 2.22600 61.7 0.888 1 1.27079 0.71457 5.74983 8.26800 2.22600 60.0 0.887 1 1.27079 0.71457 5.74983 8.42700 2.22600 59.5 0.886 1 1.27079 0.71457 5.74983 8.58600 2.22600 61.0 0.886 1 1.27079 0.71457 5.74983 8.74500 2.22600 61.2 0.887 1 1.27079 0.71457 5.74983 8.90400 2.22600 62.0 0.888 1 1.27079 0.71457 5.74983 9.06300 2.22600 56.6 0.888 1 1.27079 0.71457 5.74983 9.22200 2.22600 53.0 0.877 1 5.07193 0.76649 0.57283 9.38100 2.22600 50.2 0.851 1 5.07193 0.76649 0.57283 9.54000 2.22600 55.9 0.878 1 5.07193 0.76649 0.57283 9.69900 2.22600 59.7 0.883 1 5.07193 0.76649 0.57283 9.85800 2.22600 59.8 0.882 1 5.07193 0.76649 0.57283 10.01700 2.22600 62.3 0.880 1 5.07193 0.76649 0.57283 10.17600 2.22600 60.3 0.882 1 5.07193 0.76649 0.57283 10.33500 2.22600 60.0 0.877 1 5.07193 0.76649 0.57283 10.49400 2.22600 52.6 0.868 1 3.49805 0.65667 2.77578 10.65300 2.22600 48.5 0.849 1 3.49805 0.65667 2.77578 10.81200 2.22600 49.8 0.873 1 3.49805 0.65667 2.77578 10.97100 2.22600 53.6 0.882 1 3.49805 0.65667 2.77578 11.13000 2.22600 54.4 0.883 1 3.49805 0.65667 2.77578 11.28900 2.22600 49.3 0.876 1 3.49805 0.65667 2.77578 11.44800 2.22600 44.5 0.842 1 4.54991 0.71331 2.25320 11.60700 2.22600 51.5 0.879 1 4.54991 0.71331 2.25320 11.76600 2.22600 53.9 0.882 1 4.54991 0.71331 2.25320 11.92500 2.22600 52.7 0.882 1 5.34240 0.40884 1.56023 0.00000 2.38500 49.5 0.877 1 5.34240 0.40884 1.56023 0.15900 2.38500 53.9 0.880 1 5.34240 0.40884 1.56023 0.31800 2.38500 53.6 0.879 1 5.37673 0.43007 1.54524 0.47700 2.38500 49.4 0.871 1 5.34240 0.40884 1.56023 0.63600 2.38500 44.0 0.860 1 1.47226 0.78203 4.94823 0.79500 2.38500 45.7 0.850 1 1.47226 0.78203 4.94823 0.95400 2.38500 53.7 0.872 1 1.47226 0.78203 4.94823 1.11300 2.38500 54.7 0.876 1 1.47226 0.78203 4.94823 1.27200 2.38500 54.6 0.876 1 1.47226 0.78203 4.94823 1.43100 2.38500 49.3 0.870 1 1.47226 0.78203 4.94823 1.59000 2.38500 43.1 0.841 1 2.79951 0.44040 4.04675 1.74900 2.38500 49.9 0.874 1 2.79951 0.44040 4.04675 1.90800 2.38500 58.8 0.882 1 2.79951 0.44040 4.04675 2.06700 2.38500 57.1 0.880 1 2.79951 0.44040 4.04675 2.22600 2.38500 58.0 0.878 1 2.79951 0.44040 4.04675 2.38500 2.38500 56.5 0.876 1 2.77813 0.42500 4.07972 2.54400 2.38500 53.0 0.871 1 2.77813 0.42500 4.07972 2.70300 2.38500 44.3 0.839 1 2.92303 0.41946 2.96341 2.86200 2.38500 48.8 0.866 1 2.92303 0.41946 2.96341 3.02100 2.38500 49.7 0.865 1 2.92303 0.41946 2.96341 3.18000 2.38500 39.4 0.844 1 1.34131 0.61640 5.24311 3.33900 2.38500 37.5 0.846 1 3.86364 0.57476 2.44602 3.49800 2.38500 41.2 0.853 1 3.86364 0.57476 2.44602 3.65700 2.38500 49.4 0.877 1 3.86364 0.57476 2.44602 3.81600 2.38500 50.0 0.880 1 3.86364 0.57476 2.44602 3.97500 2.38500 51.3 0.881 1 3.86364 0.57476 2.44602 4.13400 2.38500 50.9 0.881 1 3.86364 0.57476 2.44602 4.29300 2.38500 49.0 0.874 1 3.86364 0.57476 2.44602 4.45200 2.38500 45.2 0.855 1 3.99287 0.27862 2.26454 4.61100 2.38500 43.3 0.852 1 3.99287 0.27862 2.26454 4.77000 2.38500 46.3 0.865 1 3.99287 0.27862 2.26454 4.92900 2.38500 37.4 0.837 1 5.65635 0.71202 6.25275 5.08800 2.38500 45.0 0.867 1 5.65635 0.71202 6.25275 5.24700 2.38500 52.9 0.877 1 5.65635 0.71202 6.25275 5.40600 2.38500 55.5 0.878 1 5.65635 0.71202 6.25275 5.56500 2.38500 56.3 0.879 1 5.65635 0.71202 6.25275 5.72400 2.38500 57.2 0.877 1 5.65635 0.71202 6.25275 5.88300 2.38500 57.4 0.879 1 5.65635 0.71202 6.25275 6.04200 2.38500 56.6 0.879 1 5.65635 0.71202 6.25275 6.20100 2.38500 59.3 0.878 1 5.65635 0.71202 6.25275 6.36000 2.38500 58.9 0.878 1 5.65635 0.712
I'm not sure why my images don't show up... is there a trick to make them show up ?
I figured it out; it appears that my mail program (Thunderbird) does not properly format responses to this list; here are the images:
reference image:
best fit pattern:
IPFZ:
Here is the EMsoft .ang file; simply change the extension to .ang
Hello Marc,
thank you very much for looking into the file. I went offline for the last 2 days, but thank you for waiting for my reply. I performed a DI calculation with the unrefined detector parameters (xPC = -10.584, yPC = 31.76, L = 17001.6 mm) and could achieve comparable results, ploted in IPF_Z. For comparison I added a map from the plain AZtec acquisition data:
I will provide the larger data set, however I have to check with my collegue that I'm allowed to share this specific measurement. Otherwise I will perform another measurement on a material, that I can share.
Regarding the pattern center refinement, I have two questions: What tool/programm do you use for this? I have read about EMFit in another issue (https://github.com/EMsoft-org/EMsoft/issues/131#issuecomment-722445087), but have no access to an IDL. The other question regards your simulated kikuchi pattern and the marked PC. The position of the PCcross is in the left half, however your & my xPC is negative (-13.4377 & -10.584). As far as I understood, since EMsoft 5.x the definition of the x-axis changed to "positive to the left", thus negative in the right half, with the origin in the middle. Accordingly, the reference kikuchi pattern (middle position in the map (x35|y35)) from AZtec shows the pattern center on the right half: Is it simply due to another plotting convention of the kikuchi pattern? For experimental patterns from AZtec, such as here, the origin is in the upper left corner, viewing from the detector.
Thanks again and regards, Philip
Hi Philip,
that is reasonably good agreement between the two DI results; a change in pattern center will always give a light rotational difference between the two data sets. I have a derivation of that if you are interested.
For the pattern center cross, let me look into that; it is entirely possible that I drew it on the wrong side. I use the IDL efit program to do this refinement. The EMsoft EMFit program does not work as well as the IDL version which is a bit more sophisticated. We have been working on more advanced routines, but for the time being they are still in the private EMsoft repository.
Marc.
That might be off topic regarding EMsoft, but the resulting IPf map looks well indexed. Does PyEBSDIndex achieve such a high indexation rate by hough indexing alone or was the map subjected to some cleaning and filtering afterwards? I'm wondering, since with online indexing during the measurement AZtec yields only ~60% indexation rate. I should definately take a closer look at that, thanks showing that!
@Philip-Go thanks for providing the small dataset that @hakonanes was able to do a test run with PyEBSDIndex. I have been doing some testing across different methods, and so far PyEBSDIndex has been performing well compared to EDAX's hough, which in terms of indexing rate of the vendor's software, has always had a higher hit rate in my experience. But I had been curious about how it might compare to AZtec. Certainly not a full benchmark ... but I am quite pleased that PyEBSDIndex is doing as well as it appears above.
And I would remiss to not note, EMsoft Dictionary with refinement is still the gold standard in my testing.
Finally, in PyEBSDIndex there are also some PC refinement routines (see the doc/tutorials). I have found the best results by being able to send in a batch of patterns, ideally from different orientations, and minimizing the so-called "fit" parameter common to Hough-indexing. I am not sure if they would match the accuracy of the DI refinements, but they do have the advantage of not requiring IDL. But @marcdegraef and I might argue that learning a bit of IDL is probably good for you!
Current PyEBSDIndex does not account for any kind of variations in the PC due to scanning shifts. A lot of the mechanisms to do so are in the sub-programs, but the larger program flows have not been hooked together to enable that.
Hi Philip,
that is reasonably good agreement between the two DI results; a change in pattern center will always give a light rotational difference between the two data sets. I have a derivation of that if you are interested.
For the pattern center cross, let me look into that; it is entirely possible that I drew it on the wrong side. I use the IDL efit program to do this refinement. The EMsoft EMFit program does not work as well as the IDL version which is a bit more sophisticated. We have been working on more advanced routines, but for the time being they are still in the private EMsoft repository.
Marc.
Hi Marc,
I was expecting a slight deviation and confirmed it via the misorientation angle between your and my mapping. I already made my experiences with an entirely wrong calculated yPC-value in the beginning of this year, that lead to an apparent rotation around the horizontal axis by several degrees, something about 20-30°. It was due to an error in the translation from Oxford's definition to EMsoft definition of the PC. The misorientation map is shown below. The yellow data points have a misorientation angle >=10° and are located at the grain boundary - so these points have been assigned to the respecive other grain. The main points show a constant misori between 1 - 3°.
@drowenhorst-nrl Thanks for tip with orientation refinenment! I will definately take a look at PyEBSDIndex. Regarding IDL, learning something new is always good, but for now my conventional aproches have to fail first.
Last but not least, you can find the reason for this issue, the larger Oxford-HDF5, in this link: https://faubox.rrze.uni-erlangen.de/getlink/fiAqni34HVdNHg2vBdqejc/DI_Al-SLBM_750x500.h5oina I'm excusing for the surface quality, as there was a large particle of dirt in the lower half of the scan, but in this case the issue is more about the file and data format than about material science.
Regards, Philip
@Philip-Go @marcdegraef Just for future reference, I think the detector tilt is buried in the HDF5 1/EBSD/Header/Detector Orientation Euler. The middle euler angle is 96.67, so it looks like under the EMsoft/EDAX convention, it is 6.67°. They have a few other small rotations attached, but they are pretty minor, and I bet are more a product of the specific calibration session.
I computed the Average Dot Product map for the full 750x500 data set and I got the following result: Note that there are several regions where the computation did not produce the expected result. This is likely due to bad data in the file, but I'll have to take a closer look at that. Interestingly, the EMsoft code continues to read the file despite numerous HDF5 errors being reported. I will try to run the Dictionary Indexing code as well, just to see what comes out. More later. Marc.
Here is the DI result (IPF-Z); it looks normal to me. I took a closer look at the HDF5 data, and for each line with a problem, the first pattern on the left of the bad portion of the row is the only one that is bad. HDFView lists the values of each pixel as ERROR. The rest of the row is ok, but the EMsoft routine apparently gives up at the first bad pattern. It is not clear to me what the reason is for the bad patterns, but I'm thinking it is some bug in the acquisition software...
Here is the .ang file (change the extension to .ang) Al-large.txt
and here is the Orientation Similarity Map, clearly delineating even the smallest grains...
Marc - Do you think it might have something to do with the lzf compression Oxford put on that dataset? Not sure why, but the h5py module can read those patterns where HDFView fails.
In the mean time, for the DI index, can you set the number of scan columns to 1, number scan rows to 500*750? It would be a slower read-in, but it would prevent the wonky patterns from messing up the rest of the row?
Hi Dave,
if the images in the file are compressed we wouldn't be able to read them in EMsoft... so I don't think they are compressed.
When I read the entire Processed Patterns data set into IDL I got a read error:
% H5D_READ: can't read data: Object ID:360287970189639680
When you read those patterns, what are the numerical values for the pixels?
So there's definitely a problem there. I could try to write an f90 program to overwrite the bad patterns with zeros perhaps? I might have some time in the next couple days to try that.
To work on a single long row of patterns would be problematic as well because all the patterns after the first bad one would not be read at all.
Marc.
On 10/26/22 11:00 PM, Dave Rowenhorst wrote:
Marc - Do you think it might have something to do with the lzf compression Oxford put on that dataset? Not sure why, but the h5py module can read those patterns where HDFView fails.
In the mean time, for the DI index, can you set the number of scan columns to 1, number scan rows to 500*750? It would be a slower read-in, but it would prevent the wonky patterns from messing up the rest of the row?
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Marc - My nomenclature above was not great ... my thought was to make each row just one pattern long, thus a bad pattern does not spoil the rest of the row. There would have to be a lot of messing around after to get angs/hdf5s back into their correct shape.
Can confirm that IDL will not read the full pattern array. However, if I just read in a hyperslab that does not include a bad pattern, that does work. Wonder if the f90 hdf5 program is doing something similar then, but its error behavior is different; it reads a hyperslab into memory, but when it hits a bad point, it bails out, but whatever is in memory before the error can still be processed.
Now, what is happening with h5py, and why it does not trip over itself with these bad points? I don't know. Only thought is that my version h5py is with HDF5 1.12.1 ; IDL is using 1.10.5; My installed EMsoft is linked against 1.10.7
I have attempted to attach a txt file that a bad pattern (not the first bad one in the file, just one I identified: x_indx = 311, y_indx = 375, thus should be pattern 311+375*70 = 281561). There does not appear to be any NANs, ranges from 1,255, same as the pattern before and after it. The values are different than the patterns before/after.
Some final clues:
I think you're probably right that this may be an issue of different HDF libraries causing problems. It does reflect negatively on Oxford for writing a potentially corrupt file... but that's not a real surprise...
I wrote a little f90 program to read several consecutive rows of patterns. I get an error message for each row that has an issue, but there is a pattern in each column; it's just that the pattern is exactly the same for consecutive bad rows, hence the vertical striations in the ADP map above inside the bad stripes. Next thing to try is to overwrite the bad entries and see if the ADP map comes out intact.
Marc.
Will Lenthe wrote a python script (below) to convert an HDF5 file to the up2 format; it might be interesting to apply this to the problematic Oxford data set, to see if the "bad" pattern issue is resolved.
Marc.
import h5py
import numpy as np
import struct
input_file = "C:/Users/wlenthe/datasets/ni/Ni Sequence.oh5"
input_dataset = "Scan 1/EBSD/Data/Pattern"
pats = h5py.File(input_file)[input_dataset]
output_file = '.'.join(input_file.split('.')[:-1]) + ".up"
if pats.dtype == np.dtype("u1"):
output_file += '1'
elif pats.dtype == np.dtype("u2"):
output_file += '2'
else:
raise TypeError("unsupported datatype for up1/up2 output file")
with open(output_file, 'wb') as f:
from a non-square detector header = [1, pats.shape[1], pats.shape[2], 16] # version, pattern width, pattern height, offset to data start
print (header)
f.write(struct.pack('4i', *header))
f.write(np.array(pats).tobytes())
On 10/27/22 11:14 AM, Marc De Graef wrote:
I think you're probably right that this may be an issue of different HDF libraries causing problems. It does reflect negatively on Oxford for writing a potentially corrupt file... but that's not a real surprise...
I wrote a little f90 program to read several consecutive rows of patterns. I get an error message for each row that has an issue, but there is a pattern in each column; it's just that the pattern is exactly the same for consecutive bad rows, hence the vertical striations in the ADP map above inside the bad stripes. Next thing to try is to overwrite the bad entries and see if the ADP map comes out intact.
Marc.
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ok, that conversion works fine! we do need to switch the pats.shape[1] and [2] parameters, but other than that it works perfectly... the new ADP map is shown below. So, there is no problem with the Oxford hdf5 file; it is likely an incompatibility issue between HDF5 libraries. I am going to try to use HDF5-1.12.2 with the EMsoftOO repository; this will require a few changes to the HDFsupport module, but hopefully that won't be too difficult to implement. More later.
Marc.
Especially frustrating given that HDFView reports that the compression ratio on that array is 1.0. I am not going to pretend to be an expert on compression algorithms, but I do know the one thing that does not work well is random noise. And even "low-noise" EBSD patterns like these are pretty noisy images comparatively. The extra overhead is simply not worth it. I know EDAX experimented with compression on their saved patterns, and what they found was that the extra bytes needed in the file needed to deal with the compression, and the lack of actual compression, actually made the files larger.
Hello Marc,
thank you very much for sharing the conversion script! It works smoothly and can nicely be integrated into the execution script. I have tested it over the weekend on a large sample of ~ 3 Mio. points and it worked nicely :) The preprocessing step of conversion took only about 30 min., comparatively short to the overall 36 h.
Nonetheless I'm looking forward to the integration of the h5oina read-in in EMsoftOO, as well as to EMsoftOO in general. Keep up the great work and thanks again for your help!
Philip
Hi Philip and Dave,
just wanted to let you know that I managed to get the HDF5 library built with plugin support for the lzf compression library. At this point in time, I've only done this for the object oriented version of EMsoft (EMsoftOO, which is version 6.0, currently in beta). I can now read the Oxford *.h5oina format without any errors; that means conversion to .up1 or .up2 format is not necessary. It will take me a while to propagate those changes to EMsoft v.5 but I'm hoping to do that over the next couple of weeks.
Regards, Marc.
Hi everybody,
I'm using EMsoft 5.0 in a nightly-build copiled package and was using it with OxfordBinaries .ebsp from AZtec versions 3.1 to 4.3. In that combo, the DI went smoothly and resulted great mappings of nano-crystalline metals and deformed microstructures.
However, recently one of our EBSD systems got an update of the AZtec software, from 3.1 to AZtec 6.0. With this update some changes in the OxfordBinary file must have occured, because EMEBSDDIpreview can't access the .ebsp any more. This can be related to the HDF5 file, because now the OxfordHDF5 file format .h5oina contains the uncompressed Kikuchi patternswhich are nicely accessible, for example in Python via h5py and matplotlib. The path to access them is '1/EBSD/Data/Processed Patterns'. Unfortunately, the EMsoft inputtype OxfordHDF leads to an hard coded break. From the code I could find out that as of 2019 the OxfordHDF5 did not contain any Kikuchi patterns, so no routine was implemented.
However, now the Kikuchi patterns are there. I'm not that familiar with HDF5 yet, but I asumed that it's advantage is data accessability independent of the hardware manufacturer. So I tried to run EMEBSDDIpreview on the OxfordHDF with inputtype BrukerHDF, which failed, and TSLHDF, which then was succesfull! Of course I tried the dictionary indexing EMEBSDDI on the OxfordHDF with the TSLHDF, which started out nicely. But eventually, the programm failed during Pattern Preprocessing inbetween row 260 and 265 of 500 rows with the error:
Completed row 260 of 500 rows
Error code : -1
returned by routine HDF_readHyperslabIntegerArray3D:h5dread_f:Processed Patterns
Interestingly, when I define a ROI from 1st to 250th column, the DI programm runs smoothly and returns a proper .ctf file:
Completed row 250 of 250 rows
-> experimental patterns preprocessed
Number of experimental patterns processed per second : 34883.7
-> computing Average Dot Product map (ADP)
-> Number of threads set to 8
Oct 21 2022 11:56:12.770 AM
min./max. dot product = 0.768612 / 0.867969; 1.2% complete
min./max. dot product = 0.768987 / 0.870098; 2.4% complete
etc...The dataset contains 375000 datapoint/kikuchi patterns in 750 columns and 500 rows, Kikuchi patterns have a size of 168x128 px.
My question is know, if someone has implemented but not released a routine for reading OxfordHDF files containing Kikuchi patterns or maybe has an idea, why the TSLHDF set only works until a specific row. I am neither experienced with HDF5 nor Fortran. But following the error-code, the error occurs in the h5read_f line in the HDF_readHyperslabIntegerArray3D procedure.
edit: what I maybe need to mention: if I chose the ROI from row 250 to 500 (lower half), the pattern pre processing breaks after 10 lines, probably corresponding to the exact same line/pattern where processing of the whole data set fails.
Thank you for any ideas or comments