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focal_plane_metrology.py
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focal_plane_metrology.py
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# -*- coding: utf-8 -*-
"""
Created on Sun Jun 4 13:33:19 2017
@author: Duan Yutong (dyt@physics.bu.edu)
# evaluate quality of petal-ring integration by calculating throughput
Code on SVN:
https://desi.lbl.gov/svn/code/focalplane/plate_layout/trunk/metrology_analysis/
Code on Github:
https://github.com/givoltage/desifp
Results on google drive:
https://drive.google.com/open?id=0B8mEgjxcgZeYVVFVZnYyM2Q3REE
Data on DocDB:
DESI-3542: Focal plate survey and alignment data
DESI-3543: Zeiss petal metrology data
"""
import os
# from functools import reduce
from multiprocessing import Pool
import numpy as np
import pandas as pd
from scipy.optimize import minimize, minimize_scalar
import matplotlib.pyplot as plt
import matplotlib.gridspec as gridspec
from matplotlib.backends.backend_pdf import PdfPages
from petal_metrology import (
Rxyz, matmul, angles_to_unit_vector, vector_to_angles, cs5_to_petal,
throughput_tilt, throughput_defocus)
# # 2017-11-22 (run 4)
petal_locations = [0, 1, 2, 3, 4, 6, 7, 8] # lo of petals installed
petal_id_lookup = {0: '06', # map between petal location and petal ID
1: '03',
2: '00',
3: '04',
4: '02',
5: '10',
6: '05',
7: '01',
8: '07',
9: '09'}
# final alignment, 10 official petals
# petal_locations = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] # lo of petals installed
# petal_id_lookup = {0: '04', # map between petal location and petal ID
# 1: '05',
# 2: '06',
# 3: '07',
# 4: '08',
# 5: '10',
# 6: '11',
# 7: '02',
# 8: '03',
# 9: '09'}
petal_ids = ['01', '02', '04', '00', '03', '05', '06', '07', '08', '09', '10',
'11'] # petal production sequential order
fig_save_dir = r'C:\Users\givoltage\Google Drive\DESI\model_drawings\DESI Focal Plate Assy and Integration\FP Structure\metrology\duan_plots_and_data'
fig_save_dir = r'D:\20171122 (run 4)'
''' CMM data
2017/06
# 14 ft lbs run
4.4781, -25.60003, -83.09296
-107.04049, -412.34349, -102.98927
40.8575, -423.96552, -102.94535
# run 1
# PTL 01
4.4773, -25.5948, -83.12058
-107.04192, -412.34, -102.99234
40.85639, -423.9622, -102.94688
# run 2
# PTL01
4.45612, -25.59908, -83.11410
-107.38446, -412.25313, -102.98851
40.50410, -423.99704, -102.94503
# run 3
# PTL01
4.46046, -25.59862, -83.10798
-107.33292, -412.26666, -102.98560
40.55794, -423.99204, -102.94328
# run 4
# PTL01
4.45294, -25.47059, -84.71993
-107.63671, -412.12974, -103.06178
40.23908, -423.96850, -102.99510
# run 5
# PTL01
4.40935, -25.55869, -83.35969
-107.69158, -412.14867, -103.02441
40.19443, -423.99777, -102.96807
# PTL02
22.82853, 12.03275, -83.54088
425.04125, 25.66662, -103.54869
390.20098, 170.08625, -102.84353
# PTL04
-25.71718, 3.66485, -83.57341
-359.01328, 229.15198, -103.09733
-415.87795, 91.82995, -103.02373
2017/08/09 Petal1_2_3_4_5 Position0_4_6_8_2
dtb_pos_cmm = {0: np.array([[4.4270, -25.6063, -83.2393], # DTB 0
[-107.2668, -412.3038, -102.9977], # DTB 1
[40.6288, -423.9956, -102.9422]]), # DTB 2
1: np.array([[ 23.13790, 12.17047, -82.36111], # DTB 0
[425.43710, 24.27891, -102.92469], # DTB 1
[391.25734, 168.64819, -102.90111]]), # DTB 2
2: np.array([[25.7355, -3.9524, -81.7074], # DTB 0
[358.5042, -229.9112, -102.9793], # DTB 1
[415.8817, -92.6059, -102.9030]]), # DTB 2
3: np.array([[22.82853, 12.03275, -83.54088], # DTB 0
[425.04125, 25.66662, -103.54869], # DTB 1
[390.20098, 170.08625, -102.84353]]), # DTB 2
4: np.array([[11.5034, 23.2342, -82.0262], # DTB 0
[329.2688, 270.0592, -103.4826], # DTB 1
[216.3584, 366.6220, -102.7970]]), # DTB 2
5: np.array([[ 23.13790, 12.17047, -82.36447], # DTB 0
[425.43710, 24.27891, -102.91776], # DTB 1
[391.25734, 168.64819, -102.89321]]), # DTB 2
6: np.array([[-18.6401, 18.2689, -81.4708], # DTB 0
[-155.0093, 396.7549, -102.9882], # DTB 1
[-281.8764, 319.2967 , -102.9671]]), # DTB 2
7: np.array([[-25.71718, 3.66485, -83.57341], # DTB 0
[-359.01328, 229.15198, -103.09733], # DTB 1
[-415.87795, 91.82995, -103.02373]]), # DTB 2
8: np.array([[-23.1968, -12.1067, -82.2729], # DTB 0
[-425.0534, -25.3937, -102.9956], # DTB 1
[-390.5567, -169.9256, -103.0188]]), # DTB 2
9: np.array([[ 23.13790, 12.17047, -82.36447], # DTB 0
[425.43710, 24.27891, -102.91776], # DTB 1
[391.25734, 168.64819, -102.89321]]), # DTB 2
}
2017/08/09 Petal1_2_3_4_5 Position0_4_6_8_2_A
dtb_pos_cmm = {0: np.array([[4.1872, -25.7208, -81.6723], # DTB 0
[-107.2467, -412.2113, -102.9762], # DTB 1
[41.0895, -424.1034, -102.8918]]), # DTB 2
1: np.array([[ 23.13790, 12.17047, -82.36111], # DTB 0
[425.43710, 24.27891, -102.92469], # DTB 1
[391.25734, 168.64819, -102.90111]]), # DTB 2
2: np.array([[25.8319, -3.8208, -82.3193], # DTB 0
[358.8527, -229.1334, -102.9946], # DTB 1
[415.8386, -91.9034, -103.0219]]), # DTB 2
3: np.array([[22.82853, 12.03275, -83.54088], # DTB 0
[425.04125, 25.66662, -103.54869], # DTB 1
[390.20098, 170.08625, -102.84353]]), # DTB 2
4: np.array([[11.4151, 23.3294, -83.1942], # DTB 0
[328.8552, 270.7950, -103.0001], # DTB 1
[215.9952, 367.0882, -102.9447]]), # DTB 2
5: np.array([[ 23.13790, 12.17047, -82.36447], # DTB 0
[425.43710, 24.27891, -102.91776], # DTB 1
[391.25734, 168.64819, -102.89321]]), # DTB 2
6: np.array([[-18.5823, 18.0751, -82.0959], # DTB 0
[-155.2874, 396.5124, -103.4683], # DTB 1
[-281.9814, 318.9159, -102.7907]]), # DTB 2
7: np.array([[-25.71718, 3.66485, -83.57341], # DTB 0
[-359.01328, 229.15198, -103.09733], # DTB 1
[-415.87795, 91.82995, -103.02373]]), # DTB 2
8: np.array([[-23.1689, -12.1347, -81.4020], # DTB 0
[-425.2396, -25.6328, -102.9943], # DTB 1
[-390.5036, -170.1635, -102.9757]]), # DTB 2
9: np.array([[ 23.13790, 12.17047, -82.36447], # DTB 0
[425.43710, 24.27891, -102.91776], # DTB 1
[391.25734, 168.64819, -102.89321]]), # DTB 2
}
2017/08/09 Petal1_2_3_4_5 Position0_4_6_8_2_A_Center_Ring
dtb_pos_cmm = {0: np.array([[4.1921, -25.7109, -81.7634], # DTB 0
[-107.2516, -412.2183, -103.0022], # DTB 1
[41.0836, -424.1112, -102.9165]]), # DTB 2
1: np.array([[ 23.13790, 12.17047, -82.36111], # DTB 0
[425.43710, 24.27891, -102.92469], # DTB 1
[391.25734, 168.64819, -102.90111]]), # DTB 2
2: np.array([[25.8265, -3.8083, -82.3541], # DTB 0
[358.8424, -229.1402, -102.9886], # DTB 1
[415.8300, -91.9114, -103.0040]]), # DTB 2
3: np.array([[22.82853, 12.03275, -83.54088], # DTB 0
[425.04125, 25.66662, -103.54869], # DTB 1
[390.20098, 170.08625, -102.84353]]), # DTB 2
4: np.array([[11.4455, 23.3725, -82.8678], # DTB 0
[328.8623, 270.7992, -102.9838], # DTB 1
[216.0007, 367.0942, -102.9391]]), # DTB 2
5: np.array([[ 23.13790, 12.17047, -82.36447], # DTB 0
[425.43710, 24.27891, -102.91776], # DTB 1
[391.25734, 168.64819, -102.89321]]), # DTB 2
6: np.array([[-18.5789, 18.1010, -81.9744], # DTB 0
[-155.2896, 396.5123, -103.4676], # DTB 1
[-281.9832, 318.9133, -102.7874]]), # DTB 2
7: np.array([[-25.71718, 3.66485, -83.57341], # DTB 0
[-359.01328, 229.15198, -103.09733], # DTB 1
[-415.87795, 91.82995, -103.02373]]), # DTB 2
8: np.array([[-23.1181, -12.1256, -81.7091], # DTB 0
[-425.2315, -25.6386, -102.9947], # DTB 1
[-390.4957, -170.1678, -102.9800]]), # DTB 2
9: np.array([[ 23.13790, 12.17047, -82.36447], # DTB 0
[425.43710, 24.27891, -102.91776], # DTB 1
[391.25734, 168.64819, -102.89321]]), # DTB 2
}
2017/08/09 Petal1_2_3_4_5 Position0_4_6_8_2_Center_Ring
dtb_pos_cmm = {0: np.array([[4.4375, -25.6494, -82.9543], # DTB 0
[-107.2724, -412.3054, -103.0165], # DTB 1
[40.6252, -424.0028, -102.9418]]), # DTB 2
1: np.array([[ 23.13790, 12.17047, -82.36111], # DTB 0
[425.43710, 24.27891, -102.92469], # DTB 1
[391.25734, 168.64819, -102.90111]]), # DTB 2
2: np.array([[25.6946, -3.9457, -82.0011], # DTB 0
[358.4965, -229.9100, -102.9356], # DTB 1
[415.8752, -92.6053, -102.8695]]), # DTB 2
3: np.array([[22.82853, 12.03275, -83.54088], # DTB 0
[425.04125, 25.66662, -103.54869], # DTB 1
[390.20098, 170.08625, -102.84353]]), # DTB 2
4: np.array([[11.5420, 23.2737, -81.7051], # DTB 0
[329.2849, 270.0662, -103.5248], # DTB 1
[216.3745, 366.6306, -102.8486]]), # DTB 2
5: np.array([[ 23.13790, 12.17047, -82.36447], # DTB 0
[425.43710, 24.27891, -102.91776], # DTB 1
[391.25734, 168.64819, -102.89321]]), # DTB 2
6: np.array([[-18.6197, 18.2013, -81.9046], # DTB 0
[-154.9941, 396.7444, -102.9752], # DTB 1
[-281.8636, 319.2927, -102.9304]]), # DTB 2
7: np.array([[-25.71718, 3.66485, -83.57341], # DTB 0
[-359.01328, 229.15198, -103.09733], # DTB 1
[-415.87795, 91.82995, -103.02373]]), # DTB 2
8: np.array([[-23.2258, -12.1098, -82.1010], # DTB 0
[-425.0643, -25.3830, -102.9931], # DTB 1
[-390.5664, -169.9151, -103.0403]]), # DTB 2
9: np.array([[ 23.13790, 12.17047, -82.36447], # DTB 0
[425.43710, 24.27891, -102.91776], # DTB 1
[391.25734, 168.64819, -102.89321]]), # DTB 2
}
2017/08/09 Petal1_2_3_4_5 Position0_6_4_2_8_B
dtb_pos_cmm = {0: np.array([[4.3125, -25.7488, -81.4436], # DTB 0
[-107.6097, -412.1692, -102.9695], # DTB 1
[40.5679, -423.9876, -102.9520]]), # DTB 2
1: np.array([[ 23.13790, 12.17047, -82.36111], # DTB 0
[425.43710, 24.27891, -102.92469], # DTB 1
[391.25734, 168.64819, -102.90111]]), # DTB 2
2: np.array([[25.6611, -3.7420, -82.0767], # DTB 0
[358.5348, -229.7812, -103.4887], # DTB 1
[415.5226, -92.5762, -102.8118]]), # DTB 2
3: np.array([[22.82853, 12.03275, -83.54088], # DTB 0
[425.04125, 25.66662, -103.54869], # DTB 1
[390.20098, 170.08625, -102.84353]]), # DTB 2
4: np.array([[11.7554, 23.2369, -81.6233], # DTB 0
[329.4846, 269.8851, -102.9853], # DTB 1
[216.6307, 366.8838, -102.8956]]), # DTB 2
5: np.array([[ 23.13790, 12.17047, -82.36447], # DTB 0
[425.43710, 24.27891, -102.91776], # DTB 1
[391.25734, 168.64819, -102.89321]]), # DTB 2
6: np.array([[-18.6733, 18.2631, -82.3087], # DTB 0
[-155.5033, 396.3449, -102.9803], # DTB 1
[-282.2959, 318.8688, -103.0141]]), # DTB 2
7: np.array([[-25.71718, 3.66485, -83.57341], # DTB 0
[-359.01328, 229.15198, -103.09733], # DTB 1
[-415.87795, 91.82995, -103.02373]]), # DTB 2
8: np.array([[-23.0191, -12.1486, -83.1843], # DTB 0
[-425.3163, -24.9167, -103.0161], # DTB 1
[-390.9161, -169.2275, -102.9588]]), # DTB 2
9: np.array([[ 23.13790, 12.17047, -82.36447], # DTB 0
[425.43710, 24.27891, -102.91776], # DTB 1
[391.25734, 168.64819, -102.89321]]), # DTB 2
}
2017/08/09 Petal1_2_3_4_5 Position0_6_4_2_8_B_Center_Ring
0 01 4.306151714 -25.65967876 -81.99537817
-107.5974998 -412.1497337 -102.9052737
40.58113183 -423.9656425 -102.8851082
2 00 25.71742726 -3.752707116 -81.75653534
358.5624951 -229.7844672 -103.5367403
415.5495519 -92.57838773 -102.8862439
4 02 11.70441665 23.18940413 -82.03236575
329.4829831 269.8730733 -102.9891035
216.6299119 366.8727973 -102.857263
6 04 -18.68022968 18.27740866 -82.20842223
-155.5026633 396.3509597 -102.9421877
-282.2944514 318.8704821 -103.0078759
8 03 -23.10723901 -12.18522014 -82.58056917
-425.3336435 -24.9240861 -103.0534955
-390.9336401 -169.2380798 -102.9815755
2017/08/09 Petal1_2_3_4_5 Position0_2_4_6_8_C_Center_Ring
dtb_pos_cmm = {0: np.array([[4.4409, -25.6956, -82.1555], # DTB 0
[-106.9750, -412.4034, -102.9504], # DTB 1
[40.9380, -423.9888, -102.9159]]), # DTB 2
1: np.array([[ 23.13790, 12.17047, -82.36111], # DTB 0
[425.43710, 24.27891, -102.92469], # DTB 1
[391.25734, 168.64819, -102.90111]]), # DTB 2
2: np.array([[25.7327, -3.9070, -81.8177], # DTB 0
[358.9055, -229.2893, -102.9819], # DTB 1
[416.0439, -91.8863, -102.9071]]), # DTB 2
3: np.array([[22.82853, 12.03275, -83.54088], # DTB 0
[425.04125, 25.66662, -103.54869], # DTB 1
[390.20098, 170.08625, -102.84353]]), # DTB 2
4: np.array([[11.4818, 23.2879, -81.5309], # DTB 0
[328.7666, 270.6905, -103.4652], # DTB 1
[215.6672, 367.0395, -102.7877]]), # DTB 2
5: np.array([[ 23.13790, 12.17047, -82.36447], # DTB 0
[425.43710, 24.27891, -102.91776], # DTB 1
[391.25734, 168.64819, -102.89321]]), # DTB 2
6: np.array([[-18.6736, 18.2012, -81.7480], # DTB 0
[-155.9486, 396.3813, -102.9985], # DTB 1
[-282.6288, 318.6247 , -102.9751]]), # DTB 2
7: np.array([[-25.71718, 3.66485, -83.57341], # DTB 0
[-359.01328, 229.15198, -103.09733], # DTB 1
[-415.87795, 91.82995, -103.02373]]), # DTB 2
8: np.array([[-23.2176, -12.1309, -81.8876], # DTB 0
[-425.0558, -25.6160, -102.9812], # DTB 1
[-390.4803, -170.1315, -103.0081]]), # DTB 2
9: np.array([[ 23.13790, 12.17047, -82.36447], # DTB 0
[425.43710, 24.27891, -102.91776], # DTB 1
[391.25734, 168.64819, -102.89321]]), # DTB 2
}
# 2017-11-17 run 1
dtb_pos_cmm = {0: np.array([[4.1735, -25.6740, -81.9680], # DTB 0
[-107.4897, -412.1371, -102.8910], # DTB 1
[40.8334, -424.1103, -102.8359]]), # DTB 2
1: np.array([[18.6743, -18.1074, -82.6164], # DTB 0
[155.4888, -396.6143, -102.8889], # DTB 1
[282.0296, -319.1703, -102.8710]]), # DTB 2
2: np.array([[25.7062, -3.6743, -81.7622], # DTB 0
[358.7403, -229.4145, -103.4131], # DTB 1
[415.5979, -92.1552, -102.7286]]), # DTB 2
3: np.array([[23.1556, 12.1231, -82.0438], # DTB 0
[425.0321, 25.1929, -102.9075], # DTB 1
[390.6092, 169.7450, -102.9146]]), # DTB 2
4: np.array([[11.7554, 23.2369, -81.6233], # DTB 0
[329.4846, 269.8851, -102.9853], # DTB 1
[216.6307, 366.8838, -102.8956]]), # DTB 2
5: np.array([[-4.3501, 25.7340, -81.9638], # DTB 0
[107.3870, 412.2233, -102.9615], # DTB 1
[-40.7836, 423.9673, -102.9348]]), # DTB 2
6: np.array([[-18.4454, 18.2190, -82.0118], # DTB 0
[-155.5146, 396.8222, -102.9193], # DTB 1
[-282.2076, 319.1092, -102.9615]]), # DTB 2
7: np.array([[-25.9144, 3.6912, -82.0610], # DTB 0
[-358.9540, 229.6060, -102.9805], # DTB 1
[-416.0889, 92.0545, -102.9369]]), # DTB 2
8: np.array([[-23.3388, -12.2638, -81.9155], # DTB 0
[-425.3304, -25.3912, -102.9180], # DTB 1
[-390.8561, -169.8411, -102.9696]]), # DTB 2
9: np.array([[ 23.13790, 12.17047, -82.36447], # DTB 0
[425.43710, 24.27891, -102.91776], # DTB 1
[391.25734, 168.64819, -102.89321]]), # DTB 2
}
# 20171122 (run 4)
dtb_pos_cmm = {0: np.array([[4.418, -25.781, -81.858], # DTB 0
[-107.553, -412.325, -102.839], # DTB 1
[40.924, -424.167, -102.811]]), # DTB 2
1: np.array([[18.663, -18.308, -81.955], # DTB 0
[155.414, -396.399, -102.924], # DTB 1
[282.221, -318.943, -102.959]]), # DTB 2
2: np.array([[25.761, -3.876, -81.836], # DTB 0
[358.742, -229.547, -102.913], # DTB 1
[415.987, -92.192, -102.837]]), # DTB 2
3: np.array([[23.109, 12.129, -81.804], # DTB 0
[425.231, 25.245, -102.929], # DTB 1
[390.630, 169.802, -102.902]]), # DTB 2
4: np.array([[11.487, 23.292, -81.590], # DTB 0
[329.002, 270.423, -103.408], # DTB 1
[215.990, 366.870, -102.735]]), # DTB 2
5: np.array([[-4.3501, 25.7340, -81.9638], # DTB 0
[107.3870, 412.2233, -102.9615], # DTB 1
[-40.7836, 423.9673, -102.9348]]), # DTB 2
6: np.array([[-18.476, 18.237, -81.790], # DTB 0
[-155.512, 396.829, -102.775], # DTB 1
[-282.212, 319.127, -102.832]]), # DTB 2
7: np.array([[-25.826, 3.645, -82.360], # DTB 0
[-358.962, 229.482, -102.939], # DTB 1
[-415.831, 92.454, -102.910]]), # DTB 2
8: np.array([[-23.354, -12.225, -81.847], # DTB 0
[-425.341, -25.373, -102.810], # DTB 1
[-390.863, -169.819, -102.860]]), # DTB 2
9: np.array([[ 23.13790, 12.17047, -82.36447], # DTB 0
[425.43710, 24.27891, -102.91776], # DTB 1
[391.25734, 168.64819, -102.89321]]), # DTB 2
}
# 20171122 (run 3)
dtb_pos_cmm = {0: np.array([[4.419, -25.789, -81.842], # DTB 0
[-107.554, -412.326, -102.845], # DTB 1
[40.924, -424.167, -102.816]]), # DTB 2
1: np.array([[18.651, -18.301, -82.032], # DTB 0
[155.410, -396.398, -102.929], # DTB 1
[282.218, -318.941, -102.962]]), # DTB 2
2: np.array([[25.749, -3.880, -81.876], # DTB 0
[358.738, -229.545, -102.914], # DTB 1
[415.983, -92.191, -102.839]]), # DTB 2
3: np.array([[23.121, 12.133, -81.721], # DTB 0
[425.230, 25.245, -102.932], # DTB 1
[390.630, 169.802, -102.907]]), # DTB 2
4: np.array([[11.487, 23.302, -81.542], # DTB 0
[329.001, 270.425, -103.412], # DTB 1
[215.991, 366.873, -102.738]]), # DTB 2
5: np.array([[-4.3501, 25.7340, -81.9638], # DTB 0
[107.3870, 412.2233, -102.9615], # DTB 1
[-40.7836, 423.9673, -102.9348]]), # DTB 2
6: np.array([[-18.470, 18.237, -81.804], # DTB 0
[-155.511, 396.830, -102.774], # DTB 1
[-282.211, 319.128, -102.834]]), # DTB 2
7: np.array([[-25.825, 3.646, -82.346], # DTB 0
[-358.961, 229.482, -102.942], # DTB 1
[-415.829, 92.456, -102.914]]), # DTB 2
8: np.array([[-23.357, -12.230, -81.820], # DTB 0
[-425.340, -25.373, -102.816], # DTB 1
[-390.862, -169.818, -102.865]]), # DTB 2
9: np.array([[ 23.13790, 12.17047, -82.36447], # DTB 0
[425.43710, 24.27891, -102.91776], # DTB 1
[391.25734, 168.64819, -102.89321]]), # DTB 2
}
# 20171122 (run 2)
dtb_pos_cmm = {0: np.array([[4.362, -25.710, -81.810], # DTB 0
[-107.290, -412.240, -102.917], # DTB 1
[40.886, -423.953, -102.895]]), # DTB 2
1: np.array([[18.450, -18.236, -81.783], # DTB 0
[155.607, -396.788, -102.776], # DTB 1
[282.282, -319.046, -102.833]]), # DTB 2
2: np.array([[25.917, -3.711, -81.827], # DTB 0
[358.954, -229.606, -102.861], # DTB 1
[416.083, -92.050, -102.831]]), # DTB 2
3: np.array([[23.328, 12.232, -81.836], # DTB 0
[425.314, 25.397, -102.813], # DTB 1
[390.827, 169.845, -102.865]]), # DTB 2
4: np.array([[11.487, 23.302, -81.542], # DTB 0
[329.001, 270.425, -103.412], # DTB 1
[215.991, 366.873, -102.738]]), # DTB 2
5: np.array([[-4.225, 25.692, -81.848], # DTB 0
[107.444, 412.134, -102.905], # DTB 1
[-40.878, 424.114, -102.825]]), # DTB 2
6: np.array([[-18.734, 18.110, -82.381], # DTB 0
[-155.544, 396.620, -102.928], # DTB 1
[-282.086, 319.174, -102.903]]), # DTB 2
7: np.array([[-25.724, 3.686, -81.623], # DTB 0
[-358.778, 229.445, -103.418], # DTB 1
[-415.642, 92.188, -102.750]]), # DTB 2
8: np.array([[-23.228, -12.090, -81.956], # DTB 0
[-425.072, -25.290, -102.936], # DTB 1
[-390.603, -169.830, -102.961]]), # DTB 2
9: np.array([[ 23.13790, 12.17047, -82.36447], # DTB 0
[425.43710, 24.27891, -102.91776], # DTB 1
[391.25734, 168.64819, -102.89321]]), # DTB 2
}
# 20171122 (run 1)
dtb_pos_cmm = {0: np.array([[4.363, -25.716, -81.781], # DTB 0
[-107.290, -412.239, -102.913], # DTB 1
[40.886, -423.952, -102.894]]), # DTB 2
1: np.array([[18.453, -18.235, -81.778], # DTB 0
[155.606, -396.784, -102.778], # DTB 1
[282.281, -319.044, -102.837]]), # DTB 2
2: np.array([[25.910, -3.708, -81.857], # DTB 0
[358.952, -229.604, -102.866], # DTB 1
[416.081, -92.049, -102.834]]), # DTB 2
3: np.array([[23.333, 12.232, -81.811], # DTB 0
[425.312, 25.398, -102.815], # DTB 1
[390.825, 169.845, -102.864]]), # DTB 2
4: np.array([[11.487, 23.302, -81.542], # DTB 0
[329.001, 270.425, -103.412], # DTB 1
[215.991, 366.873, -102.738]]), # DTB 2
5: np.array([[-4.228, 25.694, -81.844], # DTB 0
[107.443, 412.133, -102.903], # DTB 1
[-40.879, 424.113, -102.826]]), # DTB 2
6: np.array([[-18.736, 18.116, -82.352], # DTB 0
[-155.545, 396.622, -102.931], # DTB 1
[-282.086, 319.175, -102.906]]), # DTB 2
7: np.array([[-25.731, 3.691, -81.579], # DTB 0
[-358.778, 229.447, -103.419], # DTB 1
[-415.642, 92.188, -102.749]]), # DTB 2
8: np.array([[-23.223, -12.084, -81.984], # DTB 0
[-425.070, -25.289, -102.934], # DTB 1
[-390.601, -169.828, -102.956]]), # DTB 2
9: np.array([[ 23.13790, 12.17047, -82.36447], # DTB 0
[425.43710, 24.27891, -102.91776], # DTB 1
[391.25734, 168.64819, -102.89321]]), # DTB 2
}
"2018-01-25 (run 4)"
dtb_pos_cmm = {0: np.array([[4.362, -25.713, -81.798], # DTB 0
[-107.414, -412.211, -102.913], # DTB 1
[40.760, -423.970, -102.891]]), # DTB 2
1: np.array([[18.447, -18.242, -81.779], # DTB 0
[155.481, -396.838, -102.773], # DTB 1
[282.181, -319.136, -102.831]]), # DTB 2
2: np.array([[25.917, -3.717, -81.825], # DTB 0
[358.885, -229.714, -102.860], # DTB 1
[416.055, -92.175, -102.830]]), # DTB 2
3: np.array([[23.338, 12.239, -81.776], # DTB 0
[425.317, 25.412, -102.809], # DTB 1
[390.827, 169.856, -102.861]]), # DTB 2
4: np.array([[11.671, 23.542, -81.893], # DTB 0
[329.177, 270.374, -102.877], # DTB 1
[216.397, 367.140, -102.898]]), # DTB 2
5: np.array([[-4.388, 25.952, -81.701], # DTB 0
[107.598, 412.227, -102.772], # DTB 1
[-40.727, 424.155, -102.756]]), # DTB 2
6: np.array([[-18.723, 18.200, -81.796], # DTB 0
[-155.290, 396.507, -102.851], # DTB 1
[-282.285, 318.730, -102.672]]), # DTB 2
7: np.array([[-25.726, 3.692, -81.606], # DTB 0
[-358.859, 229.332, -103.417], # DTB 1
[-415.675, 92.053, -102.750]]), # DTB 2
8: np.array([[-23.230, -12.090, -81.938], # DTB 0
[-425.072, -25.278, -102.934], # DTB 1
[-390.606, -169.821, -102.957]]), # DTB 2
9: np.array([[-11.496, -23.316, -81.685], # DTB 0
[-329.255, -270.513, -102.869], # DTB 1
[-216.270, -367.187, -102.845]]), # DTB 2
}
'''
# 20171122 (run 4)
dtb_pos_cmm = {0: np.array([[4.418, -25.781, -81.858], # DTB 0
[-107.553, -412.325, -102.839], # DTB 1
[40.924, -424.167, -102.811]]), # DTB 2
1: np.array([[18.663, -18.308, -81.955], # DTB 0
[155.414, -396.399, -102.924], # DTB 1
[282.221, -318.943, -102.959]]), # DTB 2
2: np.array([[25.761, -3.876, -81.836], # DTB 0
[358.742, -229.547, -102.913], # DTB 1
[415.987, -92.192, -102.837]]), # DTB 2
3: np.array([[23.109, 12.129, -81.804], # DTB 0
[425.231, 25.245, -102.929], # DTB 1
[390.630, 169.802, -102.902]]), # DTB 2
4: np.array([[11.487, 23.292, -81.590], # DTB 0
[329.002, 270.423, -103.408], # DTB 1
[215.990, 366.870, -102.735]]), # DTB 2
5: np.array([[-4.3501, 25.7340, -81.9638], # DTB 0
[107.3870, 412.2233, -102.9615], # DTB 1
[-40.7836, 423.9673, -102.9348]]), # DTB 2
6: np.array([[-18.476, 18.237, -81.790], # DTB 0
[-155.512, 396.829, -102.775], # DTB 1
[-282.212, 319.127, -102.832]]), # DTB 2
7: np.array([[-25.826, 3.645, -82.360], # DTB 0
[-358.962, 229.482, -102.939], # DTB 1
[-415.831, 92.454, -102.910]]), # DTB 2
8: np.array([[-23.354, -12.225, -81.847], # DTB 0
[-425.341, -25.373, -102.810], # DTB 1
[-390.863, -169.819, -102.860]]), # DTB 2
9: np.array([[ 23.13790, 12.17047, -82.36447], # DTB 0
[425.43710, 24.27891, -102.91776], # DTB 1
[391.25734, 168.64819, -102.89321]]), # DTB 2
}
# DTB coordinates in CS5 measured by CMM
# 2018-01-25 (run 4)
# dtb_pos_cmm = {0: np.array([[4.362, -25.713, -81.798], # DTB 0
# [-107.414, -412.211, -102.913], # DTB 1
# [40.760, -423.970, -102.891]]), # DTB 2
# 1: np.array([[18.447, -18.242, -81.779], # DTB 0
# [155.481, -396.838, -102.773], # DTB 1
# [282.181, -319.136, -102.831]]), # DTB 2
# 2: np.array([[25.917, -3.717, -81.825], # DTB 0
# [358.885, -229.714, -102.860], # DTB 1
# [416.055, -92.175, -102.830]]), # DTB 2
# 3: np.array([[23.338, 12.239, -81.776], # DTB 0
# [425.317, 25.412, -102.809], # DTB 1
# [390.827, 169.856, -102.861]]), # DTB 2
# 4: np.array([[11.671, 23.542, -81.893], # DTB 0
# [329.177, 270.374, -102.877], # DTB 1
# [216.397, 367.140, -102.898]]), # DTB 2
# 5: np.array([[-4.388, 25.952, -81.701], # DTB 0
# [107.598, 412.227, -102.772], # DTB 1
# [-40.727, 424.155, -102.756]]), # DTB 2
# 6: np.array([[-18.723, 18.200, -81.796], # DTB 0
# [-155.290, 396.507, -102.851], # DTB 1
# [-282.285, 318.730, -102.672]]), # DTB 2
# 7: np.array([[-25.726, 3.692, -81.606], # DTB 0
# [-358.859, 229.332, -103.417], # DTB 1
# [-415.675, 92.053, -102.750]]), # DTB 2
# 8: np.array([[-23.230, -12.090, -81.938], # DTB 0
# [-425.072, -25.278, -102.934], # DTB 1
# [-390.606, -169.821, -102.957]]), # DTB 2
# 9: np.array([[-11.496, -23.316, -81.685], # DTB 0
# [-329.255, -270.513, -102.869], # DTB 1
# [-216.270, -367.187, -102.845]]), # DTB 2
# }
# %% function definitions
# def matmul(*args):
# return reduce(np.dot, [*args])
# def Rx(angle):
# Rx = np.array([
# [1.0, 0.0, 0.0],
# [0.0, np.cos(angle), np.sin(angle)],
# [0.0, -np.sin(angle), np.cos(angle)]
# ])
# return Rx
# def Ry(angle):
# Ry = np.array([
# [np.cos(angle), 0.0, -np.sin(angle)],
# [0.0, 1.0, 0.0],
# [np.sin(angle), 0.0, np.cos(angle)]
# ])
# return Ry
# def Rz(angle):
# Rz = np.array([
# [np.cos(angle), np.sin(angle), 0.0],
# [-np.sin(angle), np.cos(angle), 0.0],
# [0.0, 0.0, 1.0]
# ])
# return Rz
# def Rxyz(alpha, beta, gamma):
# Rxyz = matmul(Rz(gamma), Ry(beta), Rx(alpha)) # yaw-pitch-roll system
# return Rxyz
def R_general(axis, angle):
'''
axis must be a 3-element unit vector
the rotation formalism is outlined in
http://ksuweb.kennesaw.edu/~plaval/math4490/rotgen.pdf
where the arbitrary axis passes through the origin.
'''
ux = axis[0]
uy = axis[1]
uz = axis[2]
C = np.cos(angle)
S = np.sin(angle)
t = 1-C
R_general = np.array([
[t*ux**2+C, t*ux*uy-S*uz, t*ux*uz+S*uy],
[t*ux*uy+S*uz, t*uy**2+C, t*uy*uz-S*ux],
[t*ux*uz-S*uy, t*uy*uz+S*ux, t*uz**2+C]])
return R_general
# def angles_to_unit_vector(theta_deg, phi_deg):
# # returns a unit vector from polar and azimuthal angles
# theta = np.radians(theta_deg)
# phi = np.radians(phi_deg)
# return np.array([np.sin(theta)*np.cos(phi),
# np.sin(theta)*np.sin(phi),
# np.cos(theta)])
# def vector_to_angles(x, y, z):
# r = np.sqrt(np.square(x) + np.square(y) + np.square(z))
# theta = np.arccos(z/r) # radians
# phi = np.arctan(y/x)
# return [np.degrees(theta), np.degrees(phi)]
# def throughput_tilt(tilt):
# # takes degree input
# throughput_tilt = -0.0133*np.power(tilt, 2) - 0.0175*tilt + 1.0
# return np.multiply(throughput_tilt, throughput_tilt > 0)
# def throughput_defocus(delta_f):
# delta_f_um = np.abs(delta_f) * 1000
# # takes micron input
# throughput_defocus = (- 1.804e-14*np.power(delta_f_um, 5)
# + 1.593e-11*np.power(delta_f_um, 4)
# - 5.955e-10*np.power(delta_f_um, 3)
# - 3.433e-6*np.power(delta_f_um, 2)
# + 3.251e-7*delta_f_um
# + 1.0)
# return np.multiply(throughput_defocus, throughput_defocus > 0)
# def petal_to_cs5(x, petal_location):
# '''
# given a petal location (designated by interger 0 to 9) and measurement
# of a point in CS6, rotate the point by an integer number of 36 degrees
# to petal's local CS defined in the petal solid model.
# according to DESI-0742v3, the petal at location 3 shares the same
# coordinate system with CS6 (X5 Y5 Z5)
# '''
# angle = 2*np.pi/10*(petal_location-3) # the point is rotated
# x_rot = matmul(Rz(angle), x)
# return x_rot
# def cs5_to_petal(x, petal_location):
# '''
# given a petal location (designated by interger 0 to 9) and measurement
# of a point in CS6, rotate the point by an integer number of 36 degrees
# to petal's local CS defined in the petal solid model.
# according to DESI-0742v3, the petal at location 3 shares the same
# coordinate system with CS6 (X5 Y5 Z5)
# '''
# theta = 2*np.pi/10*(petal_location-3)
# x_rot = matmul(Rz(theta), x)
# return x_rot
# %% evaluate petal throughput and calculate optimal 1DF alignment
def evaluate_petal(petal_location):
petal_id = petal_id_lookup[petal_location]
# read in dataframes
df = pd.read_pickle(os.path.join(fig_save_dir,
str(petal_ids.index(petal_id)+1).zfill(2)
+ '-ptl_' + petal_id + '-df_data.pickle'),
compression='gzip')
df_transformations = pd.read_pickle(os.path.join(
fig_save_dir,
str(petal_ids.index(petal_id)+1).zfill(2)
+ '-ptl_' + petal_id + '-df_transformations.pickle'),
compression='gzip')
# %% from 3 DTB positions, calculate all petal info and throughput
df.loc[('diameter', 'ACT')] = df.loc[('diameter', 'ABC')].values
# create arrays for datum tooling ball positions in two alignments
dtb_pos_abc = np.concatenate((
df.loc[('dtb_x', 'ABC'), 'actual'].values.reshape(-1, 1),
df.loc[('dtb_y', 'ABC'), 'actual'].values.reshape(-1, 1),
df.loc[('dtb_z', 'ABC'), 'actual'].values.reshape(-1, 1)),
axis=1).T.astype(np.float64)[:, :3]
dtb_pos_act_cs5 = dtb_pos_cmm[petal_location].T
dtb_pos_act = np.empty(dtb_pos_act_cs5.shape)
# the measured actual positions are in CS5
# need to rotate by an integer multiple of 36 degrees
for j in range(3):
dtb_pos_act[:, j] = cs5_to_petal(dtb_pos_act_cs5[:, j], petal_location)
df.loc[('dtb_x', 'ACT'), 'actual'][j] = dtb_pos_act[0, j]
df.loc[('dtb_y', 'ACT'), 'actual'][j] = dtb_pos_act[1, j]
df.loc[('dtb_z', 'ACT'), 'actual'][j] = dtb_pos_act[2, j]
def total_residue(parameters):
# this is the function to be minimised
alpha = parameters[0]
beta = parameters[1]
gamma = parameters[2]
T = parameters[3:]
R = Rxyz(alpha, beta, gamma)
dtb_pos_abc_rot = np.empty(dtb_pos_abc.shape) # rotated from ABC
# rotate each column of x_abc and fill x_abc_rot
for j in range(dtb_pos_abc.shape[1]):
dtb_pos_abc_rot[:, j] = matmul(R, dtb_pos_abc[:, j]) + T
return np.sum(np.linalg.norm(dtb_pos_abc_rot - dtb_pos_act), axis=0)
# minimisation routine
# p0 = np.array([0.0, 0.0, 0.0, 0.0, 0.0, 0.0])
p0 = df_transformations.loc['ZBF'].values
bounds = ((-np.pi/2, np.pi//2), (-np.pi/2, np.pi/2), (-np.pi/2, np.pi/2),
(-10, 10), (-10, 10), (-10, 10))
solution_act = minimize(total_residue, p0,
bounds=bounds,
method='SLSQP',
options={'disp': True,
'maxiter': 1000})
print('PTL'+petal_id+' ACT transformation found as \n'
+ 'X Rotation (Roll) : {}° \n'.format(np.degrees(solution_act.x[0]))
+ 'Y Rotation (Pitch): {}° \n'.format(np.degrees(solution_act.x[1]))
+ 'Z Rotation (Yaw) : {}° \n'.format(np.degrees(solution_act.x[2]))
+ 'Translation: {} \n'.format(solution_act.x[3:])
+ 'With least square: {} \n'.format(solution_act.fun))
# save transformation parameters
df_transformations.loc['ACT'] = solution_act.x
# Calculate R and T
parameters = solution_act.x
alpha = parameters[0]
beta = parameters[1]
gamma = parameters[2]
T = parameters[3:]
R = Rxyz(alpha, beta, gamma) # yaw-pitch-roll system
# write results with these parameters to dataframe
x_abc = np.concatenate((
df.loc[('x', 'ABC'), 'actual'].values.reshape(-1, 1),
df.loc[('y', 'ABC'), 'actual'].values.reshape(-1, 1),
df.loc[('z', 'ABC'), 'actual'].values.reshape(-1, 1)),
axis=1).T.astype(np.float64)
theta_abc = np.radians(df.loc[('nutation', 'ABC'), 'actual']
.values.astype(np.float64))
phi_abc = np.radians(df.loc[('precession', 'ABC'), 'actual']
.values.astype(np.float64))
x0_abc = x_abc - np.array([np.sin(theta_abc)*np.cos(phi_abc),
np.sin(theta_abc)*np.sin(phi_abc),
np.cos(theta_abc)]) # another point along axis
x_abc_rot = np.empty(x_abc.shape) # rotated matrix from ABC
x0_abc_rot = np.empty(x_abc.shape)
# rotate each column of x_abc and fill x_abc_rot
for j in range(x_abc.shape[1]):
x_abc_rot[:, j] = matmul(R, x_abc[:, j]) + T
x0_abc_rot[:, j] = matmul(R, x0_abc[:, j]) + T
n_rot = x_abc_rot - x0_abc_rot # rotated axis direction
[theta_rot, phi_rot] = vector_to_angles(
n_rot[0, :], n_rot[1, :], n_rot[2, :])
df.loc[('x', 'ACT'), 'actual'] = x_abc_rot[0, :]
df.loc[('y', 'ACT'), 'actual'] = x_abc_rot[1, :]
df.loc[('z', 'ACT'), 'actual'] = x_abc_rot[2, :]
df.loc[('nutation', 'ACT'), 'actual'] = theta_rot
df.loc[('precession', 'ACT'), 'actual'] = phi_rot
df.loc[('x', 'ACT'), 'deviation'] = df.loc[('x', 'ACT'), 'actual'].values \
- df.loc[('x', 'ACT'), 'nominal'].values
df.loc[('y', 'ACT'), 'deviation'] = df.loc[('y', 'ACT'), 'actual'].values \
- df.loc[('y', 'ACT'), 'nominal'].values
df.loc[('z', 'ACT'), 'deviation'] = df.loc[('z', 'ACT'), 'actual'].values \
- df.loc[('z', 'ACT'), 'nominal'].values
df.loc[('nutation', 'ACT'), 'deviation'] = \
df.loc[('nutation', 'ACT'), 'actual'].values \
- df.loc[('nutation', 'ACT'), 'nominal'].values
df.loc[('precession', 'ACT'), 'deviation'] = \
df.loc[('precession', 'ACT'), 'actual'].values \
- df.loc[('precession', 'ACT'), 'nominal'].values
# calculate r
df.loc[('r', 'ACT'), 'actual'] = np.sqrt(
np.square(df.loc[('x', 'ACT'), 'actual'].values.astype(np.float64))
+ np.square(df.loc[('y', 'ACT'), 'actual'].values.astype(np.float64)))
# calculate tilt
theta0 = df.loc['nutation', 'ACT']['nominal'].values.astype(np.float64)
theta = df.loc['nutation', 'ACT']['actual'].values.astype(np.float64)
phi0 = df.loc['precession', 'ACT']['nominal'].values.astype(np.float64)
phi = df.loc['precession', 'ACT']['actual'].values.astype(np.float64)
n0 = angles_to_unit_vector(theta0, phi0)
n = angles_to_unit_vector(theta, phi)
tilt = np.array(
[np.degrees(np.arccos(np.dot(n0[:, i], n[:, i]))) for i in range(514)])
df.loc[('tilt', 'ACT'), 'actual'] = tilt
# calculate defocus
delta_r = np.array([
df.loc[('x', 'ACT'), 'deviation'].values.astype(np.float64),
df.loc[('y', 'ACT'), 'deviation'].values.astype(np.float64),
df.loc[('z', 'ACT'), 'deviation'].values.astype(np.float64)
])
delta_f = np.array([np.dot(delta_r[:, i], n0[:, i]) for i in range(514)])
df.loc[('defocus', 'ACT'), 'actual'] = delta_f
# calculate combined throughput
throughput = throughput_tilt(tilt) * throughput_defocus(delta_f)
df.loc[('throughput', 'ACT'), 'actual'] = throughput
df.loc[('throughput', 'ACT'), 'deviation'] = 1 - throughput
# %% 1DF alignment, based on 3 DTb positions
'''
the predicted 1 degree of freedom that is actually adjustable
is an axis of rotation passing through two points:
[438.99959, 0.6, -108]
[355.1584605, 258.0377258, -108]
'''
df.loc[('diameter', '1DF')] = df.loc[('diameter', 'ABC')].values
axp1 = np.array([355.1584605, 258.0377258, -108])
axp2 = np.array([438.99959, 0.6, -108])
axis = (axp1-axp2)/np.linalg.norm(axp1-axp2)
x_act = np.concatenate((
df.loc[('x', 'ACT'), 'actual'].values.reshape(-1, 1),
df.loc[('y', 'ACT'), 'actual'].values.reshape(-1, 1),
df.loc[('z', 'ACT'), 'actual'].values.reshape(-1, 1)),
axis=1).T.astype(np.float64)
theta_act = np.radians(df.loc[('nutation', 'ACT'), 'actual']
.values.astype(np.float64))
phi_act = np.radians(df.loc[('precession', 'ACT'), 'actual']
.values.astype(np.float64))
x0_act = x_act - np.array([np.sin(theta_act)*np.cos(phi_act),
np.sin(theta_act)*np.sin(phi_act),
np.cos(theta_act)]) # another point along axis
def throughput_loss_min_1df(angle):
# this is the function to be minimised
R = R_general(axis, angle)
x_act_rot = np.empty(x_act.shape) # rotated matrix from ABC
x0_act_rot = np.empty(x_act.shape)
# rotate each column of x_abc and fill x_abc_rot
for k in range(x_act.shape[1]):
x_act_rot[:, k] = matmul(R, x_act[:, k] - axp1) + axp1
x0_act_rot[:, k] = matmul(R, x0_act[:, k] - axp1) + axp1
n_rot = x_act_rot - x0_act_rot # not necessarily of unit length
[theta_rot, phi_rot] = vector_to_angles(
n_rot[0, :], n_rot[1, :], n_rot[2, :])
delta_r = np.array(
[x_act_rot[0, :] - df.loc[('x', 'ABC'), 'nominal'].values,
x_act_rot[1, :] - df.loc[('y', 'ABC'), 'nominal'].values,
x_act_rot[2, :] - df.loc[('z', 'ABC'), 'nominal'].values])
# calculate tilt
n = angles_to_unit_vector(theta_rot, phi_rot) # ensure unit length
tilt = np.array(
[np.degrees(np.arccos(np.dot(n0[:, i], n[:, i])))
for i in range(514)])
delta_f = np.array(
[np.dot(delta_r[:, i], n0[:, i]) for i in range(514)])
throughput = throughput_tilt(tilt) * throughput_defocus(delta_f)
return np.mean(1-throughput)
solution_1df = minimize_scalar(throughput_loss_min_1df,
bounds=(-np.pi/2, np.pi/2),
method='Brent')
print('PTL'+petal_id+' 1DF transformation found as \n'
+ 'Rotation: {}° \n'.format(np.degrees(solution_1df.x))
+ 'With least mean throughput loss: {} \n'.format(solution_1df.fun)
+ 'Compared with current throughput loss: {} \n'.format(
np.mean(df.loc[('throughput', 'ACT'), 'deviation'].values)))
# save transformation parameters
df_transformations.loc['1DF', 'alpha'] = solution_1df.x
R = R_general(axis, solution_1df.x)
x_act_rot = np.empty(x_act.shape) # rotated matrix from ABC
x0_act_rot = np.empty(x_act.shape)
# rotate each column of x_abc and fill x_abc_rot
for k in range(x_act.shape[1]):
x_act_rot[:, k] = matmul(R, x_act[:, k] - axp1) + axp1
x0_act_rot[:, k] = matmul(R, x0_act[:, k] - axp1) + axp1
n_rot = x_act_rot - x0_act_rot # not necessarily of unit length
[theta_rot, phi_rot] = vector_to_angles(
n_rot[0, :], n_rot[1, :], n_rot[2, :])
df.loc[('x', '1DF'), 'actual'] = x_act_rot[0, :]
df.loc[('y', '1DF'), 'actual'] = x_act_rot[1, :]
df.loc[('z', '1DF'), 'actual'] = x_act_rot[2, :]
df.loc[('nutation', '1DF'), 'actual'] = theta_rot
df.loc[('precession', '1DF'), 'actual'] = phi_rot
df.loc[('x', '1DF'), 'nominal'] = df.loc[('x', 'ABC'), 'nominal'].values
df.loc[('y', '1DF'), 'nominal'] = df.loc[('y', 'ABC'), 'nominal'].values
df.loc[('z', '1DF'), 'nominal'] = df.loc[('z', 'ABC'), 'nominal'].values
df.loc[('nutation', '1DF'), 'nominal'] = \
df.loc[('nutation', 'ABC'), 'nominal'].values
df.loc[('precession', '1DF'), 'nominal'] = \
df.loc[('precession', 'ABC'), 'nominal'].values
df.loc[('x', '1DF'), 'deviation'] = \
df.loc[('x', '1DF'), 'actual'].values \
- df.loc[('x', '1DF'), 'nominal'].values
df.loc[('y', '1DF'), 'deviation'] = \
df.loc[('y', '1DF'), 'actual'].values \
- df.loc[('y', '1DF'), 'nominal'].values
df.loc[('z', '1DF'), 'deviation'] = \
df.loc[('z', '1DF'), 'actual'].values \
- df.loc[('z', '1DF'), 'nominal'].values
df.loc[('nutation', '1DF'), 'deviation'] = \
df.loc[('nutation', '1DF'), 'actual'].values \
- df.loc[('nutation', '1DF'), 'nominal'].values
df.loc[('precession', '1DF'), 'deviation'] = \
df.loc[('precession', '1DF'), 'actual'].values \
- df.loc[('precession', '1DF'), 'nominal'].values
# datum tooilng balls
for j in range(3):
x = np.array([df.loc[('dtb_x', 'ACT'), 'actual'][j],
df.loc[('dtb_y', 'ACT'), 'actual'][j],
df.loc[('dtb_z', 'ACT'), 'actual'][j]])
xp = matmul(R, x - axp1) + axp1
df.loc[('dtb_x', '1DF'), 'actual'][j] = xp[0]
df.loc[('dtb_y', '1DF'), 'actual'][j] = xp[1]
df.loc[('dtb_z', '1DF'), 'actual'][j] = xp[2]
# calculate r
df.loc[('r', '1DF'), 'actual'] = np.sqrt(
np.square(df.loc[('x', '1DF'), 'actual'].values.astype(np.float64))
+ np.square(df.loc[('y', '1DF'), 'actual'].values.astype(np.float64)))
# calculate tilt
theta0 = df.loc['nutation', 'ABC']['nominal'].values.astype(np.float64)
theta = df.loc['nutation', '1DF']['actual'].values.astype(np.float64)
phi0 = df.loc['precession', 'ABC']['nominal'].values.astype(np.float64)
phi = df.loc['precession', '1DF']['actual'].values.astype(np.float64)