Source code for finesse.detectors.pdtypes

"""Dictionaries storing the generic beat-coefficients for simulating segmented
photoiodes.

Builtin pdtypes:
* SINGLE - single element photodiode
* XSPLIT - measuring horizontal/yaw motions
* YSPLIT - measuring vertical/pitch motions

Use the function `construct_segment_beat_matrix` to convert these dictionary definitions
into a dense or sparse CSR matrix for using in calculations.
"""

import numpy as np
import numbers
from finesse.cymath.sparsemath import CSRMatrix


[docs]def get_pdtype(pdtype: str) -> dict: """Returns a pdtype dictionary definition in this module for a given string name.""" return globals()[pdtype.upper()] if isinstance(pdtype, str) else pdtype
[docs]def construct_segment_beat_matrix( mode_index_map, beats_dict, sparse_output=False, assert_hermitian=True ): """Takes a pdtype definition dict and converts it into a matrix suitable to use with a KnmMatrix. Parameters ---------- mode_index_map : dict[(n,m), index] Dictionary of mode indices and index beats_dict : str, pdtype style dict A dictionary in the pdtype style describing a particular segmentation type for a sensor. If a string is given it will try and get a builtin pdtype dict sparse_output : bool, optional Return a sparse CSR matrix object rather than a dense one assert_hermitian : bool, optional If true then the generated matrix from the pdtype definition must be Hermitian Returns ------- 2D Complex matrix of size (N, N) with N=len(mode_index_map) or a CSRMatrix if requested. Examples -------- >>> pdtypes.construct_segment_beat_matrix(model.mode_index_map, pdtype.YSPLIT) array([[0. +0.j, 0.79788456+0.j, 0. +0.j], [0.79788456+0.j, 0. +0.j, 0. +0.j], [0. +0.j, 0. +0.j, 0. +0.j]]) Another example showing how to manually compute the segmented photodiode beat signal using this matrix output whilst misaligning some optic. >>> import finesse >>> import matplotlib.pyplot as plt >>> finesse.init_plotting() >>> # Simple laser reflecting from a steering mirror >>> model = finesse.script.parse(''' ... l l1 P=1 ... bs bs1 R=1 T=0 ... nothing n1 ... link(l1, bs1, 10, n1) ... fd E n1.p1.i f=0 ... gauss g1 l1.p1.o w=1m Rc=inf ... modes(maxtem=3) ... ''') >>> # Run the model and extract the matrix of mode amplitudes >>> sol = model.run("xaxis(bs1.xbeta, lin, 0, 1e-6, 4)") >>> E = sol['E'] >>> # Get the beat matrix for a quadrant photodiode >>> M = finesse.detectors.pdtypes.construct_segment_beat_matrix( ... model.mode_index_map, ... finesse.detectors.pdtypes.XSPLIT ... ) >>> # Compute E^* . M . E over the array >>> S = (E.conj() * (M @ E.T).T).sum(1) >>> plt.plot(sol.x1, abs(S)) >>> plt.xlabel("Misalignment [rad]") >>> plt.ylabel("Signal [W]") >>> plt.title("QPD alignment signal") """ # TODO ddb - don't need to generate the dense matrix first to then # convert it into a sparse representation, would be more efficient # to go straight to sparse. if isinstance(beats_dict, str): beats_dict = get_pdtype(beats_dict) N = len(mode_index_map) _beats = np.zeros((N, N), dtype=complex) maxtem = max(max(mode_index_map, key=lambda x: max(x))) for (n1, m1, n2, m2), factor in beats_dict.items(): if all(isinstance(k, numbers.Number) for k in (n1, m1, n2, m2)): idx = mode_index_map.get((n1, m1), -1) jdx = mode_index_map.get((n2, m2), -1) if idx >= 0 and jdx >= 0: _beats[idx, jdx] = factor _beats[jdx, idx] = factor elif all(k in ("x", "y") for k in (m1, m2)) and all( isinstance(k, numbers.Number) for k in (n1, n2) ): for m in range(maxtem + 1): idx = mode_index_map.get((n1, m), -1) jdx = mode_index_map.get((n2, m), -1) if idx >= 0 and jdx >= 0: _beats[idx, jdx] = factor _beats[jdx, idx] = factor elif all(k in ("x", "y") for k in (n1, n2)) and all( isinstance(k, numbers.Number) for k in (m1, m2) ): for n in range(maxtem + 1): idx = mode_index_map.get((n, m1), -1) jdx = mode_index_map.get((n, m2), -1) if idx >= 0 and jdx >= 0: _beats[idx, jdx] = factor _beats[jdx, idx] = factor elif n1 == n2 and m1 == m2: for n in range(maxtem + 1): for m in range(maxtem + 1): idx = mode_index_map.get((n, m), -1) jdx = mode_index_map.get((n, m), -1) if idx >= 0 and jdx >= 0: _beats[idx, jdx] = factor _beats[jdx, idx] = factor elif n1 == m2 and m1 == n2: for n in range(maxtem + 1): for m in range(maxtem + 1): idx = mode_index_map.get((n, m), -1) jdx = mode_index_map.get((m, n), -1) if idx >= 0 and jdx >= 0: _beats[idx, jdx] = factor _beats[jdx, idx] = factor else: raise NotImplementedError() if assert_hermitian: if np.all(_beats - _beats.T.conj() != 0): raise Exception(f"Matrix generated by pdtype was not Hermitian:\n{_beats}") if sparse_output: return CSRMatrix(_beats) else: return _beats
SINGLE = { ("x", "y", "x", "y"): 1, } # split detector in x-direction, for up to TEM-order 40 XSPLIT = { (0, "x", 1, "x"): 0.797884560802865, (0, "x", 3, "x"): -0.32573500793528, (0, "x", 5, "x"): 0.218509686118416, (0, "x", 7, "x"): -0.168583882836184, (0, "x", 9, "x"): 0.139074607877595, (0, "x", 11, "x"): -0.119342192152758, (0, "x", 13, "x"): 0.105105246952602, (0, "x", 15, "x"): -0.0942883643366128, (0, "x", 17, "x"): 0.085756077667627, (0, "x", 19, "x"): -0.0788316791424408, (0, "x", 21, "x"): 0.0730852493544752, (0, "x", 23, "x"): -0.0682297483293215, (0, "x", 25, "x"): 0.0640657596627177, (0, "x", 27, "x"): -0.0604501569509354, (0, "x", 29, "x"): 0.0572773850389327, (0, "x", 31, "x"): -0.0544677839262821, (0, "x", 33, "x"): 0.051960035687153, (0, "x", 35, "x"): -0.0497061241097501, (0, "x", 37, "x"): 0.0476678793880178, (0, "x", 39, "x"): -0.0458145530435871, (2, "x", 1, "x"): 0.564189583547756, (2, "x", 3, "x"): 0.690988298942671, (2, "x", 5, "x"): -0.257516134682126, (2, "x", 7, "x"): 0.166889529453114, (2, "x", 9, "x"): -0.126437912127138, (2, "x", 11, "x"): 0.103140489653524, (2, "x", 13, "x"): -0.0878334751963756, (2, "x", 15, "x"): 0.0769291636262386, (2, "x", 17, "x"): -0.0687238645863045, (2, "x", 19, "x"): 0.0623003460579352, (2, "x", 21, "x"): -0.0571189780993917, (2, "x", 23, "x"): 0.0528405479815828, (2, "x", 25, "x"): -0.0492405794558427, (2, "x", 27, "x"): 0.0461642931761014, (2, "x", 29, "x"): -0.0435013182859334, (2, "x", 31, "x"): 0.0411707144994762, (2, "x", 33, "x"): -0.0391116996228281, (2, "x", 35, "x"): 0.0372776912078078, (2, "x", 37, "x"): -0.0356323539463384, (2, "x", 39, "x"): 0.0341469044387, (4, "x", 1, "x"): -0.16286750396764, (4, "x", 3, "x"): 0.598413420602149, (4, "x", 5, "x"): 0.669046543557289, (4, "x", 7, "x"): -0.240884286886713, (4, "x", 9, "x"): 0.153297821464992, (4, "x", 11, "x"): -0.114842936826923, (4, "x", 13, "x"): 0.092969581005561, (4, "x", 15, "x"): -0.0787358118089783, (4, "x", 17, "x"): 0.0686730145130556, (4, "x", 19, "x"): -0.0611475066641648, (4, "x", 21, "x"): 0.0552860726690191, (4, "x", 23, "x"): -0.0505782313126719, (4, "x", 25, "x"): 0.0467048872492379, (4, "x", 27, "x"): -0.0434559246068004, (4, "x", 29, "x"): 0.0406871064724294, (4, "x", 31, "x"): -0.0382959872150584, (4, "x", 33, "x"): 0.0362077065246626, (4, "x", 35, "x"): -0.0343662293597736, (4, "x", 37, "x"): 0.0327287372726021, (4, "x", 39, "x"): -0.031261920230486, (6, "x", 1, "x"): 0.0892062058076385, (6, "x", 3, "x"): -0.18209140509868, (6, "x", 5, "x"): 0.61075313987865, (6, "x", 7, "x"): 0.659688788381993, (6, "x", 9, "x"): -0.233235207868822, (6, "x", 11, "x"): 0.146771489830575, (6, "x", 13, "x"): -0.109117578596892, (6, "x", 15, "x"): 0.0878479967266388, (6, "x", 17, "x"): -0.0740877073983095, (6, "x", 19, "x"): 0.0644074398753087, (6, "x", 21, "x"): -0.0571982549981952, (6, "x", 23, "x"): 0.0516033260749633, (6, "x", 25, "x"): -0.0471234847486845, (6, "x", 27, "x"): 0.043447712204836, (6, "x", 29, "x"): -0.0403718224901522, (6, "x", 31, "x"): 0.0377560369073105, (6, "x", 33, "x"): -0.0355013303057689, (6, "x", 35, "x"): 0.0335355132263835, (6, "x", 37, "x"): -0.031804668469598, (6, "x", 39, "x"): 0.0302676798757954, (8, "x", 1, "x"): -0.059603403376112, (8, "x", 3, "x"): 0.102198547643328, (8, "x", 5, "x"): -0.190435749776861, (8, "x", 7, "x"): 0.617082357005358, (8, "x", 9, "x"): 0.6545146787836, (8, "x", 11, "x"): -0.228820262121828, (8, "x", 13, "x"): 0.142898207894381, (8, "x", 15, "x"): -0.10565264117106, (8, "x", 17, "x"): 0.0847033053948983, (8, "x", 19, "x"): -0.0712017602555549, (8, "x", 21, "x"): 0.0617354634590125, (8, "x", 23, "x"): -0.0547065570873058, (8, "x", 25, "x"): 0.0492658641354183, (8, "x", 27, "x"): -0.0449196778881935, (8, "x", 29, "x"): 0.0413609897651131, (8, "x", 31, "x"): -0.0383886289102033, (8, "x", 33, "x"): 0.0358651299902981, (8, "x", 35, "x"): -0.0336932742842578, (8, "x", 37, "x"): 0.0318023047767947, (8, "x", 39, "x"): -0.030139455674167, (10, "x", 1, "x"): 0.0439792525587995, (10, "x", 3, "x"): -0.0692528965958894, (10, "x", 5, "x"): 0.108397929099021, (10, "x", 7, "x"): -0.195138575204209, (10, "x", 9, "x"): 0.620927144090899, (10, "x", 11, "x"): 0.651233882791557, (10, "x", 13, "x"): -0.225941905251249, (10, "x", 15, "x"): 0.140323254503473, (10, "x", 17, "x"): -0.103315642865758, (10, "x", 19, "x"): 0.0825585698009622, (10, "x", 21, "x"): -0.0692160218229681, (10, "x", 23, "x"): 0.0598836888491238, (10, "x", 25, "x"): -0.0529693961318701, (10, "x", 27, "x"): 0.0476280244212015, (10, "x", 29, "x"): -0.0433688465158433, (10, "x", 31, "x"): 0.0398870940423755, (10, "x", 33, "x"): -0.0369833150045722, (10, "x", 35, "x"): 0.0345213862957191, (10, "x", 37, "x"): -0.0324051535576467, (10, "x", 39, "x"): 0.0305647153283757, (12, "x", 1, "x"): -0.0344511233825375, (12, "x", 3, "x"): 0.051570244826762, (12, "x", 5, "x"): -0.0741307969600372, (12, "x", 7, "x"): 0.112098577001675, (12, "x", 9, "x"): -0.198164159898117, (12, "x", 11, "x"): 0.623508972874051, (12, "x", 13, "x"): 0.648968714596981, (12, "x", 15, "x"): -0.223915479517027, (12, "x", 17, "x"): 0.13848407598893, (12, "x", 19, "x"): -0.101627759192188, (12, "x", 21, "x"): 0.0809958057142225, (12, "x", 23, "x"): -0.0677586792014329, (12, "x", 25, "x"): 0.058516541236311, (12, "x", 27, "x"): -0.0516804098923711, (12, "x", 29, "x"): 0.0464075103789091, (12, "x", 31, "x"): -0.0422088782527226, (12, "x", 33, "x"): 0.0387810976838852, (12, "x", 35, "x"): -0.0359257728661409, (12, "x", 37, "x"): 0.0335076182428655, (12, "x", 39, "x"): -0.031431152699668, (14, "x", 1, "x"): 0.0280905588320645, (14, "x", 3, "x"): -0.0406589983848392, (14, "x", 5, "x"): 0.0555599515078389, (14, "x", 7, "x"): -0.0771577797725184, (14, "x", 9, "x"): 0.114573457526737, (14, "x", 11, "x"): -0.200276093365814, (14, "x", 13, "x"): 0.625361901098279, (14, "x", 15, "x"): 0.647311065109173, (14, "x", 17, "x"): -0.222410991173016, (14, "x", 19, "x"): 0.137103342840115, (14, "x", 21, "x"): -0.100349371709367, (14, "x", 23, "x"): 0.0798036519532965, (14, "x", 25, "x"): -0.0666403046237177, (14, "x", 27, "x"): 0.0574621027762285, (14, "x", 29, "x"): -0.0506819820916291, (14, "x", 31, "x"): 0.0454586096116469, (14, "x", 33, "x"): -0.041304127205318, (14, "x", 35, "x"): 0.0379159829603672, (14, "x", 37, "x"): -0.0350964661555485, (14, "x", 39, "x"): 0.0327108419265415, (16, "x", 1, "x"): -0.0235720910841532, (16, "x", 3, "x"): 0.0333113049961062, (16, "x", 5, "x"): -0.0440146568671265, (16, "x", 7, "x"): 0.0581059881284756, (16, "x", 9, "x"): -0.0792394808782953, (16, "x", 11, "x"): 0.116349896137392, (16, "x", 13, "x"): -0.201834685692187, (16, "x", 15, "x"): 0.626756243745903, (16, "x", 17, "x"): 0.646045548619932, (16, "x", 19, "x"): -0.221249568137138, (16, "x", 21, "x"): 0.136028005901464, (16, "x", 23, "x"): -0.0993465691012448, (16, "x", 25, "x"): 0.0788629080536757, (16, "x", 27, "x"): -0.0657533402767068, (16, "x", 29, "x"): 0.0566222517097102, (16, "x", 31, "x"): -0.0498837907575016, (16, "x", 33, "x"): 0.04469755498707, (16, "x", 35, "x"): -0.0405764129180567, (16, "x", 37, "x"): 0.0372183888740113, (16, "x", 39, "x"): -0.034426235332043, (18, "x", 1, "x"): 0.0202129013489131, (18, "x", 3, "x"): -0.0280564002314289, (18, "x", 5, "x"): 0.0361938566085091, (18, "x", 7, "x"): -0.0462018029426718, (18, "x", 9, "x"): 0.0598942816336477, (18, "x", 11, "x"): -0.0807655532556404, (18, "x", 13, "x"): 0.117688834298236, (18, "x", 15, "x"): -0.203032528170905, (18, "x", 17, "x"): 0.627843419313627, (18, "x", 19, "x"): 0.645047794281474, (18, "x", 21, "x"): -0.220325766323103, (18, "x", 23, "x"): 0.135166515247699, (18, "x", 25, "x"): -0.0985383906746981, (18, "x", 27, "x"): 0.07810092971977, (18, "x", 29, "x"): -0.0650318354039826, (18, "x", 31, "x"): 0.055936535430677, (18, "x", 33, "x"): -0.0492299775566192, (18, "x", 35, "x"): 0.0440723835688313, (18, "x", 37, "x"): -0.0399771169972641, (18, "x", 39, "x"): 0.0366426000734971, (20, "x", 1, "x"): -0.017627299334295, (20, "x", 3, "x"): 0.0241288202745342, (20, "x", 5, "x"): -0.0305737533320824, (20, "x", 7, "x"): 0.0381039552927518, (20, "x", 9, "x"): -0.047763592814719, (20, "x", 11, "x"): 0.0612270740454677, (20, "x", 13, "x"): -0.0819349188989436, (20, "x", 15, "x"): 0.118734977843307, (20, "x", 17, "x"): -0.203982022959719, (20, "x", 19, "x"): 0.628714819343417, (20, "x", 21, "x"): 0.644240979964118, (20, "x", 23, "x"): -0.219573371070635, (20, "x", 25, "x"): 0.134460680056461, (20, "x", 27, "x"): -0.0978729043007541, (20, "x", 29, "x"): 0.0774707909003214, (20, "x", 31, "x"): -0.0644329526695553, (20, "x", 33, "x"): 0.0553655154050687, (20, "x", 35, "x"): -0.0486839720121728, (20, "x", 37, "x"): 0.0435489765855488, (20, "x", 39, "x"): -0.039474240161498, (22, "x", 1, "x"): 0.0155818275174025, (22, "x", 3, "x"): -0.0210925805324099, (22, "x", 5, "x"): 0.0263566009981115, (22, "x", 7, "x"): -0.0322641671658076, (22, "x", 9, "x"): 0.0394861351020212, (22, "x", 11, "x"): -0.0489431183977767, (22, "x", 13, "x"): 0.0622619711245261, (22, "x", 15, "x"): -0.082860766578907, (22, "x", 17, "x"): 0.119575292488569, (22, "x", 19, "x"): -0.204753224284902, (22, "x", 21, "x"): 0.629428862525661, (22, "x", 23, "x"): 0.643575097636349, (22, "x", 25, "x"): -0.218948694495961, (22, "x", 27, "x"): 0.133871712354208, (22, "x", 29, "x"): -0.0973152193947713, (22, "x", 31, "x"): 0.0769407678634122, (22, "x", 33, "x"): -0.0639275883754644, (22, "x", 35, "x"): 0.0548822891765173, (22, "x", 37, "x"): -0.0482207457593204, (22, "x", 39, "x"): 0.0431039197585667, (24, "x", 1, "x"): -0.0139273390571125, (24, "x", 3, "x"): 0.0186819548996952, (24, "x", 5, "x"): -0.0230856985072204, (24, "x", 7, "x"): 0.0278689812889355, (24, "x", 9, "x"): -0.0335007876120844, (24, "x", 11, "x"): 0.040541449001796, (24, "x", 13, "x"): -0.0498690376104398, (24, "x", 15, "x"): 0.0630903264429405, (24, "x", 17, "x"): -0.0836125971039459, (24, "x", 19, "x"): 0.120265288362839, (24, "x", 21, "x"): -0.205392081451324, (24, "x", 23, "x"): 0.630024630631138, (24, "x", 25, "x"): 0.643016196013222, (24, "x", 27, "x"): -0.218421741398637, (24, "x", 29, "x"): 0.133372747843751, (24, "x", 31, "x"): -0.0968410038781554, (24, "x", 33, "x"): 0.0764886144798256, (24, "x", 35, "x"): -0.0634952419012075, (24, "x", 37, "x"): 0.054467836681766, (24, "x", 39, "x"): -0.0478225494651678, (26, "x", 1, "x"): 0.012564329179744, (26, "x", 3, "x"): -0.0167261931797469, (26, "x", 5, "x"): 0.0204814479513874, (26, "x", 7, "x"): -0.0244511756080565, (26, "x", 9, "x"): 0.0289854926054433, (26, "x", 11, "x"): -0.0344536065949141, (26, "x", 13, "x"): 0.0413774431197777, (26, "x", 15, "x"): -0.0506169449451649, (26, "x", 17, "x"): 0.0637691420834689, (26, "x", 19, "x"): -0.0842355840892829, (26, "x", 21, "x"): 0.120842103606662, (26, "x", 23, "x"): -0.205929992668735, (26, "x", 25, "x"): 0.63052925596685, (26, "x", 27, "x"): 0.64254041629879, (26, "x", 29, "x"): -0.217971231998968, (26, "x", 31, "x"): 0.1329445838244, (26, "x", 33, "x"): -0.0964327593462296, (26, "x", 35, "x"): 0.0760982532525654, (26, "x", 37, "x"): -0.0631210368417068, (26, "x", 39, "x"): 0.0541083090782501, (28, "x", 1, "x"): -0.0114240058576427, (28, "x", 3, "x"): 0.015110811991687, (28, "x", 5, "x"): -0.0183634797872995, (28, "x", 7, "x"): 0.021723856102418, (28, "x", 9, "x"): -0.025467063571133, (28, "x", 11, "x"): 0.0298524441527061, (28, "x", 13, "x"): -0.0352142635297349, (28, "x", 15, "x"): 0.0420579527183231, (28, "x", 17, "x"): -0.0512345899753054, (28, "x", 19, "x"): 0.0643359900496595, (28, "x", 21, "x"): -0.0847604214666164, (28, "x", 23, "x"): 0.121331543048508, (28, "x", 25, "x"): -0.206389145953734, (28, "x", 27, "x"): 0.630962163162352, (28, "x", 29, "x"): 0.642130502115889, (28, "x", 31, "x"): -0.21758164950347, (28, "x", 33, "x"): 0.132573125753267, (28, "x", 35, "x"): -0.0960775730220675, (28, "x", 37, "x"): 0.0757577671900808, (28, "x", 39, "x"): -0.0627939055909658, (30, "x", 1, "x"): 0.0104573719402441, (30, "x", 3, "x"): -0.0137563247003482, (30, "x", 5, "x"): 0.0166104416612905, (30, "x", 7, "x"): -0.019501442987836, (30, "x", 9, "x"): 0.0226543470950928, (30, "x", 11, "x"): -0.0262611407020985, (30, "x", 13, "x"): 0.0305491632478923, (30, "x", 15, "x"): -0.0358375732209661, (30, "x", 17, "x"): 0.0426236826218798, (30, "x", 19, "x"): -0.0517537930024467, (30, "x", 21, "x"): 0.0648167139702787, (30, "x", 23, "x"): -0.0852087230070191, (30, "x", 25, "x"): 0.121752104250785, (30, "x", 27, "x"): -0.206785667252914, (30, "x", 29, "x"): 0.63133762416741, (30, "x", 31, "x"): 0.641773663798743, (30, "x", 33, "x"): -0.217241412157705, (30, "x", 35, "x"): 0.132247792438937, (30, "x", 37, "x"): -0.0957657043526452, (30, "x", 39, "x"): 0.0754581308127959, (32, "x", 1, "x"): -0.00962863484261943, (32, "x", 3, "x"): 0.0126059053586902, (32, "x", 5, "x"): -0.0151378181055341, (32, "x", 7, "x"): 0.0176587692986935, (32, "x", 9, "x"): -0.020358644867144, (32, "x", 11, "x"): 0.0233858818137396, (32, "x", 13, "x"): -0.0269029867321868, (32, "x", 15, "x"): 0.0311233823964002, (32, "x", 17, "x"): -0.0363587480299401, (32, "x", 19, "x"): 0.0431019952858045, (32, "x", 21, "x"): -0.0521966573355218, (32, "x", 23, "x"): 0.0652297096005878, (32, "x", 25, "x"): -0.0855961631739456, (32, "x", 27, "x"): 0.122117397913667, (32, "x", 29, "x"): -0.207131559327254, (32, "x", 31, "x"): 0.631666360260589, (32, "x", 33, "x"): 0.641460221209205, (32, "x", 35, "x"): -0.216941699788514, (32, "x", 37, "x"): 0.131960484273278, (32, "x", 39, "x"): -0.0954896651000627, (34, "x", 1, "x"): 0.00891107260430101, (34, "x", 3, "x"): -0.0116179059849555, (34, "x", 5, "x"): 0.0138850216154384, (34, "x", 7, "x"): -0.0161084661466783, (34, "x", 9, "x"): 0.0184524571478648, (34, "x", 11, "x"): -0.0210359786164796, (34, "x", 13, "x"): 0.0239801731757788, (34, "x", 15, "x"): -0.0274346624154534, (34, "x", 17, "x"): 0.0316059442338158, (34, "x", 19, "x"): -0.0368016236511537, (34, "x", 21, "x"): 0.0435120491147015, (34, "x", 23, "x"): -0.0525790555417618, (34, "x", 25, "x"): 0.0655884458140045, (34, "x", 27, "x"): -0.0859343937562171, (34, "x", 29, "x"): 0.122437664390516, (34, "x", 31, "x"): -0.207435940915892, (34, "x", 33, "x"): 0.631956581438438, (34, "x", 35, "x"): 0.641182712988902, (34, "x", 37, "x"): -0.216675676757992, (34, "x", 39, "x"): 0.131704895258842, (36, "x", 1, "x"): -0.00828435401829169, (36, "x", 3, "x"): 0.0107611425267978, (36, "x", 5, "x"): -0.0128075374964671, (36, "x", 7, "x"): 0.0147877713476547, (36, "x", 9, "x"): -0.0168466371421289, (36, "x", 11, "x"): 0.0190824142643028, (36, "x", 13, "x"): -0.0215887026965906, (36, "x", 15, "x"): 0.0244746617600977, (36, "x", 17, "x"): -0.0278834727283041, (36, "x", 19, "x"): 0.0320178443629164, (36, "x", 21, "x"): -0.0371829978128156, (36, "x", 23, "x"): 0.043867702084051, (36, "x", 25, "x"): -0.0529127015843396, (36, "x", 27, "x"): 0.0659030205003435, (36, "x", 29, "x"): -0.0862322608322223, (36, "x", 31, "x"): 0.122720757634075, (36, "x", 33, "x"): -0.20770586418026, (36, "x", 35, "x"): 0.632214680931101, (36, "x", 37, "x"): 0.640935295378691, (36, "x", 39, "x"): -0.216437963382246, (38, "x", 1, "x"): 0.00773275113661403, (38, "x", 3, "x"): -0.0100118271418192, (38, "x", 5, "x"): 0.0118719607936816, (38, "x", 7, "x"): -0.0136504853925913, (38, "x", 9, "x"): 0.0154770452283758, (38, "x", 11, "x"): -0.017434866570091, (38, "x", 13, "x"): 0.019598527229861, (38, "x", 15, "x"): -0.022050438024718, (38, "x", 17, "x"): 0.0248937447207395, (38, "x", 19, "x"): -0.0282680905210534, (38, "x", 21, "x"): 0.0323739582618915, (38, "x", 23, "x"): -0.0375150942942534, (38, "x", 25, "x"): 0.0441792493621718, (38, "x", 27, "x"): -0.0532064407664412, (38, "x", 29, "x"): 0.0661811587512815, (38, "x", 31, "x"): -0.0864966038327677, (38, "x", 33, "x"): 0.122972802996398, (38, "x", 35, "x"): -0.207946868938393, (38, "x", 37, "x"): 0.632445711335645, (38, "x", 39, "x"): 0.64071332643857, (40, "x", 1, "x"): -0.00724391688001674, (40, "x", 3, "x"): 0.00935151491502463, (40, "x", 5, "x"): -0.0110527578939448, (40, "x", 7, "x"): 0.012661878924004, (40, "x", 9, "x"): -0.014296399105208, (40, "x", 11, "x"): 0.0160282719391012, (40, "x", 13, "x"): -0.0179185139453499, (40, "x", 15, "x"): 0.0200312179442163, (40, "x", 17, "x"): -0.0224431596178727, (40, "x", 19, "x"): 0.0252541692908214, (40, "x", 21, "x"): -0.0286018042974914, (40, "x", 23, "x"): 0.0326851654679604, (40, "x", 25, "x"): -0.0378070449564994, (40, "x", 27, "x"): 0.0444545121459287, (40, "x", 29, "x"): -0.0534670839867032, (40, "x", 31, "x"): 0.0664288744972003, (40, "x", 33, "x"): -0.0867327955058567, (40, "x", 35, "x"): 0.123198648554883, (40, "x", 37, "x"): -0.208163367559173, (40, "x", 39, "x"): 0.632653718481981, } # split detector in y-direction, for up to TEM-order 40 YSPLIT = { ("x", 0, "x", 1): 0.797884560802865, ("x", 0, "x", 3): -0.32573500793528, ("x", 0, "x", 5): 0.218509686118416, ("x", 0, "x", 7): -0.168583882836184, ("x", 0, "x", 9): 0.139074607877595, ("x", 0, "x", 11): -0.119342192152758, ("x", 0, "x", 13): 0.105105246952602, ("x", 0, "x", 15): -0.0942883643366128, ("x", 0, "x", 17): 0.085756077667627, ("x", 0, "x", 19): -0.0788316791424408, ("x", 0, "x", 21): 0.0730852493544752, ("x", 0, "x", 23): -0.0682297483293215, ("x", 0, "x", 25): 0.0640657596627177, ("x", 0, "x", 27): -0.0604501569509354, ("x", 0, "x", 29): 0.0572773850389327, ("x", 0, "x", 31): -0.0544677839262821, ("x", 0, "x", 33): 0.051960035687153, ("x", 0, "x", 35): -0.0497061241097501, ("x", 0, "x", 37): 0.0476678793880178, ("x", 0, "x", 39): -0.0458145530435871, ("x", 2, "x", 1): 0.564189583547756, ("x", 2, "x", 3): 0.690988298942671, ("x", 2, "x", 5): -0.257516134682126, ("x", 2, "x", 7): 0.166889529453114, ("x", 2, "x", 9): -0.126437912127138, ("x", 2, "x", 11): 0.103140489653524, ("x", 2, "x", 13): -0.0878334751963756, ("x", 2, "x", 15): 0.0769291636262386, ("x", 2, "x", 17): -0.0687238645863045, ("x", 2, "x", 19): 0.0623003460579352, ("x", 2, "x", 21): -0.0571189780993917, ("x", 2, "x", 23): 0.0528405479815828, ("x", 2, "x", 25): -0.0492405794558427, ("x", 2, "x", 27): 0.0461642931761014, ("x", 2, "x", 29): -0.0435013182859334, ("x", 2, "x", 31): 0.0411707144994762, ("x", 2, "x", 33): -0.0391116996228281, ("x", 2, "x", 35): 0.0372776912078078, ("x", 2, "x", 37): -0.0356323539463384, ("x", 2, "x", 39): 0.0341469044387, ("x", 4, "x", 1): -0.16286750396764, ("x", 4, "x", 3): 0.598413420602149, ("x", 4, "x", 5): 0.669046543557289, ("x", 4, "x", 7): -0.240884286886713, ("x", 4, "x", 9): 0.153297821464992, ("x", 4, "x", 11): -0.114842936826923, ("x", 4, "x", 13): 0.092969581005561, ("x", 4, "x", 15): -0.0787358118089783, ("x", 4, "x", 17): 0.0686730145130556, ("x", 4, "x", 19): -0.0611475066641648, ("x", 4, "x", 21): 0.0552860726690191, ("x", 4, "x", 23): -0.0505782313126719, ("x", 4, "x", 25): 0.0467048872492379, ("x", 4, "x", 27): -0.0434559246068004, ("x", 4, "x", 29): 0.0406871064724294, ("x", 4, "x", 31): -0.0382959872150584, ("x", 4, "x", 33): 0.0362077065246626, ("x", 4, "x", 35): -0.0343662293597736, ("x", 4, "x", 37): 0.0327287372726021, ("x", 4, "x", 39): -0.031261920230486, ("x", 6, "x", 1): 0.0892062058076385, ("x", 6, "x", 3): -0.18209140509868, ("x", 6, "x", 5): 0.61075313987865, ("x", 6, "x", 7): 0.659688788381993, ("x", 6, "x", 9): -0.233235207868822, ("x", 6, "x", 11): 0.146771489830575, ("x", 6, "x", 13): -0.109117578596892, ("x", 6, "x", 15): 0.0878479967266388, ("x", 6, "x", 17): -0.0740877073983095, ("x", 6, "x", 19): 0.0644074398753087, ("x", 6, "x", 21): -0.0571982549981952, ("x", 6, "x", 23): 0.0516033260749633, ("x", 6, "x", 25): -0.0471234847486845, ("x", 6, "x", 27): 0.043447712204836, ("x", 6, "x", 29): -0.0403718224901522, ("x", 6, "x", 31): 0.0377560369073105, ("x", 6, "x", 33): -0.0355013303057689, ("x", 6, "x", 35): 0.0335355132263835, ("x", 6, "x", 37): -0.031804668469598, ("x", 6, "x", 39): 0.0302676798757954, ("x", 8, "x", 1): -0.059603403376112, ("x", 8, "x", 3): 0.102198547643328, ("x", 8, "x", 5): -0.190435749776861, ("x", 8, "x", 7): 0.617082357005358, ("x", 8, "x", 9): 0.6545146787836, ("x", 8, "x", 11): -0.228820262121828, ("x", 8, "x", 13): 0.142898207894381, ("x", 8, "x", 15): -0.10565264117106, ("x", 8, "x", 17): 0.0847033053948983, ("x", 8, "x", 19): -0.0712017602555549, ("x", 8, "x", 21): 0.0617354634590125, ("x", 8, "x", 23): -0.0547065570873058, ("x", 8, "x", 25): 0.0492658641354183, ("x", 8, "x", 27): -0.0449196778881935, ("x", 8, "x", 29): 0.0413609897651131, ("x", 8, "x", 31): -0.0383886289102033, ("x", 8, "x", 33): 0.0358651299902981, ("x", 8, "x", 35): -0.0336932742842578, ("x", 8, "x", 37): 0.0318023047767947, ("x", 8, "x", 39): -0.030139455674167, ("x", 10, "x", 1): 0.0439792525587995, ("x", 10, "x", 3): -0.0692528965958894, ("x", 10, "x", 5): 0.108397929099021, ("x", 10, "x", 7): -0.195138575204209, ("x", 10, "x", 9): 0.620927144090899, ("x", 10, "x", 11): 0.651233882791557, ("x", 10, "x", 13): -0.225941905251249, ("x", 10, "x", 15): 0.140323254503473, ("x", 10, "x", 17): -0.103315642865758, ("x", 10, "x", 19): 0.0825585698009622, ("x", 10, "x", 21): -0.0692160218229681, ("x", 10, "x", 23): 0.0598836888491238, ("x", 10, "x", 25): -0.0529693961318701, ("x", 10, "x", 27): 0.0476280244212015, ("x", 10, "x", 29): -0.0433688465158433, ("x", 10, "x", 31): 0.0398870940423755, ("x", 10, "x", 33): -0.0369833150045722, ("x", 10, "x", 35): 0.0345213862957191, ("x", 10, "x", 37): -0.0324051535576467, ("x", 10, "x", 39): 0.0305647153283757, ("x", 12, "x", 1): -0.0344511233825375, ("x", 12, "x", 3): 0.051570244826762, ("x", 12, "x", 5): -0.0741307969600372, ("x", 12, "x", 7): 0.112098577001675, ("x", 12, "x", 9): -0.198164159898117, ("x", 12, "x", 11): 0.623508972874051, ("x", 12, "x", 13): 0.648968714596981, ("x", 12, "x", 15): -0.223915479517027, ("x", 12, "x", 17): 0.13848407598893, ("x", 12, "x", 19): -0.101627759192188, ("x", 12, "x", 21): 0.0809958057142225, ("x", 12, "x", 23): 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