Lidar polarisation GHK-parameter and error calculation: lidar_correction

lidar_correction_ghk.py@28b5510492ba (annotated)

lidar_correction_ghk.py

Wed, 15 Nov 2017 12:34:36 +0100

author: Volker Freudenthaler <volker.freudenthaler@lmu.de>
date: Wed, 15 Nov 2017 12:34:36 +0100
changeset 26: 28b5510492ba
parent 25: 4c66b9ca23be
child 28: 79fa4a41420f
permissions: -rw-r--r--

Changed description of y=+-1 orientation;
Corrected calculation of LDRsimx

 # -*- coding: utf-8 -*-
 """
 Copyright 2016, 2017 Volker Freudenthaler
 Licensed under the EUPL, Version 1.1 only (the "Licence").
 You may not use this work except in compliance with the Licence.
 A copy of the licence is distributed with the code. Alternatively, you may obtain
 a copy of the Licence at:
 https://joinup.ec.europa.eu/community/eupl/og_page/eupl
 Unless required by applicable law or agreed to in writing, software distributed
 under the Licence is distributed on an "AS IS" basis, WITHOUT WARRANTIES OR CONDITIONS
 OF ANY KIND, either express or implied. See the Licence for the specific language governing
 permissions and limitations under the Licence.
 Equation reference: http://www.atmos-meas-tech-discuss.net/amt-2015-338/amt-2015-338.pdf
 With equations code from Appendix C
 Python 3.4.2
 Code description:
 From measured lidar signals we cannot directly determine the desired backscatter coefficient (F11) and the linear depolarization ratio (LDR)
 because of the cross talk between the channles and systematic errors of a lidar system.
 http://www.atmos-meas-tech-discuss.net/amt-2015-338/amt-2015-338.pdf provides an analytical model for the description of these errors,
 with which the measured signals can be corrected.
 This code simulates the lidar measurements with "assumed true" model parameters from an input file, and calculates the correction parameters (G,H, and K).
 The "assumed true" system parameters are the ones we think are the right ones, but in reality these parameters probably deviate from the assumed truth due to
 uncertainties. The uncertainties of the "assumed true" parameters can be described in the input file. Then this code calculates the lidar signals and the
 gain ratio eta* with all possible combinations of "errors", which represents the distribution of "possibly real" signals, and "corrects" them with the "assumed true"
 GHK parameters (GT0, GR0, HT0, HR0, and K0) to derive finally the distributions of "possibly real" linear depolarization ratios (LDRcorr),
 which are plotted for five different input linear depolarization ratios (LDRtrue). The red bars in the plots represent the input values of LDRtrue.
 A complication arises from the fact that the correction parameter K = eta*/eta (Eq. 83) can depend on the LDR during the calibration measurement, i.e. LDRcal or aCal
 in the code (see e.g. Eqs. (103), (115), and (141); mind the mistake in Eq. (116)). Therefor values of K for LDRcal = 0.004, 0.2, and 0.45 are calculated for
 "assumed true" system parameters and printed in the output file behind the GH parameters. The full impact of the LDRcal dependent K can be considered in the error
 calculation by specifying a range of possible LDRcal values in the input file. For the real calibration measurements a calibration range with low or no aerosol
 content should be chosen, and the default in the input file is a range of LDRcal between 0.004 and 0.014 (i.e. 0.009 +-0.005).
 Tip: In case you run the code with Spyder, all output text and plots can be displayed together in an IPython console, which can be saved as an html file.
 """
 # Comment:  The code works with Python 2.7  with the help of following line, which enables Python2 to correctly interpret the Python 3 print statements.
 from __future__ import print_function
 # !/usr/bin/env python3
 import os
 import sys
 import numpy as np
 # Comment: the seaborn library makes nicer plots, but the code works also without it.
 try:
     import seaborn as sns
     sns_loaded = True
 except ImportError:
     sns_loaded = False
 import matplotlib.pyplot as plt
 from time import clock
 # from matplotlib.backends.backend_pdf import PdfPages
 # pdffile = '{}.pdf'.format('path')
 # pp = PdfPages(pdffile)
 ## pp.savefig can be called multiple times to save to multiple pages
 # pp.savefig()
 # pp.close()
 from contextlib import contextmanager
 @contextmanager
 def redirect_stdout(new_target):
     old_target, sys.stdout = sys.stdout, new_target  # replace sys.stdout
     try:
         yield new_target  # run some code with the replaced stdout
     finally:
         sys.stdout.flush()
         sys.stdout = old_target  # restore to the previous value
 '''
 real_raw_input = vars(__builtins__).get('raw_input',input)
 '''
 try:
     import __builtin__
     input = getattr(__builtin__, 'raw_input')
 except (ImportError, AttributeError):
     pass
 from distutils.util import strtobool
 def user_yes_no_query(question):
     sys.stdout.write('%s [y/n]\n' % question)
     while True:
         try:
             return strtobool(input().lower())
         except ValueError:
             sys.stdout.write('Please respond with \'y\' or \'n\'.\n')
 # if user_yes_no_query('want to exit?') == 1: sys.exit()
 abspath = os.path.abspath(__file__)
 dname = os.path.dirname(abspath)
 fname = os.path.basename(abspath)
 os.chdir(dname)
 # PrintToOutputFile = True
 sqr05 = 0.5 ** 0.5
 # ---- Initial definition of variables; the actual values will be read in with exec(open('./optic_input.py').read()) below
 # Do you want to calculate the errors? If not, just the GHK-parameters are determined.
 Error_Calc = True
 LID = "internal"
 EID = "internal"
 # --- IL Laser IL and +-Uncertainty
 DOLP, dDOLP, nDOLP = 0.995, 0.005, 1  # degree of linear polarization; default 1
 RotL, dRotL, nRotL = 0.0, 0.0, 1  # alpha; rotation of laser polarization in degrees; default 0
 # --- ME Emitter and +-Uncertainty
 DiE, dDiE, nDiE = 0., 0.00, 1  # Diattenuation
 TiE = 1.  # Unpolarized transmittance
 RetE, dRetE, nRetE = 0., 180.0, 0  # Retardance in degrees
 RotE, dRotE, nRotE = 0., 0.0, 0  # beta: Rotation of optical element in degrees
 # --- MO Receiver Optics including telescope
 DiO, dDiO, nDiO = -0.055, 0.003, 1
 TiO = 0.9
 RetO, dRetO, nRetO = 0., 180.0, 2
 RotO, dRotO, nRotO = 0., 0.1, 1  # gamma
 # --- PBS MT transmitting path defined with (TS,TP);  and +-Uncertainty
 TP, dTP, nTP = 0.98, 0.02, 1
 TS, dTS, nTS = 0.001, 0.001, 1
 TiT = 0.5 * (TP + TS)
 DiT = (TP - TS) / (TP + TS)
 # PolFilter
 RetT, dRetT, nRetT = 0., 180., 0
 ERaT, dERaT, nERaT = 0.001, 0.001, 1
 RotaT, dRotaT, nRotaT = 0., 3., 1
 DaT = (1 - ERaT) / (1 + ERaT)
 TaT = 0.5 * (1 + ERaT)
 # --- PBS MR reflecting path defined with (RS,RP);  and +-Uncertainty
 RS_RP_depend_on_TS_TP = False
 if (RS_RP_depend_on_TS_TP):
     RP, dRP, nRP = 1 - TP, 0.00, 0
     RS, dRS, nRS = 1 - TS, 0.00, 0
 else:
     RP, dRP, nRP = 0.05, 0.01, 1
     RS, dRS, nRS = 0.98, 0.01, 1
 TiR = 0.5 * (RP + RS)
 DiR = (RP - RS) / (RP + RS)
 # PolFilter
 RetR, dRetR, nRetR = 0., 180., 0
 ERaR, dERaR, nERaR = 0.001, 0.001, 1
 RotaR, dRotaR, nRotaR = 90., 3., 1
 DaR = (1 - ERaR) / (1 + ERaR)
 TaR = 0.5 * (1 + ERaR)
 # Parellel signal detected in the transmitted channel => Y = 1, or in the reflected channel => Y = -1
 Y = -1.
 # Calibrator =  type defined by matrix values
 LocC = 4  # location of calibrator: behind laser = 1; behind emitter = 2; before receiver = 3; before PBS = 4
 TypeC = 3  # linear polarizer calibrator
 # example with extinction ratio 0.001
 DiC, dDiC, nDiC = 1.0, 0., 0  # ideal 1.0
 TiC = 0.5  # ideal 0.5
 RetC, dRetC, nRetC = 0., 0., 0
 RotC, dRotC, nRotC = 0.0, 0.1, 0  # constant calibrator offset epsilon
 RotationErrorEpsilonForNormalMeasurements = False  # is in general False for TypeC == 3 calibrator
 # Rotation error without calibrator: if False, then epsilon = 0 for normal measurements
 RotationErrorEpsilonForNormalMeasurements = True
 # LDRCal assumed atmospheric linear depolarization ratio during the calibration measurements (first guess)
 LDRCal0, dLDRCal, nLDRCal = 0.25, 0.04, 1
 LDRCal = LDRCal0
 # measured LDRm will be corrected with calculated parameters
 LDRmeas = 0.015
 # LDRtrue for simulation of measurement => LDRsim
 LDRtrue = 0.5
 LDRtrue2 = 0.004
 # Initialize other values to 0
 ER, nER, dER = 0.001, 0, 0.001
 K = 0.
 Km = 0.
 Kp = 0.
 LDRcorr = 0.
 Eta = 0.
 Ir = 0.
 It = 0.
 h = 1.
 Loc = ['', 'behind laser', 'behind emitter', 'before receiver', 'before PBS']
 Type = ['', 'mechanical rotator', 'hwp rotator', 'linear polarizer', 'qwp rotator', 'circular polarizer',
         'real HWP +-22.5°']
 dY = ['reflected channel', '', 'transmitted channel']
 #  end of initial definition of variables
 # *******************************************************************************************************************************
 # --- Read actual lidar system parameters from optic_input.py  (should be in sub-directory 'system_settings')
 InputFile = 'optic_input_crossed_mirrors_test.py'
 InputFile = 'optic_input_crossed_mirrors_test_combined.py'
 InputFile = 'optic_input_ver8c_POLIS_355_Mar2017.py'
 # InputFile = 'optic_input_ver8c_POLIS_532_Mar2017.py'
 InputFile = 'optic_input_example_lidar_0.9.5.py'
 InputFile = 'optic_input_ver8c_PollyXT_532_Lacros.py'
 InputFile = 'optic_input_ver8c_CUT_532_May2017.py'
 InputFile = 'optic_input_ver8c_MUSA.py'
 InputFile = 'optic_input_ver10_RALI_JA.py'
 InputFile = 'optic_input_ver10_RALI_act.py'
 InputFile = 'optic_input_ver8c-IPRAL-170331.py'
 '''
 print("From ", dname)
 print("Running ", fname)
 print("Reading input file ", InputFile, " for")
 '''
 input_path = os.path.join('.', 'system_settings', InputFile)
 # this works with Python 2 and 3!
 exec (open(input_path).read(), globals())
 #  end of read actual system parameters
 # --- Manual Parameter Change ---
 #  (use for quick parameter changes without changing the input file )
 # DiO = 0.
 # LDRtrue = 0.45
 # LDRtrue2 = 0.004
 # Y = -1
 # LocC = 4 #location of calibrator: 1 = behind laser; 2 = behind emitter; 3 = before receiver; 4 = before PBS
 ##TypeC = 6  Don't change the TypeC here
 # RotationErrorEpsilonForNormalMeasurements = True
 # LDRCal = 0.25
 ## --- Errors
 DOLP0, dDOLP, nDOLP = DOLP, dDOLP, nDOLP
 RotL0, dRotL, nRotL = RotL, dRotL, nRotL
 DiE0, dDiE, nDiE = DiE, dDiE, nDiE
 RetE0, dRetE, nRetE = RetE, dRetE, nRetE
 RotE0, dRotE, nRotE = RotE, dRotE, nRotE
 DiO0, dDiO, nDiO = DiO, dDiO, nDiO
 RetO0, dRetO, nRetO = RetO, dRetO, nRetO
 RotO0, dRotO, nRotO = RotO, dRotO, nRotO
 DiC0, dDiC, nDiC = DiC, dDiC, nDiC
 RetC0, dRetC, nRetC = RetC, dRetC, nRetC
 RotC0, dRotC, nRotC = RotC, dRotC, nRotC
 TP0, dTP, nTP = TP, dTP, nTP
 TS0, dTS, nTS = TS, dTS, nTS
 RetT0, dRetT, nRetT = RetT, dRetT, nRetT
 ERaT0, dERaT, nERaT = ERaT, dERaT, nERaT
 RotaT0, dRotaT, nRotaT = RotaT, dRotaT, nRotaT
 RP0, dRP, nRP = RP, dRP, nRP
 RS0, dRS, nRS = RS, dRS, nRS
 RetR0, dRetR, nRetR = RetR, dRetR, nRetR
 ERaR0, dERaR, nERaR = ERaR, dERaR, nERaR
 RotaR0, dRotaR, nRotaR = RotaR, dRotaR, nRotaR
 LDRCal0, dLDRCal, nLDRCal = LDRCal, dLDRCal, nLDRCal
 # LDRCal0,dLDRCal,nLDRCal=LDRCal,dLDRCal,0
 # ---------- End of manual parameter change
 RotL, RotE, RetE, DiE, RotO, RetO, DiO, RotC, RetC, DiC = RotL0, RotE0, RetE0, DiE0, RotO0, RetO0, DiO0, RotC0, RetC0, DiC0
 TP, TS, RP, RS, ERaT, RotaT, RetT, ERaR, RotaR, RetR = TP0, TS0, RP0, RS0, ERaT0, RotaT0, RetT0, ERaR0, RotaR0, RetR0
 LDRCal = LDRCal0
 DTa0, TTa0, DRa0, TRa0, LDRsimx, LDRCorr = 0, 0, 0, 0, 0, 0
 TiT = 0.5 * (TP + TS)
 DiT = (TP - TS) / (TP + TS)
 ZiT = (1. - DiT ** 2) ** 0.5
 TiR = 0.5 * (RP + RS)
 DiR = (RP - RS) / (RP + RS)
 ZiR = (1. - DiR ** 2) ** 0.5
 # --- this subroutine is for the calculation with certain fixed parameters -----------------------------------------------------
 def Calc(DOLP, RotL, RotE, RetE, DiE, RotO, RetO, DiO, RotC, RetC, DiC, TP, TS, RP, RS, ERaT, RotaT, RetT, ERaR, RotaR, RetR,
          LDRCal):
     # ---- Do the calculations of bra-ket vectors
     h = -1. if TypeC == 2 else 1
     # from input file:  assumed LDRCal for calibration measurements
     aCal = (1. - LDRCal) / (1 + LDRCal)
     # from input file: measured LDRm and true LDRtrue, LDRtrue2  =>
     # ameas = (1.-LDRmeas)/(1+LDRmeas)
     atrue = (1. - LDRtrue) / (1 + LDRtrue)
     # atrue2 = (1.-LDRtrue2)/(1+LDRtrue2)
     # angles of emitter and laser and calibrator and receiver optics
     # RotL = alpha, RotE = beta, RotO = gamma, RotC = epsilon
     S2a = np.sin(2 * np.deg2rad(RotL))
     C2a = np.cos(2 * np.deg2rad(RotL))
     S2b = np.sin(2 * np.deg2rad(RotE))
     C2b = np.cos(2 * np.deg2rad(RotE))
     S2ab = np.sin(np.deg2rad(2 * RotL - 2 * RotE))
     C2ab = np.cos(np.deg2rad(2 * RotL - 2 * RotE))
     S2g = np.sin(np.deg2rad(2 * RotO))
     C2g = np.cos(np.deg2rad(2 * RotO))
     # Laser with Degree of linear polarization DOLP
     IinL = 1.
     QinL = DOLP
     UinL = 0.
     VinL = (1. - DOLP ** 2) ** 0.5
     # Stokes Input Vector rotation Eq. E.4
     A = C2a * QinL - S2a * UinL
     B = S2a * QinL + C2a * UinL
     # Stokes Input Vector rotation Eq. E.9
     C = C2ab * QinL - S2ab * UinL
     D = S2ab * QinL + C2ab * UinL
     # emitter optics
     CosE = np.cos(np.deg2rad(RetE))
     SinE = np.sin(np.deg2rad(RetE))
     ZiE = (1. - DiE ** 2) ** 0.5
     WiE = (1. - ZiE * CosE)
     # Stokes Input Vector after emitter optics equivalent to Eq. E.9 with already rotated input vector from Eq. E.4
     # b = beta
     IinE = (IinL + DiE * C)
     QinE = (C2b * DiE * IinL + A + S2b * (WiE * D - ZiE * SinE * VinL))
     UinE = (S2b * DiE * IinL + B - C2b * (WiE * D - ZiE * SinE * VinL))
     VinE = (-ZiE * SinE * D + ZiE * CosE * VinL)
     # Stokes Input Vector before receiver optics Eq. E.19 (after atmosphere F)
     IinF = IinE
     QinF = aCal * QinE
     UinF = -aCal * UinE
     VinF = (1. - 2. * aCal) * VinE
     # receiver optics
     CosO = np.cos(np.deg2rad(RetO))
     SinO = np.sin(np.deg2rad(RetO))
     ZiO = (1. - DiO ** 2) ** 0.5
     WiO = (1. - ZiO * CosO)
     # calibrator
     CosC = np.cos(np.deg2rad(RetC))
     SinC = np.sin(np.deg2rad(RetC))
     ZiC = (1. - DiC ** 2) ** 0.5
     WiC = (1. - ZiC * CosC)
     # Stokes Input Vector before the polarising beam splitter Eq. E.31
     A = C2g * QinE - S2g * UinE
     B = S2g * QinE + C2g * UinE
     IinP = (IinE + DiO * aCal * A)
     QinP = (C2g * DiO * IinE + aCal * QinE - S2g * (WiO * aCal * B + ZiO * SinO * (1 - 2 * aCal) * VinE))
     UinP = (S2g * DiO * IinE - aCal * UinE + C2g * (WiO * aCal * B + ZiO * SinO * (1 - 2 * aCal) * VinE))
     VinP = (ZiO * SinO * aCal * B + ZiO * CosO * (1 - 2 * aCal) * VinE)
     # -------------------------
     # F11 assuemd to be = 1  => measured: F11m = IinP / IinE with atrue
     # F11sim = TiO*(IinE + DiO*atrue*A)/IinE
     # -------------------------
     # analyser
     if (RS_RP_depend_on_TS_TP):
         RS = 1 - TS
         RP = 1 - TP
     TiT = 0.5 * (TP + TS)
     DiT = (TP - TS) / (TP + TS)
     ZiT = (1. - DiT ** 2) ** 0.5
     TiR = 0.5 * (RP + RS)
     DiR = (RP - RS) / (RP + RS)
     ZiR = (1. - DiR ** 2) ** 0.5
     CosT = np.cos(np.deg2rad(RetT))
     SinT = np.sin(np.deg2rad(RetT))
     CosR = np.cos(np.deg2rad(RetR))
     SinR = np.sin(np.deg2rad(RetR))
     DaT = (1 - ERaT) / (1 + ERaT)
     DaR = (1 - ERaR) / (1 + ERaR)
     TaT = 0.5 * (1 + ERaT)
     TaR = 0.5 * (1 + ERaR)
     S2aT = np.sin(np.deg2rad(h * 2 * RotaT))
     C2aT = np.cos(np.deg2rad(2 * RotaT))
     S2aR = np.sin(np.deg2rad(h * 2 * RotaR))
     C2aR = np.cos(np.deg2rad(2 * RotaR))
     # Analyzer As before the PBS Eq. D.5
     ATP1 = (1 + C2aT * DaT * DiT)
     ATP2 = Y * (DiT + C2aT * DaT)
     ATP3 = Y * S2aT * DaT * ZiT * CosT
     ATP4 = S2aT * DaT * ZiT * SinT
     ATP = np.array([ATP1, ATP2, ATP3, ATP4])
     ARP1 = (1 + C2aR * DaR * DiR)
     ARP2 = Y * (DiR + C2aR * DaR)
     ARP3 = Y * S2aR * DaR * ZiR * CosR
     ARP4 = S2aR * DaR * ZiR * SinR
     ARP = np.array([ARP1, ARP2, ARP3, ARP4])
     DTa = ATP2 * Y / ATP1
     DRa = ARP2 * Y / ARP1
     # ---- Calculate signals and correction parameters for diffeent locations and calibrators
     if LocC == 4:  # Calibrator before the PBS
         # print("Calibrator location not implemented yet")
         # S2ge = np.sin(np.deg2rad(2*RotO + h*2*RotC))
         # C2ge = np.cos(np.deg2rad(2*RotO + h*2*RotC))
         S2e = np.sin(np.deg2rad(h * 2 * RotC))
         C2e = np.cos(np.deg2rad(2 * RotC))
         # rotated AinP by epsilon Eq. C.3
         ATP2e = C2e * ATP2 + S2e * ATP3
         ATP3e = C2e * ATP3 - S2e * ATP2
         ARP2e = C2e * ARP2 + S2e * ARP3
         ARP3e = C2e * ARP3 - S2e * ARP2
         ATPe = np.array([ATP1, ATP2e, ATP3e, ATP4])
         ARPe = np.array([ARP1, ARP2e, ARP3e, ARP4])
         # Stokes Input Vector before the polarising beam splitter Eq. E.31
         A = C2g * QinE - S2g * UinE
         B = S2g * QinE + C2g * UinE
         # C = (WiO*aCal*B + ZiO*SinO*(1-2*aCal)*VinE)
         Co = ZiO * SinO * VinE
         Ca = (WiO * B - 2 * ZiO * SinO * VinE)
         # C = Co + aCal*Ca
         # IinP = (IinE + DiO*aCal*A)
         # QinP = (C2g*DiO*IinE + aCal*QinE - S2g*C)
         # UinP = (S2g*DiO*IinE - aCal*UinE + C2g*C)
         # VinP = (ZiO*SinO*aCal*B + ZiO*CosO*(1-2*aCal)*VinE)
         IinPo = IinE
         QinPo = (C2g * DiO * IinE - S2g * Co)
         UinPo = (S2g * DiO * IinE + C2g * Co)
         VinPo = ZiO * CosO * VinE
         IinPa = DiO * A
         QinPa = QinE - S2g * Ca
         UinPa = -UinE + C2g * Ca
         VinPa = ZiO * (SinO * B - 2 * CosO * VinE)
         IinP = IinPo + aCal * IinPa
         QinP = QinPo + aCal * QinPa
         UinP = UinPo + aCal * UinPa
         VinP = VinPo + aCal * VinPa
         # Stokes Input Vector before the polarising beam splitter rotated by epsilon Eq. C.3
         # QinPe = C2e*QinP + S2e*UinP
         # UinPe = C2e*UinP - S2e*QinP
         QinPoe = C2e * QinPo + S2e * UinPo
         UinPoe = C2e * UinPo - S2e * QinPo
         QinPae = C2e * QinPa + S2e * UinPa
         UinPae = C2e * UinPa - S2e * QinPa
         QinPe = C2e * QinP + S2e * UinP
         UinPe = C2e * UinP - S2e * QinP
         # Calibration signals and Calibration correction K from measurements with LDRCal / aCal
         if (TypeC == 2) or (TypeC == 1):  # rotator calibration Eq. C.4
             # parameters for calibration with aCal
             AT = ATP1 * IinP + h * ATP4 * VinP
             BT = ATP3e * QinP - h * ATP2e * UinP
             AR = ARP1 * IinP + h * ARP4 * VinP
             BR = ARP3e * QinP - h * ARP2e * UinP
             # Correction parameters for normal measurements; they are independent of LDR
             if (not RotationErrorEpsilonForNormalMeasurements):  # calibrator taken out
                 IS1 = np.array([IinPo, QinPo, UinPo, VinPo])
                 IS2 = np.array([IinPa, QinPa, UinPa, VinPa])
                 GT = np.dot(ATP, IS1)
                 GR = np.dot(ARP, IS1)
                 HT = np.dot(ATP, IS2)
                 HR = np.dot(ARP, IS2)
             else:
                 IS1 = np.array([IinPo, QinPo, UinPo, VinPo])
                 IS2 = np.array([IinPa, QinPa, UinPa, VinPa])
                 GT = np.dot(ATPe, IS1)
                 GR = np.dot(ARPe, IS1)
                 HT = np.dot(ATPe, IS2)
                 HR = np.dot(ARPe, IS2)
         elif (TypeC == 3) or (TypeC == 4):  # linear polariser calibration Eq. C.5
             # parameters for calibration with aCal
             AT = ATP1 * IinP + ATP3e * UinPe + ZiC * CosC * (ATP2e * QinPe + ATP4 * VinP)
             BT = DiC * (ATP1 * UinPe + ATP3e * IinP) - ZiC * SinC * (ATP2e * VinP - ATP4 * QinPe)
             AR = ARP1 * IinP + ARP3e * UinPe + ZiC * CosC * (ARP2e * QinPe + ARP4 * VinP)
             BR = DiC * (ARP1 * UinPe + ARP3e * IinP) - ZiC * SinC * (ARP2e * VinP - ARP4 * QinPe)
             # Correction parameters for normal measurements; they are independent of LDR
             if (not RotationErrorEpsilonForNormalMeasurements):  # calibrator taken out
                 IS1 = np.array([IinPo, QinPo, UinPo, VinPo])
                 IS2 = np.array([IinPa, QinPa, UinPa, VinPa])
                 GT = np.dot(ATP, IS1)
                 GR = np.dot(ARP, IS1)
                 HT = np.dot(ATP, IS2)
                 HR = np.dot(ARP, IS2)
             else:
                 IS1e = np.array([IinPo + DiC * QinPoe, DiC * IinPo + QinPoe, ZiC * (CosC * UinPoe + SinC * VinPo),
                                  -ZiC * (SinC * UinPoe - CosC * VinPo)])
                 IS2e = np.array([IinPa + DiC * QinPae, DiC * IinPa + QinPae, ZiC * (CosC * UinPae + SinC * VinPa),
                                  -ZiC * (SinC * UinPae - CosC * VinPa)])
                 GT = np.dot(ATPe, IS1e)
                 GR = np.dot(ARPe, IS1e)
                 HT = np.dot(ATPe, IS2e)
                 HR = np.dot(ARPe, IS2e)
         elif (TypeC == 6):  # diattenuator calibration +-22.5° rotated_diattenuator_X22x5deg.odt
             # parameters for calibration with aCal
             AT = ATP1 * IinP + sqr05 * DiC * (ATP1 * QinPe + ATP2e * IinP) + (1 - 0.5 * WiC) * (
             ATP2e * QinPe + ATP3e * UinPe) + ZiC * (sqr05 * SinC * (ATP3e * VinP - ATP4 * UinPe) + ATP4 * CosC * VinP)
             BT = sqr05 * DiC * (ATP1 * UinPe + ATP3e * IinP) + 0.5 * WiC * (
             ATP2e * UinPe + ATP3e * QinPe) - sqr05 * ZiC * SinC * (ATP2e * VinP - ATP4 * QinPe)
             AR = ARP1 * IinP + sqr05 * DiC * (ARP1 * QinPe + ARP2e * IinP) + (1 - 0.5 * WiC) * (
             ARP2e * QinPe + ARP3e * UinPe) + ZiC * (sqr05 * SinC * (ARP3e * VinP - ARP4 * UinPe) + ARP4 * CosC * VinP)
             BR = sqr05 * DiC * (ARP1 * UinPe + ARP3e * IinP) + 0.5 * WiC * (
             ARP2e * UinPe + ARP3e * QinPe) - sqr05 * ZiC * SinC * (ARP2e * VinP - ARP4 * QinPe)
             # Correction parameters for normal measurements; they are independent of LDR
             if (not RotationErrorEpsilonForNormalMeasurements):  # calibrator taken out
                 IS1 = np.array([IinPo, QinPo, UinPo, VinPo])
                 IS2 = np.array([IinPa, QinPa, UinPa, VinPa])
                 GT = np.dot(ATP, IS1)
                 GR = np.dot(ARP, IS1)
                 HT = np.dot(ATP, IS2)
                 HR = np.dot(ARP, IS2)
             else:
                 IS1e = np.array([IinPo + DiC * QinPoe, DiC * IinPo + QinPoe, ZiC * (CosC * UinPoe + SinC * VinPo),
                                  -ZiC * (SinC * UinPoe - CosC * VinPo)])
                 IS2e = np.array([IinPa + DiC * QinPae, DiC * IinPa + QinPae, ZiC * (CosC * UinPae + SinC * VinPa),
                                  -ZiC * (SinC * UinPae - CosC * VinPa)])
                 GT = np.dot(ATPe, IS1e)
                 GR = np.dot(ARPe, IS1e)
                 HT = np.dot(ATPe, IS2e)
                 HR = np.dot(ARPe, IS2e)
         else:
             print("Calibrator not implemented yet")
             sys.exit()
     elif LocC == 3:  # C before receiver optics Eq.57
         # S2ge = np.sin(np.deg2rad(2*RotO - 2*RotC))
         # C2ge = np.cos(np.deg2rad(2*RotO - 2*RotC))
         S2e = np.sin(np.deg2rad(2 * RotC))
         C2e = np.cos(np.deg2rad(2 * RotC))
         # As with C before the receiver optics (rotated_diattenuator_X22x5deg.odt)
         AF1 = np.array([1, C2g * DiO, S2g * DiO, 0])
         AF2 = np.array([C2g * DiO, 1 - S2g ** 2 * WiO, S2g * C2g * WiO, -S2g * ZiO * SinO])
         AF3 = np.array([S2g * DiO, S2g * C2g * WiO, 1 - C2g ** 2 * WiO, C2g * ZiO * SinO])
         AF4 = np.array([0, S2g * SinO, -C2g * SinO, CosO])
         ATF = (ATP1 * AF1 + ATP2 * AF2 + ATP3 * AF3 + ATP4 * AF4)
         ARF = (ARP1 * AF1 + ARP2 * AF2 + ARP3 * AF3 + ARP4 * AF4)
         ATF2 = ATF[1]
         ATF3 = ATF[2]
         ARF2 = ARF[1]
         ARF3 = ARF[2]
         # rotated AinF by epsilon
         ATF1 = ATF[0]
         ATF4 = ATF[3]
         ATF2e = C2e * ATF[1] + S2e * ATF[2]
         ATF3e = C2e * ATF[2] - S2e * ATF[1]
         ARF1 = ARF[0]
         ARF4 = ARF[3]
         ARF2e = C2e * ARF[1] + S2e * ARF[2]
         ARF3e = C2e * ARF[2] - S2e * ARF[1]
         ATFe = np.array([ATF1, ATF2e, ATF3e, ATF4])
         ARFe = np.array([ARF1, ARF2e, ARF3e, ARF4])
         QinEe = C2e * QinE + S2e * UinE
         UinEe = C2e * UinE - S2e * QinE
         # Stokes Input Vector before receiver optics Eq. E.19 (after atmosphere F)
         IinF = IinE
         QinF = aCal * QinE
         UinF = -aCal * UinE
         VinF = (1. - 2. * aCal) * VinE
         IinFo = IinE
         QinFo = 0.
         UinFo = 0.
         VinFo = VinE
         IinFa = 0.
         QinFa = QinE
         UinFa = -UinE
         VinFa = -2. * VinE
         # Stokes Input Vector before receiver optics rotated by epsilon Eq. C.3
         QinFe = C2e * QinF + S2e * UinF
         UinFe = C2e * UinF - S2e * QinF
         QinFoe = C2e * QinFo + S2e * UinFo
         UinFoe = C2e * UinFo - S2e * QinFo
         QinFae = C2e * QinFa + S2e * UinFa
         UinFae = C2e * UinFa - S2e * QinFa
         # Calibration signals and Calibration correction K from measurements with LDRCal / aCal
         if (TypeC == 2) or (TypeC == 1):  # rotator calibration Eq. C.4
             # parameters for calibration with aCal
             AT = ATF1 * IinF + ATF4 * h * VinF
             BT = ATF3e * QinF - ATF2e * h * UinF
             AR = ARF1 * IinF + ARF4 * h * VinF
             BR = ARF3e * QinF - ARF2e * h * UinF
             # Correction parameters for normal measurements; they are independent of LDR
             if (not RotationErrorEpsilonForNormalMeasurements):
                 GT = ATF1 * IinE + ATF4 * VinE
                 GR = ARF1 * IinE + ARF4 * VinE
                 HT = ATF2 * QinE - ATF3 * UinE - ATF4 * 2 * VinE
                 HR = ARF2 * QinE - ARF3 * UinE - ARF4 * 2 * VinE
             else:
                 GT = ATF1 * IinE + ATF4 * h * VinE
                 GR = ARF1 * IinE + ARF4 * h * VinE
                 HT = ATF2e * QinE - ATF3e * h * UinE - ATF4 * h * 2 * VinE
                 HR = ARF2e * QinE - ARF3e * h * UinE - ARF4 * h * 2 * VinE
         elif (TypeC == 3) or (TypeC == 4):  # linear polariser calibration Eq. C.5
             # p = +45°, m = -45°
             IF1e = np.array([IinF, ZiC * CosC * QinFe, UinFe, ZiC * CosC * VinF])
             IF2e = np.array([DiC * UinFe, -ZiC * SinC * VinF, DiC * IinF, ZiC * SinC * QinFe])
             AT = np.dot(ATFe, IF1e)
             AR = np.dot(ARFe, IF1e)
             BT = np.dot(ATFe, IF2e)
             BR = np.dot(ARFe, IF2e)
             # Correction parameters for normal measurements; they are independent of LDR  --- the same as for TypeC = 6
             if (not RotationErrorEpsilonForNormalMeasurements):  # calibrator taken out
                 IS1 = np.array([IinE, 0, 0, VinE])
                 IS2 = np.array([0, QinE, -UinE, -2 * VinE])
                 GT = np.dot(ATF, IS1)
                 GR = np.dot(ARF, IS1)
                 HT = np.dot(ATF, IS2)
                 HR = np.dot(ARF, IS2)
             else:
                 IS1e = np.array([IinFo + DiC * QinFoe, DiC * IinFo + QinFoe, ZiC * (CosC * UinFoe + SinC * VinFo),
                                  -ZiC * (SinC * UinFoe - CosC * VinFo)])
                 IS2e = np.array([IinFa + DiC * QinFae, DiC * IinFa + QinFae, ZiC * (CosC * UinFae + SinC * VinFa),
                                  -ZiC * (SinC * UinFae - CosC * VinFa)])
                 GT = np.dot(ATFe, IS1e)
                 GR = np.dot(ARFe, IS1e)
                 HT = np.dot(ATFe, IS2e)
                 HR = np.dot(ARFe, IS2e)
         elif (TypeC == 6):  # diattenuator calibration +-22.5° rotated_diattenuator_X22x5deg.odt
             # parameters for calibration with aCal
             IF1e = np.array([IinF + sqr05 * DiC * QinFe, sqr05 * DiC * IinF + (1 - 0.5 * WiC) * QinFe,
                              (1 - 0.5 * WiC) * UinFe + sqr05 * ZiC * SinC * VinF,
                              -sqr05 * ZiC * SinC * UinFe + ZiC * CosC * VinF])
             IF2e = np.array([sqr05 * DiC * UinFe, 0.5 * WiC * UinFe - sqr05 * ZiC * SinC * VinF,
                              sqr05 * DiC * IinF + 0.5 * WiC * QinFe, sqr05 * ZiC * SinC * QinFe])
             AT = np.dot(ATFe, IF1e)
             AR = np.dot(ARFe, IF1e)
             BT = np.dot(ATFe, IF2e)
             BR = np.dot(ARFe, IF2e)
             # Correction parameters for normal measurements; they are independent of LDR
             if (not RotationErrorEpsilonForNormalMeasurements):  # calibrator taken out
                 # IS1 = np.array([IinE,0,0,VinE])
                 # IS2 = np.array([0,QinE,-UinE,-2*VinE])
                 IS1 = np.array([IinFo, 0, 0, VinFo])
                 IS2 = np.array([0, QinFa, UinFa, VinFa])
                 GT = np.dot(ATF, IS1)
                 GR = np.dot(ARF, IS1)
                 HT = np.dot(ATF, IS2)
                 HR = np.dot(ARF, IS2)
             else:
                 IS1e = np.array([IinFo + DiC * QinFoe, DiC * IinFo + QinFoe, ZiC * (CosC * UinFoe + SinC * VinFo),
                                  -ZiC * (SinC * UinFoe - CosC * VinFo)])
                 IS2e = np.array([IinFa + DiC * QinFae, DiC * IinFa + QinFae, ZiC * (CosC * UinFae + SinC * VinFa),
                                  -ZiC * (SinC * UinFae - CosC * VinFa)])
                 # IS1e = np.array([IinFo,0,0,VinFo])
                 # IS2e = np.array([0,QinFae,UinFae,VinFa])
                 GT = np.dot(ATFe, IS1e)
                 GR = np.dot(ARFe, IS1e)
                 HT = np.dot(ATFe, IS2e)
                 HR = np.dot(ARFe, IS2e)
         else:
             print('Calibrator not implemented yet')
             sys.exit()
     elif LocC == 2:  # C behind emitter optics Eq.57 -------------------------------------------------------
         # print("Calibrator location not implemented yet")
         S2e = np.sin(np.deg2rad(2 * RotC))
         C2e = np.cos(np.deg2rad(2 * RotC))
         # AS with C before the receiver optics (see document rotated_diattenuator_X22x5deg.odt)
         AF1 = np.array([1, C2g * DiO, S2g * DiO, 0])
         AF2 = np.array([C2g * DiO, 1 - S2g ** 2 * WiO, S2g * C2g * WiO, -S2g * ZiO * SinO])
         AF3 = np.array([S2g * DiO, S2g * C2g * WiO, 1 - C2g ** 2 * WiO, C2g * ZiO * SinO])
         AF4 = np.array([0, S2g * SinO, -C2g * SinO, CosO])
         ATF = (ATP1 * AF1 + ATP2 * AF2 + ATP3 * AF3 + ATP4 * AF4)
         ARF = (ARP1 * AF1 + ARP2 * AF2 + ARP3 * AF3 + ARP4 * AF4)
         ATF1 = ATF[0]
         ATF2 = ATF[1]
         ATF3 = ATF[2]
         ATF4 = ATF[3]
         ARF1 = ARF[0]
         ARF2 = ARF[1]
         ARF3 = ARF[2]
         ARF4 = ARF[3]
         # AS with C behind the emitter
         # terms without aCal
         ATE1o, ARE1o = ATF1, ARF1
         ATE2o, ARE2o = 0., 0.
         ATE3o, ARE3o = 0., 0.
         ATE4o, ARE4o = ATF4, ARF4
         # terms with aCal
         ATE1a, ARE1a = 0., 0.
         ATE2a, ARE2a = ATF2, ARF2
         ATE3a, ARE3a = -ATF3, -ARF3
         ATE4a, ARE4a = -2 * ATF4, -2 * ARF4
         # rotated AinEa by epsilon
         ATE2ae = C2e * ATF2 + S2e * ATF3
         ATE3ae = -S2e * ATF2 - C2e * ATF3
         ARE2ae = C2e * ARF2 + S2e * ARF3
         ARE3ae = -S2e * ARF2 - C2e * ARF3
         ATE1 = ATE1o
         ATE2e = aCal * ATE2ae
         ATE3e = aCal * ATE3ae
         ATE4 = (1 - 2 * aCal) * ATF4
         ARE1 = ARE1o
         ARE2e = aCal * ARE2ae
         ARE3e = aCal * ARE3ae
         ARE4 = (1 - 2 * aCal) * ARF4
         # rotated IinE
         QinEe = C2e * QinE + S2e * UinE
         UinEe = C2e * UinE - S2e * QinE
         # Calibration signals and Calibration correction K from measurements with LDRCal / aCal
         if (TypeC == 2) or (TypeC == 1):  # +++++++++ rotator calibration Eq. C.4
             AT = ATE1o * IinE + (ATE4o + aCal * ATE4a) * h * VinE
             BT = aCal * (ATE3ae * QinEe - ATE2ae * h * UinEe)
             AR = ARE1o * IinE + (ARE4o + aCal * ARE4a) * h * VinE
             BR = aCal * (ARE3ae * QinEe - ARE2ae * h * UinEe)
             # Correction parameters for normal measurements; they are independent of LDR
             if (not RotationErrorEpsilonForNormalMeasurements):
                 # Stokes Input Vector before receiver optics Eq. E.19 (after atmosphere F)
                 GT = ATE1o * IinE + ATE4o * h * VinE
                 GR = ARE1o * IinE + ARE4o * h * VinE
                 HT = ATE2a * QinE + ATE3a * h * UinEe + ATE4a * h * VinE
                 HR = ARE2a * QinE + ARE3a * h * UinEe + ARE4a * h * VinE
             else:
                 GT = ATE1o * IinE + ATE4o * h * VinE
                 GR = ARE1o * IinE + ARE4o * h * VinE
                 HT = ATE2ae * QinE + ATE3ae * h * UinEe + ATE4a * h * VinE
                 HR = ARE2ae * QinE + ARE3ae * h * UinEe + ARE4a * h * VinE
         elif (TypeC == 3) or (TypeC == 4):  # +++++++++ linear polariser calibration Eq. C.5
             # p = +45°, m = -45°
             AT = ATE1 * IinE + ZiC * CosC * (ATE2e * QinEe + ATE4 * VinE) + ATE3e * UinEe
             BT = DiC * (ATE1 * UinEe + ATE3e * IinE) + ZiC * SinC * (ATE4 * QinEe - ATE2e * VinE)
             AR = ARE1 * IinE + ZiC * CosC * (ARE2e * QinEe + ARE4 * VinE) + ARE3e * UinEe
             BR = DiC * (ARE1 * UinEe + ARE3e * IinE) + ZiC * SinC * (ARE4 * QinEe - ARE2e * VinE)
             # Correction parameters for normal measurements; they are independent of LDR
             if (not RotationErrorEpsilonForNormalMeasurements):
                 # Stokes Input Vector before receiver optics Eq. E.19 (after atmosphere F)
                 GT = ATE1o * IinE + ATE4o * VinE
                 GR = ARE1o * IinE + ARE4o * VinE
                 HT = ATE2a * QinE + ATE3a * UinE + ATE4a * VinE
                 HR = ARE2a * QinE + ARE3a * UinE + ARE4a * VinE
             else:
                 D = IinE + DiC * QinEe
                 A = DiC * IinE + QinEe
                 B = ZiC * (CosC * UinEe + SinC * VinE)
                 C = -ZiC * (SinC * UinEe - CosC * VinE)
                 GT = ATE1o * D + ATE4o * C
                 GR = ARE1o * D + ARE4o * C
                 HT = ATE2a * A + ATE3a * B + ATE4a * C
                 HR = ARE2a * A + ARE3a * B + ARE4a * C
         elif (TypeC == 6):  # real HWP calibration +-22.5° rotated_diattenuator_X22x5deg.odt
             # p = +22.5°, m = -22.5°
             IE1e = np.array([IinE + sqr05 * DiC * QinEe, sqr05 * DiC * IinE + (1 - 0.5 * WiC) * QinEe,
                              (1 - 0.5 * WiC) * UinEe + sqr05 * ZiC * SinC * VinE,
                              -sqr05 * ZiC * SinC * UinEe + ZiC * CosC * VinE])
             IE2e = np.array([sqr05 * DiC * UinEe, 0.5 * WiC * UinEe - sqr05 * ZiC * SinC * VinE,
                              sqr05 * DiC * IinE + 0.5 * WiC * QinEe, sqr05 * ZiC * SinC * QinEe])
             ATEe = np.array([ATE1, ATE2e, ATE3e, ATE4])
             AREe = np.array([ARE1, ARE2e, ARE3e, ARE4])
             AT = np.dot(ATEe, IE1e)
             AR = np.dot(AREe, IE1e)
             BT = np.dot(ATEe, IE2e)
             BR = np.dot(AREe, IE2e)
             # Correction parameters for normal measurements; they are independent of LDR
             if (not RotationErrorEpsilonForNormalMeasurements):  # calibrator taken out
                 GT = ATE1o * IinE + ATE4o * VinE
                 GR = ARE1o * IinE + ARE4o * VinE
                 HT = ATE2a * QinE + ATE3a * UinE + ATE4a * VinE
                 HR = ARE2a * QinE + ARE3a * UinE + ARE4a * VinE
             else:
                 D = IinE + DiC * QinEe
                 A = DiC * IinE + QinEe
                 B = ZiC * (CosC * UinEe + SinC * VinE)
                 C = -ZiC * (SinC * UinEe - CosC * VinE)
                 GT = ATE1o * D + ATE4o * C
                 GR = ARE1o * D + ARE4o * C
                 HT = ATE2a * A + ATE3a * B + ATE4a * C
                 HR = ARE2a * A + ARE3a * B + ARE4a * C
         else:
             print('Calibrator not implemented yet')
             sys.exit()
     else:
         print("Calibrator location not implemented yet")
         sys.exit()
     # Determination of the correction K of the calibration factor
     IoutTp = TaT * TiT * TiO * TiE * (AT + BT)
     IoutTm = TaT * TiT * TiO * TiE * (AT - BT)
     IoutRp = TaR * TiR * TiO * TiE * (AR + BR)
     IoutRm = TaR * TiR * TiO * TiE * (AR - BR)
     # --- Results and Corrections; electronic etaR and etaT are assumed to be 1
     Etapx = IoutRp / IoutTp
     Etamx = IoutRm / IoutTm
     Etax = (Etapx * Etamx) ** 0.5
     Eta = (TaR * TiR) / (TaT * TiT)  # Eta = Eta*/K  Eq. 84
     K = Etax / Eta
     #  For comparison with Volkers Libreoffice Müller Matrix spreadsheet
     # Eta_test_p = (IoutRp/IoutTp)
     # Eta_test_m = (IoutRm/IoutTm)
     # Eta_test = (Eta_test_p*Eta_test_m)**0.5
     # ----- Forward simulated signals and LDRsim with atrue; from input file
     It = TaT * TiT * TiO * TiE * (GT + atrue * HT)
     Ir = TaR * TiR * TiO * TiE * (GR + atrue * HR)
     # LDRsim = 1/Eta*Ir/It  # simulated LDR* with Y from input file
     LDRsim = Ir / It  # simulated uncorrected LDR with Y from input file
     # Corrected LDRsimCorr from forward simulated LDRsim (atrue)
     # LDRsimCorr = (1./Eta*LDRsim*(GT+HT)-(GR+HR))/((GR-HR)-1./Eta*LDRsim*(GT-HT))
     '''
     if ((Y == -1.) and (abs(RotL0) < 45)) or ((Y == +1.) and (abs(RotL0) > 45)):
         LDRsimx = 1. / LDRsim / Etax
     else:
         LDRsimx = LDRsim / Etax
     '''
     LDRsimx = LDRsim
     # The following is correct without doubt
     # LDRCorr = (LDRsim*K/Etax*(GT+HT)-(GR+HR))/((GR-HR)-LDRsim*K/Etax*(GT-HT))
     # The following is a test whether the equations for calibration Etax and normal  signal (GHK, LDRsim) are consistent
     LDRCorr = (LDRsim / Eta * (GT + HT) - (GR + HR)) / ((GR - HR) - LDRsim * K / Etax * (GT - HT))
     #LDRCorr = LDRsimx  # for test only
     TTa = TiT * TaT  # *ATP1
     TRa = TiR * TaR  # *ARP1
     F11sim = 1 / (TiO * TiE) * (
     (HR * Etax / K * It / TTa - HT * Ir / TRa) / (HR * GT - HT * GR))  # IL = 1, Etat = Etar = 1  ;  AMT Eq.64; what is Etax/K? => see about 20 lines above: = Eta
     return (GT, HT, GR, HR, K, Eta, LDRsimx, LDRCorr, DTa, DRa, TTa, TRa, F11sim)
 # *******************************************************************************************************************************
 # --- CALC truth with assumed true parameters from the input file
 GT0, HT0, GR0, HR0, K0, Eta0, LDRsimx, LDRCorr, DTa0, DRa0, TTa0, TRa0, F11sim0 = Calc(DOLP0, RotL0, RotE0, RetE0, DiE0, RotO0,
                                                                                        RetO0, DiO0, RotC0, RetC0, DiC0,
                                                                                        TP0, TS0, RP0, RS0, ERaT0,
                                                                                        RotaT0, RetT0, ERaR0, RotaR0,
                                                                                        RetR0, LDRCal0)
 # --- Print parameters to console and output file
 with open('output_files\output_' + LID + '.dat', 'w') as f:
     with redirect_stdout(f):
         print("From ", dname)
         print("Running ", fname)
         print("Reading input file ", InputFile)  # , "  for Lidar system :", EID, ", ", LID)
         print("for Lidar system: ", EID, ", ", LID)
         # --- Print iput information*********************************
         print(" --- Input parameters: value ±error / ±steps  ----------------------")
         print("{0:5}{1:5} {2:6.4f}±{3:7.4f}/{4:2d}; {5:8} {6:8.4f}±{7:7.4f}/{8:2d}".format("Laser: ", "DOLP =", DOLP0, dDOLP, nDOLP,
                                                                             " Rotation alpha =  ", RotL0, dRotL,
                                                                             nRotL))
         print("              Diatt.,             Tunpol,   Retard.,   Rotation (deg)")
         print("{0:12} {1:7.4f}±{2:7.4f}/{8:2d}, {3:7.4f}, {4:3.0f}±{5:3.0f}/{9:2d}, {6:7.4f}±{7:7.4f}/{10:2d}".format(
             "Emitter    ", DiE0, dDiE, TiE, RetE0, dRetE, RotE0, dRotE, nDiE, nRetE, nRotE))
         print("{0:12} {1:7.4f}±{2:7.4f}/{8:2d}, {3:7.4f}, {4:3.0f}±{5:3.0f}/{9:2d}, {6:7.4f}±{7:7.4f}/{10:2d}".format(
             "Receiver   ", DiO0, dDiO, TiO, RetO0, dRetO, RotO0, dRotO, nDiO, nRetO, nRotO))
         print("{0:12} {1:7.4f}±{2:7.4f}/{8:2d}, {3:7.4f}, {4:3.0f}±{5:3.0f}/{9:2d}, {6:7.4f}±{7:7.4f}/{10:2d}".format(
             "Calibrator ", DiC0, dDiC, TiC, RetC0, dRetC, RotC0, dRotC, nDiC, nRetC, nRotC))
         print("{0:12}".format(" --- Pol.-filter ---"))
         print(
             "{0:12}{1:7.4f}±{2:7.4f}/{3:2d}, {4:7.4f}±{5:7.4f}/{6:2d}".format("ERT, RotT       :", ERaT0, dERaT, nERaT,
                                                                               RotaT0, dRotaT, nRotaT))
         print(
             "{0:12}{1:7.4f}±{2:7.4f}/{3:2d}, {4:7.4f}±{5:7.4f}/{6:2d}".format("ERR, RotR       :", ERaR0, dERaR, nERaR,
                                                                               RotaR0, dRotaR, nRotaR))
         print("{0:12}".format(" --- PBS ---"))
         print("{0:12}{1:7.4f}±{2:7.4f}/{3:2d}, {4:7.4f}±{5:7.4f}/{6:2d}".format("TP,TS           :", TP0, dTP, nTP, TS0,
                                                                                 dTS, nTS))
         print("{0:12}{1:7.4f}±{2:7.4f}/{3:2d}, {4:7.4f}±{5:7.4f}/{6:2d}".format("RP,RS           :", RP0, dRP, nRP, RS0,
                                                                                 dRS, nRS))
         print("{0:12}{1:7.4f},{2:7.4f}, {3:7.4f},{4:7.4f}, {5:1.0f}".format("DT,TT,DR,TR,Y   :", DiT, TiT, DiR, TiR, Y))
         print("{0:12}".format(" --- Combined PBS + Pol.-filter ---"))
         print("{0:12}{1:7.4f},{2:7.4f}, {3:7.4f},{4:7.4f}".format("DT,TT,DR,TR     :", DTa0, TTa0, DRa0, TRa0))
         print("{0:26}: {1:6.3f}± {2:5.3f}/{3:2d}".format("LDRCal during calibration in calibration range", LDRCal0,
                                                         dLDRCal, nLDRCal))
         print()
         print("Rotation Error Epsilon For Normal Measurements = ", RotationErrorEpsilonForNormalMeasurements)
         print(Type[TypeC], Loc[LocC])
         print("Parallel signal detected in", dY[int(Y + 1)])
         print("RS_RP_depend_on_TS_TP = ", RS_RP_depend_on_TS_TP)
         #  end of print actual system parameters
         # ******************************************************************************
         # print()
         # print(" --- LDRCal during calibration | simulated and corrected LDRs -------------")
         # print("{0:8} |{1:8}->{2:8},{3:9}->{4:9} |{5:8}->{6:8}".format(" LDRCal"," LDRtrue", " LDRsim"," LDRtrue2", " LDRsim2", " LDRmeas", " LDRcorr"))
         # print("{0:8.5f} |{1:8.5f}->{2:8.5f},{3:9.5f}->{4:9.5f} |{5:8.5f}->{6:8.5f}".format(LDRCal, LDRtrue, LDRsim, LDRtrue2, LDRsim2, LDRmeas, LDRCorr))
         # print("{0:8}       |{1:8}->{2:8}->{3:8}".format(" LDRCal"," LDRtrue", " LDRsimx", " LDRcorr"))
         # print("{0:6.3f}±{1:5.3f}/{2:2d}|{3:8.5f}->{4:8.5f}->{5:8.5f}".format(LDRCal0, dLDRCal, nLDRCal, LDRtrue, LDRsimx, LDRCorr))
         # print("{0:8}       |{1:8}->{2:8}->{3:8}".format(" LDRCal"," LDRtrue", " LDRsimx", " LDRcorr"))
         # print(" --- LDRCal during calibration")
         # print("{0:8}={1:8.5f};{2:8}={3:8.5f}".format(" IinP",IinP," F11sim",F11sim))
         print()
         K0List = np.zeros(3)
         LDRsimxList = np.zeros(3)
         LDRCalList = 0.004, 0.2, 0.45
         # The loop over LDRCalList is ony for checking whether and how much the LDR depends on the LDRCal during calibration and whether the corrections work.
         # Still with assumed true parameters in input file
         for i, LDRCal in enumerate(LDRCalList):
             GT0, HT0, GR0, HR0, K0, Eta0, LDRsimx, LDRCorr, DTa0, DRa0, TTa0, TRa0, F11sim0 = Calc(DOLP0, RotL0, RotE0, RetE0,
                                                                                                    DiE0, RotO0, RetO0,
                                                                                                    DiO0, RotC0, RetC0,
                                                                                                    DiC0, TP0, TS0, RP0,
                                                                                                    RS0, ERaT0, RotaT0,
                                                                                                    RetT0, ERaR0, RotaR0,
                                                                                                    RetR0, LDRCal)
             K0List[i] = K0
             LDRsimxList[i] = LDRsimx
         print('========================================================================')
         print("{0:8},{1:8},{2:8},{3:8},{4:9},{5:8},{6:9}".format(" GR", " GT", " HR", " HT", "  K(0.004)", " K(0.2)",
                                                                  "  K(0.45)"))
         print("{0:8.5f},{1:8.5f},{2:8.5f},{3:8.5f},{4:9.5f},{5:9.5f},{6:9.5f}".format(GR0, GT0, HR0, HT0, K0List[0],
                                                                                       K0List[1], K0List[2]))
         print('========================================================================')
         print("{0:10},{1:10},{2:10},{3:10}".format("  LDRtrue", "  LDRsimx", "  1/LDRsimx", "  LDRCorr"))
         #LDRtrueList = 0.004, 0.02, 0.2, 0.45
         aF11sim0 = np.zeros(5)
         LDRrange = np.zeros(5)
         LDRrange = 0.004, 0.02, 0.1, 0.3, 0.45
         # The loop over LDRtrueList is ony for checking how much the uncorrected LDRsimx deviates from LDRtrue ... and whether the corrections work.
         # LDRsimx = LDRsim = Ir / It    or      1/LDRsim
         # Still with assumed true parameters in input file
         for i, LDRtrue in enumerate(LDRrange):
         #for LDRtrue in LDRrange:
             GT0, HT0, GR0, HR0, K0, Eta0, LDRsimx, LDRCorr, DTa0, DRa0, TTa0, TRa0, F11sim0 = Calc(DOLP0, RotL0, RotE0, RetE0,
                                                                                                    DiE0, RotO0, RetO0,
                                                                                                    DiO0, RotC0, RetC0,
                                                                                                    DiC0, TP0, TS0, RP0,
                                                                                                    RS0, ERaT0, RotaT0,
                                                                                                    RetT0, ERaR0, RotaR0,
                                                                                                    RetR0, LDRCal0)
             print("{0:10.5f},{1:10.5f},{2:10.5f},{3:10.5f}".format(LDRtrue, LDRsimx, 1/LDRsimx, LDRCorr))
             aF11sim0[i] = F11sim0
             # the assumed true aF11sim0 results will be used below to calc the deviation from the real signals
         print("Note: LDRsimx = LDR of the nominal system directly from measured signals without GHK-corrections")
 file = open('output_files\output_' + LID + '.dat', 'r')
 print(file.read())
 file.close()
 '''
 if(PrintToOutputFile):
     f = open('output_ver7.dat', 'w')
     old_target = sys.stdout
     sys.stdout = f
     print("something")
 if(PrintToOutputFile):
     sys.stdout.flush()
     f.close
     sys.stdout = old_target
 '''
 if (Error_Calc):
     # --- CALC again assumed truth with LDRCal0 and with assumed true parameters in input file to reset all 0-values
     GT0, HT0, GR0, HR0, K0, Eta0, LDRsimx, LDRCorr, DTa0, DRa0, TTa0, TRa0, F11sim0 = Calc(DOLP0, RotL0, RotE0, RetE0, DiE0,
                                                                                            RotO0, RetO0, DiO0, RotC0,
                                                                                            RetC0, DiC0, TP0, TS0, RP0,
                                                                                            RS0, ERaT0, RotaT0, RetT0,
                                                                                            ERaR0, RotaR0, RetR0,
                                                                                            LDRCal0)
     # --- Start Errors calculation with variable parameters ------------------------------------------------------------------
     iN = -1
     N = ((nDOLP * 2 + 1) * (nRotL * 2 + 1) *
          (nRotE * 2 + 1) * (nRetE * 2 + 1) * (nDiE * 2 + 1) *
          (nRotO * 2 + 1) * (nRetO * 2 + 1) * (nDiO * 2 + 1) *
          (nRotC * 2 + 1) * (nRetC * 2 + 1) * (nDiC * 2 + 1) *
          (nTP * 2 + 1) * (nTS * 2 + 1) * (nRP * 2 + 1) * (nRS * 2 + 1) * (nERaT * 2 + 1) * (nERaR * 2 + 1) *
          (nRotaT * 2 + 1) * (nRotaR * 2 + 1) * (nRetT * 2 + 1) * (nRetR * 2 + 1) * (nLDRCal * 2 + 1))
     print("N = ", N, " ", end="")
     if N > 1e6:
         if user_yes_no_query('Warning: processing ' + str(
             N) + ' samples will take very long. Do you want to proceed?') == 0: sys.exit()
     if N > 5e6:
         if user_yes_no_query('Warning: the memory required for ' + str(N) + ' samples might be ' + '{0:5.1f}'.format(
                     N / 4e6) + ' GB. Do you anyway want to proceed?') == 0: sys.exit()
     # if user_yes_no_query('Warning: processing' + str(N) + ' samples will take very long. Do you want to proceed?') == 0: sys.exit()
     # --- Arrays for plotting ------
     LDRmin = np.zeros(5)
     LDRmax = np.zeros(5)
     F11min = np.zeros(5)
     F11max = np.zeros(5)
     #LDRrange = np.zeros(5)
     #LDRrange = 0.004, 0.02, 0.1, 0.3, 0.45
     # aLDRsimx = np.zeros(N)
     # aLDRsimx2 = np.zeros(N)
     # aLDRcorr = np.zeros(N)
     # aLDRcorr2 = np.zeros(N)
     aDOLP = np.zeros(N)
     aERaT = np.zeros(N)
     aERaR = np.zeros(N)
     aRotaT = np.zeros(N)
     aRotaR = np.zeros(N)
     aRetT = np.zeros(N)
     aRetR = np.zeros(N)
     aTP = np.zeros(N)
     aTS = np.zeros(N)
     aRP = np.zeros(N)
     aRS = np.zeros(N)
     aDiE = np.zeros(N)
     aDiO = np.zeros(N)
     aDiC = np.zeros(N)
     aRotC = np.zeros(N)
     aRetC = np.zeros(N)
     aRotL = np.zeros(N)
     aRetE = np.zeros(N)
     aRotE = np.zeros(N)
     aRetO = np.zeros(N)
     aRotO = np.zeros(N)
     aLDRCal = np.zeros(N)
     aA = np.zeros((5, N))
     aX = np.zeros((5, N))
     aF11corr = np.zeros((5, N))
     atime = clock()
     dtime = clock()
     # --- Calc Error signals
     # ---- Do the calculations of bra-ket vectors
     h = -1. if TypeC == 2 else 1
     '''
     # from input file: measured LDRm and true LDRtrue, LDRtrue2  =>
     ameas = (1. - LDRmeas) / (1 + LDRmeas)
     atrue = (1. - LDRtrue) / (1 + LDRtrue)
     atrue2 = (1. - LDRtrue2) / (1 + LDRtrue2)
     '''
     for iLDRCal in range(-nLDRCal, nLDRCal + 1):
         # from input file:  assumed LDRCal for calibration measurements
         LDRCal = LDRCal0
         if nLDRCal > 0: LDRCal = LDRCal0 + iLDRCal * dLDRCal / nLDRCal
         GT0, HT0, GR0, HR0, K0, Eta0, LDRsimx, LDRCorr, DTa0, DRa0, TTa0, TRa0, F11sim = Calc(DOLP0, RotL0, RotE0, RetE0,
                                                                                                DiE0, RotO0, RetO0, DiO0,
                                                                                                RotC0, RetC0, DiC0, TP0,
                                                                                                TS0, RP0, RS0, ERaT0,
                                                                                                RotaT0, RetT0, ERaR0,
                                                                                                RotaR0, RetR0, LDRCal)
         aCal = (1. - LDRCal) / (1 + LDRCal)
         for iDOLP, iRotL, iRotE, iRetE, iDiE \
                 in [(iDOLP, iRotL, iRotE, iRetE, iDiE)
                     for iDOLP in range(-nDOLP, nDOLP + 1)
                     for iRotL in range(-nRotL, nRotL + 1)
                     for iRotE in range(-nRotE, nRotE + 1)
                     for iRetE in range(-nRetE, nRetE + 1)
                     for iDiE in range(-nDiE, nDiE + 1)]:
             if nDOLP > 0: DOLP = DOLP0 + iDOLP * dDOLP / nDOLP
             if nRotL > 0: RotL = RotL0 + iRotL * dRotL / nRotL
             if nRotE > 0: RotE = RotE0 + iRotE * dRotE / nRotE
             if nRetE > 0: RetE = RetE0 + iRetE * dRetE / nRetE
             if nDiE > 0:  DiE = DiE0 + iDiE * dDiE / nDiE
             # angles of emitter and laser and calibrator and receiver optics
             # RotL = alpha, RotE = beta, RotO = gamma, RotC = epsilon
             S2a = np.sin(2 * np.deg2rad(RotL))
             C2a = np.cos(2 * np.deg2rad(RotL))
             S2b = np.sin(2 * np.deg2rad(RotE))
             C2b = np.cos(2 * np.deg2rad(RotE))
             S2ab = np.sin(np.deg2rad(2 * RotL - 2 * RotE))
             C2ab = np.cos(np.deg2rad(2 * RotL - 2 * RotE))
             # Laser with Degree of linear polarization DOLP
             IinL = 1.
             QinL = DOLP
             UinL = 0.
             VinL = (1. - DOLP ** 2) ** 0.5
             # Stokes Input Vector rotation Eq. E.4
             A = C2a * QinL - S2a * UinL
             B = S2a * QinL + C2a * UinL
             # Stokes Input Vector rotation Eq. E.9
             C = C2ab * QinL - S2ab * UinL
             D = S2ab * QinL + C2ab * UinL
             # emitter optics
             CosE = np.cos(np.deg2rad(RetE))
             SinE = np.sin(np.deg2rad(RetE))
             ZiE = (1. - DiE ** 2) ** 0.5
             WiE = (1. - ZiE * CosE)
             # Stokes Input Vector after emitter optics equivalent to Eq. E.9 with already rotated input vector from Eq. E.4
             # b = beta
             IinE = (IinL + DiE * C)
             QinE = (C2b * DiE * IinL + A + S2b * (WiE * D - ZiE * SinE * VinL))
             UinE = (S2b * DiE * IinL + B - C2b * (WiE * D - ZiE * SinE * VinL))
             VinE = (-ZiE * SinE * D + ZiE * CosE * VinL)
             # -------------------------
             # F11 assuemd to be = 1  => measured: F11m = IinP / IinE with atrue
             # F11sim = (IinE + DiO*atrue*(C2g*QinE - S2g*UinE))/IinE
             # -------------------------
             for iRotO, iRetO, iDiO, iRotC, iRetC, iDiC, iTP, iTS, iRP, iRS, iERaT, iRotaT, iRetT, iERaR, iRotaR, iRetR \
                     in [
                 (iRotO, iRetO, iDiO, iRotC, iRetC, iDiC, iTP, iTS, iRP, iRS, iERaT, iRotaT, iRetT, iERaR, iRotaR, iRetR)
                 for iRotO in range(-nRotO, nRotO + 1)
                 for iRetO in range(-nRetO, nRetO + 1)
                 for iDiO in range(-nDiO, nDiO + 1)
                 for iRotC in range(-nRotC, nRotC + 1)
                 for iRetC in range(-nRetC, nRetC + 1)
                 for iDiC in range(-nDiC, nDiC + 1)
                 for iTP in range(-nTP, nTP + 1)
                 for iTS in range(-nTS, nTS + 1)
                 for iRP in range(-nRP, nRP + 1)
                 for iRS in range(-nRS, nRS + 1)
                 for iERaT in range(-nERaT, nERaT + 1)
                 for iRotaT in range(-nRotaT, nRotaT + 1)
                 for iRetT in range(-nRetT, nRetT + 1)
                 for iERaR in range(-nERaR, nERaR + 1)
                 for iRotaR in range(-nRotaR, nRotaR + 1)
                 for iRetR in range(-nRetR, nRetR + 1)]:
                 iN = iN + 1
                 if (iN == 10001):
                     ctime = clock()
                     print(" estimated time ", "{0:4.2f}".format(N / 10000 * (ctime - atime)), "sec ")  # , end="")
                     print("\r elapsed time ", "{0:5.0f}".format((ctime - atime)), "sec ", end="\r")
                 ctime = clock()
                 if ((ctime - dtime) > 10):
                     print("\r elapsed time ", "{0:5.0f}".format((ctime - atime)), "sec ", end="\r")
                     dtime = ctime
                 if nRotO > 0: RotO = RotO0 + iRotO * dRotO / nRotO
                 if nRetO > 0: RetO = RetO0 + iRetO * dRetO / nRetO
                 if nDiO > 0:  DiO = DiO0 + iDiO * dDiO / nDiO
                 if nRotC > 0: RotC = RotC0 + iRotC * dRotC / nRotC
                 if nRetC > 0: RetC = RetC0 + iRetC * dRetC / nRetC
                 if nDiC > 0:  DiC = DiC0 + iDiC * dDiC / nDiC
                 if nTP > 0:   TP = TP0 + iTP * dTP / nTP
                 if nTS > 0:   TS = TS0 + iTS * dTS / nTS
                 if nRP > 0:   RP = RP0 + iRP * dRP / nRP
                 if nRS > 0:   RS = RS0 + iRS * dRS / nRS
                 if nERaT > 0: ERaT = ERaT0 + iERaT * dERaT / nERaT
                 if nRotaT > 0: RotaT = RotaT0 + iRotaT * dRotaT / nRotaT
                 if nRetT > 0: RetT = RetT0 + iRetT * dRetT / nRetT
                 if nERaR > 0: ERaR = ERaR0 + iERaR * dERaR / nERaR
                 if nRotaR > 0: RotaR = RotaR0 + iRotaR * dRotaR / nRotaR
                 if nRetR > 0: RetR = RetR0 + iRetR * dRetR / nRetR
                 # print("{0:5.2f}, {1:5.2f}, {2:5.2f}, {3:10d}".format(RotL, RotE, RotO, iN))
                 # receiver optics
                 CosO = np.cos(np.deg2rad(RetO))
                 SinO = np.sin(np.deg2rad(RetO))
                 ZiO = (1. - DiO ** 2) ** 0.5
                 WiO = (1. - ZiO * CosO)
                 S2g = np.sin(np.deg2rad(2 * RotO))
                 C2g = np.cos(np.deg2rad(2 * RotO))
                 # calibrator
                 CosC = np.cos(np.deg2rad(RetC))
                 SinC = np.sin(np.deg2rad(RetC))
                 ZiC = (1. - DiC ** 2) ** 0.5
                 WiC = (1. - ZiC * CosC)
                 # analyser
                 # For POLLY_XTs
                 if (RS_RP_depend_on_TS_TP):
                     RS = 1 - TS
                     RP = 1 - TP
                 TiT = 0.5 * (TP + TS)
                 DiT = (TP - TS) / (TP + TS)
                 ZiT = (1. - DiT ** 2) ** 0.5
                 TiR = 0.5 * (RP + RS)
                 DiR = (RP - RS) / (RP + RS)
                 ZiR = (1. - DiR ** 2) ** 0.5
                 CosT = np.cos(np.deg2rad(RetT))
                 SinT = np.sin(np.deg2rad(RetT))
                 CosR = np.cos(np.deg2rad(RetR))
                 SinR = np.sin(np.deg2rad(RetR))
                 DaT = (1 - ERaT) / (1 + ERaT)
                 DaR = (1 - ERaR) / (1 + ERaR)
                 TaT = 0.5 * (1 + ERaT)
                 TaR = 0.5 * (1 + ERaR)
                 S2aT = np.sin(np.deg2rad(h * 2 * RotaT))
                 C2aT = np.cos(np.deg2rad(2 * RotaT))
                 S2aR = np.sin(np.deg2rad(h * 2 * RotaR))
                 C2aR = np.cos(np.deg2rad(2 * RotaR))
                 # Aanalyzer As before the PBS Eq. D.5
                 ATP1 = (1 + C2aT * DaT * DiT)
                 ATP2 = Y * (DiT + C2aT * DaT)
                 ATP3 = Y * S2aT * DaT * ZiT * CosT
                 ATP4 = S2aT * DaT * ZiT * SinT
                 ATP = np.array([ATP1, ATP2, ATP3, ATP4])
                 ARP1 = (1 + C2aR * DaR * DiR)
                 ARP2 = Y * (DiR + C2aR * DaR)
                 ARP3 = Y * S2aR * DaR * ZiR * CosR
                 ARP4 = S2aR * DaR * ZiR * SinR
                 ARP = np.array([ARP1, ARP2, ARP3, ARP4])
                 TTa = TiT * TaT  # *ATP1
                 TRa = TiR * TaR  # *ARP1
                 # ---- Calculate signals and correction parameters for diffeent locations and calibrators
                 if LocC == 4:  # Calibrator before the PBS
                     # print("Calibrator location not implemented yet")
                     # S2ge = np.sin(np.deg2rad(2*RotO + h*2*RotC))
                     # C2ge = np.cos(np.deg2rad(2*RotO + h*2*RotC))
                     S2e = np.sin(np.deg2rad(h * 2 * RotC))
                     C2e = np.cos(np.deg2rad(2 * RotC))
                     # rotated AinP by epsilon Eq. C.3
                     ATP2e = C2e * ATP2 + S2e * ATP3
                     ATP3e = C2e * ATP3 - S2e * ATP2
                     ARP2e = C2e * ARP2 + S2e * ARP3
                     ARP3e = C2e * ARP3 - S2e * ARP2
                     ATPe = np.array([ATP1, ATP2e, ATP3e, ATP4])
                     ARPe = np.array([ARP1, ARP2e, ARP3e, ARP4])
                     # Stokes Input Vector before the polarising beam splitter Eq. E.31
                     A = C2g * QinE - S2g * UinE
                     B = S2g * QinE + C2g * UinE
                     # C = (WiO*aCal*B + ZiO*SinO*(1-2*aCal)*VinE)
                     Co = ZiO * SinO * VinE
                     Ca = (WiO * B - 2 * ZiO * SinO * VinE)
                     # C = Co + aCal*Ca
                     # IinP = (IinE + DiO*aCal*A)
                     # QinP = (C2g*DiO*IinE + aCal*QinE - S2g*C)
                     # UinP = (S2g*DiO*IinE - aCal*UinE + C2g*C)
                     # VinP = (ZiO*SinO*aCal*B + ZiO*CosO*(1-2*aCal)*VinE)
                     IinPo = IinE
                     QinPo = (C2g * DiO * IinE - S2g * Co)
                     UinPo = (S2g * DiO * IinE + C2g * Co)
                     VinPo = ZiO * CosO * VinE
                     IinPa = DiO * A
                     QinPa = QinE - S2g * Ca
                     UinPa = -UinE + C2g * Ca
                     VinPa = ZiO * (SinO * B - 2 * CosO * VinE)
                     IinP = IinPo + aCal * IinPa
                     QinP = QinPo + aCal * QinPa
                     UinP = UinPo + aCal * UinPa
                     VinP = VinPo + aCal * VinPa
                     # Stokes Input Vector before the polarising beam splitter rotated by epsilon Eq. C.3
                     # QinPe = C2e*QinP + S2e*UinP
                     # UinPe = C2e*UinP - S2e*QinP
                     QinPoe = C2e * QinPo + S2e * UinPo
                     UinPoe = C2e * UinPo - S2e * QinPo
                     QinPae = C2e * QinPa + S2e * UinPa
                     UinPae = C2e * UinPa - S2e * QinPa
                     QinPe = C2e * QinP + S2e * UinP
                     UinPe = C2e * UinP - S2e * QinP
                     # Calibration signals and Calibration correction K from measurements with LDRCal / aCal
                     if (TypeC == 2) or (TypeC == 1):  # rotator calibration Eq. C.4
                         # parameters for calibration with aCal
                         AT = ATP1 * IinP + h * ATP4 * VinP
                         BT = ATP3e * QinP - h * ATP2e * UinP
                         AR = ARP1 * IinP + h * ARP4 * VinP
                         BR = ARP3e * QinP - h * ARP2e * UinP
                         # Correction parameters for normal measurements; they are independent of LDR
                         if (not RotationErrorEpsilonForNormalMeasurements):  # calibrator taken out
                             IS1 = np.array([IinPo, QinPo, UinPo, VinPo])
                             IS2 = np.array([IinPa, QinPa, UinPa, VinPa])
                             GT = np.dot(ATP, IS1)
                             GR = np.dot(ARP, IS1)
                             HT = np.dot(ATP, IS2)
                             HR = np.dot(ARP, IS2)
                         else:
                             IS1 = np.array([IinPo, QinPo, UinPo, VinPo])
                             IS2 = np.array([IinPa, QinPa, UinPa, VinPa])
                             GT = np.dot(ATPe, IS1)
                             GR = np.dot(ARPe, IS1)
                             HT = np.dot(ATPe, IS2)
                             HR = np.dot(ARPe, IS2)
                     elif (TypeC == 3) or (TypeC == 4):  # linear polariser calibration Eq. C.5
                         # parameters for calibration with aCal
                         AT = ATP1 * IinP + ATP3e * UinPe + ZiC * CosC * (ATP2e * QinPe + ATP4 * VinP)
                         BT = DiC * (ATP1 * UinPe + ATP3e * IinP) - ZiC * SinC * (ATP2e * VinP - ATP4 * QinPe)
                         AR = ARP1 * IinP + ARP3e * UinPe + ZiC * CosC * (ARP2e * QinPe + ARP4 * VinP)
                         BR = DiC * (ARP1 * UinPe + ARP3e * IinP) - ZiC * SinC * (ARP2e * VinP - ARP4 * QinPe)
                         # Correction parameters for normal measurements; they are independent of LDR
                         if (not RotationErrorEpsilonForNormalMeasurements):  # calibrator taken out
                             IS1 = np.array([IinPo, QinPo, UinPo, VinPo])
                             IS2 = np.array([IinPa, QinPa, UinPa, VinPa])
                             GT = np.dot(ATP, IS1)
                             GR = np.dot(ARP, IS1)
                             HT = np.dot(ATP, IS2)
                             HR = np.dot(ARP, IS2)
                         else:
                             IS1e = np.array(
                                 [IinPo + DiC * QinPoe, DiC * IinPo + QinPoe, ZiC * (CosC * UinPoe + SinC * VinPo),
                                  -ZiC * (SinC * UinPoe - CosC * VinPo)])
                             IS2e = np.array(
                                 [IinPa + DiC * QinPae, DiC * IinPa + QinPae, ZiC * (CosC * UinPae + SinC * VinPa),
                                  -ZiC * (SinC * UinPae - CosC * VinPa)])
                             GT = np.dot(ATPe, IS1e)
                             GR = np.dot(ARPe, IS1e)
                             HT = np.dot(ATPe, IS2e)
                             HR = np.dot(ARPe, IS2e)
                     elif (TypeC == 6):  # diattenuator calibration +-22.5° rotated_diattenuator_X22x5deg.odt
                         # parameters for calibration with aCal
                         AT = ATP1 * IinP + sqr05 * DiC * (ATP1 * QinPe + ATP2e * IinP) + (1 - 0.5 * WiC) * (
                         ATP2e * QinPe + ATP3e * UinPe) + ZiC * (
                         sqr05 * SinC * (ATP3e * VinP - ATP4 * UinPe) + ATP4 * CosC * VinP)
                         BT = sqr05 * DiC * (ATP1 * UinPe + ATP3e * IinP) + 0.5 * WiC * (
                         ATP2e * UinPe + ATP3e * QinPe) - sqr05 * ZiC * SinC * (ATP2e * VinP - ATP4 * QinPe)
                         AR = ARP1 * IinP + sqr05 * DiC * (ARP1 * QinPe + ARP2e * IinP) + (1 - 0.5 * WiC) * (
                         ARP2e * QinPe + ARP3e * UinPe) + ZiC * (
                         sqr05 * SinC * (ARP3e * VinP - ARP4 * UinPe) + ARP4 * CosC * VinP)
                         BR = sqr05 * DiC * (ARP1 * UinPe + ARP3e * IinP) + 0.5 * WiC * (
                         ARP2e * UinPe + ARP3e * QinPe) - sqr05 * ZiC * SinC * (ARP2e * VinP - ARP4 * QinPe)
                         # Correction parameters for normal measurements; they are independent of LDR
                         if (not RotationErrorEpsilonForNormalMeasurements):  # calibrator taken out
                             IS1 = np.array([IinPo, QinPo, UinPo, VinPo])
                             IS2 = np.array([IinPa, QinPa, UinPa, VinPa])
                             GT = np.dot(ATP, IS1)
                             GR = np.dot(ARP, IS1)
                             HT = np.dot(ATP, IS2)
                             HR = np.dot(ARP, IS2)
                         else:
                             IS1e = np.array(
                                 [IinPo + DiC * QinPoe, DiC * IinPo + QinPoe, ZiC * (CosC * UinPoe + SinC * VinPo),
                                  -ZiC * (SinC * UinPoe - CosC * VinPo)])
                             IS2e = np.array(
                                 [IinPa + DiC * QinPae, DiC * IinPa + QinPae, ZiC * (CosC * UinPae + SinC * VinPa),
                                  -ZiC * (SinC * UinPae - CosC * VinPa)])
                             GT = np.dot(ATPe, IS1e)
                             GR = np.dot(ARPe, IS1e)
                             HT = np.dot(ATPe, IS2e)
                             HR = np.dot(ARPe, IS2e)
                     else:
                         print("Calibrator not implemented yet")
                         sys.exit()
                 elif LocC == 3:  # C before receiver optics Eq.57
                     # S2ge = np.sin(np.deg2rad(2*RotO - 2*RotC))
                     # C2ge = np.cos(np.deg2rad(2*RotO - 2*RotC))
                     S2e = np.sin(np.deg2rad(2 * RotC))
                     C2e = np.cos(np.deg2rad(2 * RotC))
                     # AS with C before the receiver optics (see document rotated_diattenuator_X22x5deg.odt)
                     AF1 = np.array([1, C2g * DiO, S2g * DiO, 0])
                     AF2 = np.array([C2g * DiO, 1 - S2g ** 2 * WiO, S2g * C2g * WiO, -S2g * ZiO * SinO])
                     AF3 = np.array([S2g * DiO, S2g * C2g * WiO, 1 - C2g ** 2 * WiO, C2g * ZiO * SinO])
                     AF4 = np.array([0, S2g * SinO, -C2g * SinO, CosO])
                     ATF = (ATP1 * AF1 + ATP2 * AF2 + ATP3 * AF3 + ATP4 * AF4)
                     ARF = (ARP1 * AF1 + ARP2 * AF2 + ARP3 * AF3 + ARP4 * AF4)
                     ATF1 = ATF[0]
                     ATF2 = ATF[1]
                     ATF3 = ATF[2]
                     ATF4 = ATF[3]
                     ARF1 = ARF[0]
                     ARF2 = ARF[1]
                     ARF3 = ARF[2]
                     ARF4 = ARF[3]
                     # rotated AinF by epsilon
                     ATF2e = C2e * ATF[1] + S2e * ATF[2]
                     ATF3e = C2e * ATF[2] - S2e * ATF[1]
                     ARF2e = C2e * ARF[1] + S2e * ARF[2]
                     ARF3e = C2e * ARF[2] - S2e * ARF[1]
                     ATFe = np.array([ATF1, ATF2e, ATF3e, ATF4])
                     ARFe = np.array([ARF1, ARF2e, ARF3e, ARF4])
                     QinEe = C2e * QinE + S2e * UinE
                     UinEe = C2e * UinE - S2e * QinE
                     # Stokes Input Vector before receiver optics Eq. E.19 (after atmosphere F)
                     IinF = IinE
                     QinF = aCal * QinE
                     UinF = -aCal * UinE
                     VinF = (1. - 2. * aCal) * VinE
                     IinFo = IinE
                     QinFo = 0.
                     UinFo = 0.
                     VinFo = VinE
                     IinFa = 0.
                     QinFa = QinE
                     UinFa = -UinE
                     VinFa = -2. * VinE
                     # Stokes Input Vector before receiver optics rotated by epsilon Eq. C.3
                     QinFe = C2e * QinF + S2e * UinF
                     UinFe = C2e * UinF - S2e * QinF
                     QinFoe = C2e * QinFo + S2e * UinFo
                     UinFoe = C2e * UinFo - S2e * QinFo
                     QinFae = C2e * QinFa + S2e * UinFa
                     UinFae = C2e * UinFa - S2e * QinFa
                     # Calibration signals and Calibration correction K from measurements with LDRCal / aCal
                     if (TypeC == 2) or (TypeC == 1):  # rotator calibration Eq. C.4
                         AT = ATF1 * IinF + ATF4 * h * VinF
                         BT = ATF3e * QinF - ATF2e * h * UinF
                         AR = ARF1 * IinF + ARF4 * h * VinF
                         BR = ARF3e * QinF - ARF2e * h * UinF
                         # Correction parameters for normal measurements; they are independent of LDR
                         if (not RotationErrorEpsilonForNormalMeasurements):
                             GT = ATF1 * IinE + ATF4 * VinE
                             GR = ARF1 * IinE + ARF4 * VinE
                             HT = ATF2 * QinE - ATF3 * UinE - ATF4 * 2 * VinE
                             HR = ARF2 * QinE - ARF3 * UinE - ARF4 * 2 * VinE
                         else:
                             GT = ATF1 * IinE + ATF4 * h * VinE
                             GR = ARF1 * IinE + ARF4 * h * VinE
                             HT = ATF2e * QinE - ATF3e * h * UinE - ATF4 * h * 2 * VinE
                             HR = ARF2e * QinE - ARF3e * h * UinE - ARF4 * h * 2 * VinE
                     elif (TypeC == 3) or (TypeC == 4):  # linear polariser calibration Eq. C.5
                         # p = +45°, m = -45°
                         IF1e = np.array([IinF, ZiC * CosC * QinFe, UinFe, ZiC * CosC * VinF])
                         IF2e = np.array([DiC * UinFe, -ZiC * SinC * VinF, DiC * IinF, ZiC * SinC * QinFe])
                         AT = np.dot(ATFe, IF1e)
                         AR = np.dot(ARFe, IF1e)
                         BT = np.dot(ATFe, IF2e)
                         BR = np.dot(ARFe, IF2e)
                         # Correction parameters for normal measurements; they are independent of LDR  --- the same as for TypeC = 6
                         if (not RotationErrorEpsilonForNormalMeasurements):  # calibrator taken out
                             IS1 = np.array([IinE, 0, 0, VinE])
                             IS2 = np.array([0, QinE, -UinE, -2 * VinE])
                             GT = np.dot(ATF, IS1)
                             GR = np.dot(ARF, IS1)
                             HT = np.dot(ATF, IS2)
                             HR = np.dot(ARF, IS2)
                         else:
                             IS1e = np.array(
                                 [IinFo + DiC * QinFoe, DiC * IinFo + QinFoe, ZiC * (CosC * UinFoe + SinC * VinFo),
                                  -ZiC * (SinC * UinFoe - CosC * VinFo)])
                             IS2e = np.array(
                                 [IinFa + DiC * QinFae, DiC * IinFa + QinFae, ZiC * (CosC * UinFae + SinC * VinFa),
                                  -ZiC * (SinC * UinFae - CosC * VinFa)])
                             GT = np.dot(ATFe, IS1e)
                             GR = np.dot(ARFe, IS1e)
                             HT = np.dot(ATFe, IS2e)
                             HR = np.dot(ARFe, IS2e)
                     elif (TypeC == 6):  # diattenuator calibration +-22.5° rotated_diattenuator_X22x5deg.odt
                         # p = +22.5°, m = -22.5°
                         IF1e = np.array([IinF + sqr05 * DiC * QinFe, sqr05 * DiC * IinF + (1 - 0.5 * WiC) * QinFe,
                                          (1 - 0.5 * WiC) * UinFe + sqr05 * ZiC * SinC * VinF,
                                          -sqr05 * ZiC * SinC * UinFe + ZiC * CosC * VinF])
                         IF2e = np.array([sqr05 * DiC * UinFe, 0.5 * WiC * UinFe - sqr05 * ZiC * SinC * VinF,
                                          sqr05 * DiC * IinF + 0.5 * WiC * QinFe, sqr05 * ZiC * SinC * QinFe])
                         AT = np.dot(ATFe, IF1e)
                         AR = np.dot(ARFe, IF1e)
                         BT = np.dot(ATFe, IF2e)
                         BR = np.dot(ARFe, IF2e)
                         # Correction parameters for normal measurements; they are independent of LDR
                         if (not RotationErrorEpsilonForNormalMeasurements):  # calibrator taken out
                             # IS1 = np.array([IinE,0,0,VinE])
                             # IS2 = np.array([0,QinE,-UinE,-2*VinE])
                             IS1 = np.array([IinFo, 0, 0, VinFo])
                             IS2 = np.array([0, QinFa, UinFa, VinFa])
                             GT = np.dot(ATF, IS1)
                             GR = np.dot(ARF, IS1)
                             HT = np.dot(ATF, IS2)
                             HR = np.dot(ARF, IS2)
                         else:
                             # IS1e = np.array([IinE,DiC*IinE,ZiC*SinC*VinE,ZiC*CosC*VinE])
                             # IS2e = np.array([DiC*QinEe,QinEe,-ZiC*(CosC*UinEe+2*SinC*VinE),ZiC*(SinC*UinEe-2*CosC*VinE)])
                             IS1e = np.array(
                                 [IinFo + DiC * QinFoe, DiC * IinFo + QinFoe, ZiC * (CosC * UinFoe + SinC * VinFo),
                                  -ZiC * (SinC * UinFoe - CosC * VinFo)])
                             IS2e = np.array(
                                 [IinFa + DiC * QinFae, DiC * IinFa + QinFae, ZiC * (CosC * UinFae + SinC * VinFa),
                                  -ZiC * (SinC * UinFae - CosC * VinFa)])
                             GT = np.dot(ATFe, IS1e)
                             GR = np.dot(ARFe, IS1e)
                             HT = np.dot(ATFe, IS2e)
                             HR = np.dot(ARFe, IS2e)
                     else:
                         print('Calibrator not implemented yet')
                         sys.exit()
                 elif LocC == 2:  # C behind emitter optics Eq.57
                     # print("Calibrator location not implemented yet")
                     S2e = np.sin(np.deg2rad(2 * RotC))
                     C2e = np.cos(np.deg2rad(2 * RotC))
                     # AS with C before the receiver optics (see document rotated_diattenuator_X22x5deg.odt)
                     AF1 = np.array([1, C2g * DiO, S2g * DiO, 0])
                     AF2 = np.array([C2g * DiO, 1 - S2g ** 2 * WiO, S2g * C2g * WiO, -S2g * ZiO * SinO])
                     AF3 = np.array([S2g * DiO, S2g * C2g * WiO, 1 - C2g ** 2 * WiO, C2g * ZiO * SinO])
                     AF4 = np.array([0, S2g * SinO, -C2g * SinO, CosO])
                     ATF = (ATP1 * AF1 + ATP2 * AF2 + ATP3 * AF3 + ATP4 * AF4)
                     ARF = (ARP1 * AF1 + ARP2 * AF2 + ARP3 * AF3 + ARP4 * AF4)
                     ATF1 = ATF[0]
                     ATF2 = ATF[1]
                     ATF3 = ATF[2]
                     ATF4 = ATF[3]
                     ARF1 = ARF[0]
                     ARF2 = ARF[1]
                     ARF3 = ARF[2]
                     ARF4 = ARF[3]
                     # AS with C behind the emitter  --------------------------------------------
                     # terms without aCal
                     ATE1o, ARE1o = ATF1, ARF1
                     ATE2o, ARE2o = 0., 0.
                     ATE3o, ARE3o = 0., 0.
                     ATE4o, ARE4o = ATF4, ARF4
                     # terms with aCal
                     ATE1a, ARE1a = 0., 0.
                     ATE2a, ARE2a = ATF2, ARF2
                     ATE3a, ARE3a = -ATF3, -ARF3
                     ATE4a, ARE4a = -2 * ATF4, -2 * ARF4
                     # rotated AinEa by epsilon
                     ATE2ae = C2e * ATF2 + S2e * ATF3
                     ATE3ae = -S2e * ATF2 - C2e * ATF3
                     ARE2ae = C2e * ARF2 + S2e * ARF3
                     ARE3ae = -S2e * ARF2 - C2e * ARF3
                     ATE1 = ATE1o
                     ATE2e = aCal * ATE2ae
                     ATE3e = aCal * ATE3ae
                     ATE4 = (1 - 2 * aCal) * ATF4
                     ARE1 = ARE1o
                     ARE2e = aCal * ARE2ae
                     ARE3e = aCal * ARE3ae
                     ARE4 = (1 - 2 * aCal) * ARF4
                     # rotated IinE
                     QinEe = C2e * QinE + S2e * UinE
                     UinEe = C2e * UinE - S2e * QinE
                     # --- Calibration signals and Calibration correction K from measurements with LDRCal / aCal
                     if (TypeC == 2) or (TypeC == 1):  # +++++++++ rotator calibration Eq. C.4
                         AT = ATE1o * IinE + (ATE4o + aCal * ATE4a) * h * VinE
                         BT = aCal * (ATE3ae * QinEe - ATE2ae * h * UinEe)
                         AR = ARE1o * IinE + (ARE4o + aCal * ARE4a) * h * VinE
                         BR = aCal * (ARE3ae * QinEe - ARE2ae * h * UinEe)
                         # Correction parameters for normal measurements; they are independent of LDR
                         if (not RotationErrorEpsilonForNormalMeasurements):
                             # Stokes Input Vector before receiver optics Eq. E.19 (after atmosphere F)
                             GT = ATE1o * IinE + ATE4o * h * VinE
                             GR = ARE1o * IinE + ARE4o * h * VinE
                             HT = ATE2a * QinE + ATE3a * h * UinEe + ATE4a * h * VinE
                             HR = ARE2a * QinE + ARE3a * h * UinEe + ARE4a * h * VinE
                         else:
                             GT = ATE1o * IinE + ATE4o * h * VinE
                             GR = ARE1o * IinE + ARE4o * h * VinE
                             HT = ATE2ae * QinE + ATE3ae * h * UinEe + ATE4a * h * VinE
                             HR = ARE2ae * QinE + ARE3ae * h * UinEe + ARE4a * h * VinE
                     elif (TypeC == 3) or (TypeC == 4):  # +++++++++ linear polariser calibration Eq. C.5
                         # p = +45°, m = -45°
                         AT = ATE1 * IinE + ZiC * CosC * (ATE2e * QinEe + ATE4 * VinE) + ATE3e * UinEe
                         BT = DiC * (ATE1 * UinEe + ATE3e * IinE) + ZiC * SinC * (ATE4 * QinEe - ATE2e * VinE)
                         AR = ARE1 * IinE + ZiC * CosC * (ARE2e * QinEe + ARE4 * VinE) + ARE3e * UinEe
                         BR = DiC * (ARE1 * UinEe + ARE3e * IinE) + ZiC * SinC * (ARE4 * QinEe - ARE2e * VinE)
                         # Correction parameters for normal measurements; they are independent of LDR
                         if (not RotationErrorEpsilonForNormalMeasurements):
                             # Stokes Input Vector before receiver optics Eq. E.19 (after atmosphere F)
                             GT = ATE1o * IinE + ATE4o * VinE
                             GR = ARE1o * IinE + ARE4o * VinE
                             HT = ATE2a * QinE + ATE3a * UinE + ATE4a * VinE
                             HR = ARE2a * QinE + ARE3a * UinE + ARE4a * VinE
                         else:
                             D = IinE + DiC * QinEe
                             A = DiC * IinE + QinEe
                             B = ZiC * (CosC * UinEe + SinC * VinE)
                             C = -ZiC * (SinC * UinEe - CosC * VinE)
                             GT = ATE1o * D + ATE4o * C
                             GR = ARE1o * D + ARE4o * C
                             HT = ATE2a * A + ATE3a * B + ATE4a * C
                             HR = ARE2a * A + ARE3a * B + ARE4a * C
                     elif (TypeC == 6):  # real HWP calibration +-22.5° rotated_diattenuator_X22x5deg.odt
                         # p = +22.5°, m = -22.5°
                         IE1e = np.array([IinE + sqr05 * DiC * QinEe, sqr05 * DiC * IinE + (1 - 0.5 * WiC) * QinEe,
                                          (1 - 0.5 * WiC) * UinEe + sqr05 * ZiC * SinC * VinE,
                                          -sqr05 * ZiC * SinC * UinEe + ZiC * CosC * VinE])
                         IE2e = np.array([sqr05 * DiC * UinEe, 0.5 * WiC * UinEe - sqr05 * ZiC * SinC * VinE,
                                          sqr05 * DiC * IinE + 0.5 * WiC * QinEe, sqr05 * ZiC * SinC * QinEe])
                         ATEe = np.array([ATE1, ATE2e, ATE3e, ATE4])
                         AREe = np.array([ARE1, ARE2e, ARE3e, ARE4])
                         AT = np.dot(ATEe, IE1e)
                         AR = np.dot(AREe, IE1e)
                         BT = np.dot(ATEe, IE2e)
                         BR = np.dot(AREe, IE2e)
                         # Correction parameters for normal measurements; they are independent of LDR
                         if (not RotationErrorEpsilonForNormalMeasurements):  # calibrator taken out
                             GT = ATE1o * IinE + ATE4o * VinE
                             GR = ARE1o * IinE + ARE4o * VinE
                             HT = ATE2a * QinE + ATE3a * UinE + ATE4a * VinE
                             HR = ARE2a * QinE + ARE3a * UinE + ARE4a * VinE
                         else:
                             D = IinE + DiC * QinEe
                             A = DiC * IinE + QinEe
                             B = ZiC * (CosC * UinEe + SinC * VinE)
                             C = -ZiC * (SinC * UinEe - CosC * VinE)
                             GT = ATE1o * D + ATE4o * C
                             GR = ARE1o * D + ARE4o * C
                             HT = ATE2a * A + ATE3a * B + ATE4a * C
                             HR = ARE2a * A + ARE3a * B + ARE4a * C
                     else:
                         print('Calibrator not implemented yet')
                         sys.exit()
                 # Calibration signals with aCal => Determination of the correction K of the real calibration factor
                 IoutTp = TaT * TiT * TiO * TiE * (AT + BT)
                 IoutTm = TaT * TiT * TiO * TiE * (AT - BT)
                 IoutRp = TaR * TiR * TiO * TiE * (AR + BR)
                 IoutRm = TaR * TiR * TiO * TiE * (AR - BR)
                 # --- Results and Corrections; electronic etaR and etaT are assumed to be 1
                 # Eta = TiR/TiT   # Eta = Eta*/K  Eq. 84
                 Etapx = IoutRp / IoutTp
                 Etamx = IoutRm / IoutTm
                 Etax = (Etapx * Etamx) ** 0.5
                 K = Etax / Eta0
                 # print("{0:6.3f},{1:6.3f},{2:6.3f},{3:6.3f},{4:6.3f},{5:6.3f},{6:6.3f},{7:6.3f},{8:6.3f},{9:6.3f},{10:6.3f}".format(AT, BT, AR, BR, DiC, ZiC, RetO, TP, TS, Kp, Km))
                 # print("{0:6.3f},{1:6.3f},{2:6.3f},{3:6.3f}".format(DiC, ZiC, Kp, Km))
                 #  For comparison with Volkers Libreoffice Müller Matrix spreadsheet
                 # Eta_test_p = (IoutRp/IoutTp)
                 # Eta_test_m = (IoutRm/IoutTm)
                 # Eta_test = (Eta_test_p*Eta_test_m)**0.5
                 # *************************************************************************
                 iLDR = -1
                 for LDRTrue in LDRrange:
                     iLDR = iLDR + 1
                     atrue = (1 - LDRTrue) / (1 + LDRTrue)
                     # ----- Forward simulated signals and LDRsim with atrue; from input file
                     It = TaT * TiT * TiO * TiE * (GT + atrue * HT)  # TaT*TiT*TiC*TiO*IinL*(GT+atrue*HT)
                     Ir = TaR * TiR * TiO * TiE * (GR + atrue * HR)  # TaR*TiR*TiC*TiO*IinL*(GR+atrue*HR)
                     # LDRsim = 1/Eta*Ir/It  # simulated LDR* with Y from input file
                     LDRsim = Ir / It  # simulated uncorrected LDR with Y from input file
                     '''
                     if Y == 1.:
                         LDRsimx = LDRsim
                         LDRsimx2 = LDRsim2
                     else:
                         LDRsimx = 1./LDRsim
                         LDRsimx2 = 1./LDRsim2
                     '''
                     # ----- Backward correction
                     # Corrected LDRCorr  with assumed true G0,H0,K0 from forward simulated (real) LDRsim (atrue)
                     LDRCorr = (LDRsim * K0 / Etax * (GT0 + HT0) - (GR0 + HR0)) / (
                     (GR0 - HR0) - LDRsim * K0 / Etax * (GT0 - HT0))
                     '''
                     # -- F11corr from It and Ir and calibration EtaX
                     Text1 = "!!! EXPERIMENTAL !!!  F11corr from It and Ir with calibration EtaX: x-axis: F11corr(LDRtrue) / F11corr(LDRtrue = 0.004) - 1"
                     F11corr = 1 / (TiO * TiE) * (
                     (HR0 * Etax / K0 * It / TTa - HT0 * Ir / TRa) / (HR0 * GT0 - HT0 * GR0))  # IL = 1  Eq.(64); Etax/K0 = Eta0.
                     '''
                     # Corrected F11corr  with assumed true G0,H0,K0 from forward simulated (real) It and Ir (atrue)
                     Text1 = "!!! EXPERIMENTAL !!!  F11corr from real It and Ir with real calibration EtaX: x-axis: F11corr(LDRtrue) / aF11sim0(LDRtrue) - 1"
                     F11corr = 1 / (TiO * TiE) * (
                     (HR0 * Etax / K0 * It / TTa - HT0 * Ir / TRa) / (HR0 * GT0 - HT0 * GR0))  # IL = 1  Eq.(64); Etax/K0 = Eta0.
                     # Text1 = "F11corr from It and Ir without corrections but with calibration EtaX: x-axis: F11corr(LDRtrue) devided by F11corr(LDRtrue = 0.004)"
                     # F11corr = 0.5/(TiO*TiE)*(Etax*It/TTa+Ir/TRa)    # IL = 1  Eq.(64)
                     # -- It from It only with atrue without corrections - for BERTHA (and PollyXTs)
                     # Text1 = " x-axis: IT(LDRtrue) / IT(LDRtrue = 0.004) - 1"
                     # F11corr = It/(TaT*TiT*TiO*TiE)   #/(TaT*TiT*TiO*TiE*(GT0+atrue*HT0))
                     # !!! see below line 1673ff
                     aF11corr[iLDR, iN] = F11corr
                     aA[iLDR, iN] = LDRCorr # LDRCorr # LDRsim # for test only
                     aX[0, iN] = GR
                     aX[1, iN] = GT
                     aX[2, iN] = HR
                     aX[3, iN] = HT
                     aX[4, iN] = K
                     aLDRCal[iN] = iLDRCal
                     aDOLP[iN] = iDOLP
                     aERaT[iN] = iERaT
                     aERaR[iN] = iERaR
                     aRotaT[iN] = iRotaT
                     aRotaR[iN] = iRotaR
                     aRetT[iN] = iRetT
                     aRetR[iN] = iRetR
                     aRotL[iN] = iRotL
                     aRotE[iN] = iRotE
                     aRetE[iN] = iRetE
                     aRotO[iN] = iRotO
                     aRetO[iN] = iRetO
                     aRotC[iN] = iRotC
                     aRetC[iN] = iRetC
                     aDiO[iN] = iDiO
                     aDiE[iN] = iDiE
                     aDiC[iN] = iDiC
                     aTP[iN] = iTP
                     aTS[iN] = iTS
                     aRP[iN] = iRP
                     aRS[iN] = iRS
     # --- END loop
     btime = clock()
     print("\r done in      ", "{0:5.0f}".format(btime - atime), "sec")  # , end="\r")
     # --- Plot -----------------------------------------------------------------
     if (sns_loaded):
         sns.set_style("whitegrid")
         sns.set_palette("bright", 6)
     '''
     fig2 = plt.figure()
     plt.plot(aA[2,:],'b.')
     plt.plot(aA[3,:],'r.')
     plt.plot(aA[4,:],'g.')
     #plt.plot(aA[6,:],'c.')
     plt.show
     '''
     # Plot LDR
     def PlotSubHist(aVar, aX, X0, daX, iaX, naX):
         fig, ax = plt.subplots(nrows=1, ncols=5, sharex=True, sharey=True, figsize=(25, 2))
         iLDR = -1
         for LDRTrue in LDRrange:
             iLDR = iLDR + 1
             LDRmin[iLDR] = np.min(aA[iLDR, :])
             LDRmax[iLDR] = np.max(aA[iLDR, :])
             Rmin = LDRmin[iLDR] * 0.995  # np.min(aA[iLDR,:])    * 0.995
             Rmax = LDRmax[iLDR] * 1.005  # np.max(aA[iLDR,:])    * 1.005
             # plt.subplot(5,2,iLDR+1)
             plt.subplot(1, 5, iLDR + 1)
             (n, bins, patches) = plt.hist(aA[iLDR, :],
                                           bins=100, log=False,
                                           range=[Rmin, Rmax],
                                           alpha=0.5, normed=False, color='0.5', histtype='stepfilled')
             for iaX in range(-naX, naX + 1):
                 plt.hist(aA[iLDR, aX == iaX],
                          range=[Rmin, Rmax],
                          bins=100, log=False, alpha=0.3, normed=False, histtype='stepfilled',
                          label=str(round(X0 + iaX * daX / naX, 5)))
                 if (iLDR == 2): plt.legend()
             plt.tick_params(axis='both', labelsize=9)
             plt.plot([LDRTrue, LDRTrue], [0, np.max(n)], 'r-', lw=2)
         # plt.title(LID + '  ' + aVar, fontsize=18)
         # plt.ylabel('frequency', fontsize=10)
         # plt.xlabel('LDRcorr', fontsize=10)
         # fig.tight_layout()
         fig.suptitle(LID + ' with ' + str(Type[TypeC]) + ' ' + str(Loc[LocC]) + ' - ' + aVar, fontsize=14, y=1.05)
         # plt.show()
         # fig.savefig(LID + '_' + aVar + '.png', dpi=150, bbox_inches='tight', pad_inches=0)
         # plt.close
         return
     if (nDOLP > 0): PlotSubHist("DOLP", aDOLP, DOLP0, dDOLP, iDOLP, nDOLP)
     if (nRotL > 0): PlotSubHist("RotL", aRotL, RotL0, dRotL, iRotL, nRotL)
     if (nRetE > 0): PlotSubHist("RetE", aRetE, RetE0, dRetE, iRetE, nRetE)
     if (nRotE > 0): PlotSubHist("RotE", aRotE, RotE0, dRotE, iRotE, nRotE)
     if (nDiE > 0): PlotSubHist("DiE", aDiE, DiE0, dDiE, iDiE, nDiE)
     if (nRetO > 0): PlotSubHist("RetO", aRetO, RetO0, dRetO, iRetO, nRetO)
     if (nRotO > 0): PlotSubHist("RotO", aRotO, RotO0, dRotO, iRotO, nRotO)
     if (nDiO > 0): PlotSubHist("DiO", aDiO, DiO0, dDiO, iDiO, nDiO)
     if (nDiC > 0): PlotSubHist("DiC", aDiC, DiC0, dDiC, iDiC, nDiC)
     if (nRotC > 0): PlotSubHist("RotC", aRotC, RotC0, dRotC, iRotC, nRotC)
     if (nRetC > 0): PlotSubHist("RetC", aRetC, RetC0, dRetC, iRetC, nRetC)
     if (nTP > 0): PlotSubHist("TP", aTP, TP0, dTP, iTP, nTP)
     if (nTS > 0): PlotSubHist("TS", aTS, TS0, dTS, iTS, nTS)
     if (nRP > 0): PlotSubHist("RP", aRP, RP0, dRP, iRP, nRP)
     if (nRS > 0): PlotSubHist("RS", aRS, RS0, dRS, iRS, nRS)
     if (nRetT > 0): PlotSubHist("RetT", aRetT, RetT0, dRetT, iRetT, nRetT)
     if (nRetR > 0): PlotSubHist("RetR", aRetR, RetR0, dRetR, iRetR, nRetR)
     if (nERaT > 0): PlotSubHist("ERaT", aERaT, ERaT0, dERaT, iERaT, nERaT)
     if (nERaR > 0): PlotSubHist("ERaR", aERaR, ERaR0, dERaR, iERaR, nERaR)
     if (nRotaT > 0): PlotSubHist("RotaT", aRotaT, RotaT0, dRotaT, iRotaT, nRotaT)
     if (nRotaR > 0): PlotSubHist("RotaR", aRotaR, RotaR0, dRotaR, iRotaR, nRotaR)
     if (nLDRCal > 0): PlotSubHist("LDRCal", aLDRCal, LDRCal0, dLDRCal, iLDRCal, nLDRCal)
     plt.show()
     plt.close
     '''
     # --- Plot F11 histograms
     print()
     print(" ############################################################################## ")
     print(Text1)
     print()
     iLDR = 5
     for LDRTrue in LDRrange:
         iLDR = iLDR - 1
         #aF11corr[iLDR,:] = aF11corr[iLDR,:] / aF11corr[0,:] - 1.0
         aF11corr[iLDR,:] = aF11corr[iLDR,:] / aF11sim0[iLDR] - 1.0
     # Plot F11
     def PlotSubHistF11(aVar, aX, X0, daX, iaX, naX):
         fig, ax = plt.subplots(nrows=1, ncols=5, sharex=True, sharey=True, figsize=(25, 2))
         iLDR = -1
         for LDRTrue in LDRrange:
             iLDR = iLDR + 1
             #F11min[iLDR] = np.min(aF11corr[iLDR,:])
             #F11max[iLDR] = np.max(aF11corr[iLDR,:])
             #Rmin = F11min[iLDR] * 0.995 #  np.min(aA[iLDR,:])    * 0.995
             #Rmax = F11max[iLDR] * 1.005 #  np.max(aA[iLDR,:])    * 1.005
             #Rmin = 0.8
             #Rmax = 1.2
             #plt.subplot(5,2,iLDR+1)
             plt.subplot(1,5,iLDR+1)
             (n, bins, patches) = plt.hist(aF11corr[iLDR,:],
                      bins=100, log=False,
                      alpha=0.5, normed=False, color = '0.5', histtype='stepfilled')
             for iaX in range(-naX,naX+1):
                 plt.hist(aF11corr[iLDR,aX == iaX],
                          bins=100, log=False, alpha=0.3, normed=False, histtype='stepfilled', label = str(round(X0 + iaX*daX/naX,5)))
                 if (iLDR == 2): plt.legend()
             plt.tick_params(axis='both', labelsize=9)
             #plt.plot([LDRTrue, LDRTrue], [0, np.max(n)], 'r-', lw=2)
         #plt.title(LID + '  ' + aVar, fontsize=18)
         #plt.ylabel('frequency', fontsize=10)
         #plt.xlabel('LDRcorr', fontsize=10)
         #fig.tight_layout()
         fig.suptitle(LID + '  ' + str(Type[TypeC]) + ' ' + str(Loc[LocC])  + ' - ' + aVar, fontsize=14, y=1.05)
         #plt.show()
         #fig.savefig(LID + '_' + aVar + '.png', dpi=150, bbox_inches='tight', pad_inches=0)
         #plt.close
         return
     if (nDOLP > 0): PlotSubHistF11("DOLP", aDOLP, DOLP0, dDOLP, iDOLP, nDOLP)
     if (nRotL > 0): PlotSubHistF11("RotL", aRotL, RotL0, dRotL, iRotL, nRotL)
     if (nRetE > 0): PlotSubHistF11("RetE", aRetE, RetE0, dRetE, iRetE, nRetE)
     if (nRotE > 0): PlotSubHistF11("RotE", aRotE, RotE0, dRotE, iRotE, nRotE)
     if (nDiE > 0): PlotSubHistF11("DiE", aDiE, DiE0, dDiE, iDiE, nDiE)
     if (nRetO > 0): PlotSubHistF11("RetO", aRetO, RetO0, dRetO, iRetO, nRetO)
     if (nRotO > 0): PlotSubHistF11("RotO", aRotO, RotO0, dRotO, iRotO, nRotO)
     if (nDiO > 0): PlotSubHistF11("DiO", aDiO, DiO0, dDiO, iDiO, nDiO)
     if (nDiC > 0): PlotSubHistF11("DiC", aDiC, DiC0, dDiC, iDiC, nDiC)
     if (nRotC > 0): PlotSubHistF11("RotC", aRotC, RotC0, dRotC, iRotC, nRotC)
     if (nRetC > 0): PlotSubHistF11("RetC", aRetC, RetC0, dRetC, iRetC, nRetC)
     if (nTP > 0): PlotSubHistF11("TP", aTP, TP0, dTP, iTP, nTP)
     if (nTS > 0): PlotSubHistF11("TS", aTS, TS0, dTS, iTS, nTS)
     if (nRP > 0): PlotSubHistF11("RP", aRP, RP0, dRP, iRP, nRP)
     if (nRS > 0): PlotSubHistF11("RS", aRS, RS0, dRS, iRS, nRS)
     if (nRetT > 0): PlotSubHistF11("RetT", aRetT, RetT0, dRetT, iRetT, nRetT)
     if (nRetR > 0): PlotSubHistF11("RetR", aRetR, RetR0, dRetR, iRetR, nRetR)
     if (nERaT > 0): PlotSubHistF11("ERaT", aERaT, ERaT0, dERaT, iERaT, nERaT)
     if (nERaR > 0): PlotSubHistF11("ERaR", aERaR, ERaR0, dERaR, iERaR, nERaR)
     if (nRotaT > 0): PlotSubHistF11("RotaT", aRotaT, RotaT0, dRotaT, iRotaT, nRotaT)
     if (nRotaR > 0): PlotSubHistF11("RotaR", aRotaR, RotaR0, dRotaR, iRotaR, nRotaR)
     if (nLDRCal > 0): PlotSubHistF11("LDRCal", aLDRCal, LDRCal0, dLDRCal, iLDRCal, nLDRCal)
     plt.show()
     plt.close
     '''
     '''
     # only histogram
     #print("******************* " + aVar + " *******************")
     fig, ax = plt.subplots(nrows=5, ncols=2, sharex=True, sharey=True, figsize=(10, 10))
     iLDR = -1
     for LDRTrue in LDRrange:
         iLDR = iLDR + 1
         LDRmin[iLDR] = np.min(aA[iLDR,:])
         LDRmax[iLDR] = np.max(aA[iLDR,:])
         Rmin = np.min(aA[iLDR,:])    * 0.999
         Rmax = np.max(aA[iLDR,:])    * 1.001
         plt.subplot(5,2,iLDR+1)
         (n, bins, patches) = plt.hist(aA[iLDR,:],
                  range=[Rmin, Rmax],
                  bins=200, log=False, alpha=0.2, normed=False, color = '0.5', histtype='stepfilled')
         plt.tick_params(axis='both', labelsize=9)
         plt.plot([LDRTrue, LDRTrue], [0, np.max(n)], 'r-', lw=2)
     plt.show()
     plt.close
      # --- End of Plot F11 histograms
     '''
     # --- Plot LDRmin, LDRmax
     fig2 = plt.figure()
     plt.plot(LDRrange, LDRmax - LDRrange, linewidth=2.0, color='b')
     plt.plot(LDRrange, LDRmin - LDRrange, linewidth=2.0, color='g')
     plt.xlabel('LDRtrue', fontsize=18)
     plt.ylabel('LDRTrue-LDRmin, LDRTrue-LDRmax', fontsize=14)
     plt.title(LID + ' ' + str(Type[TypeC]) + ' ' + str(Loc[LocC]), fontsize=18)
     # plt.ylimit(-0.07, 0.07)
     plt.show()
     plt.close
     # --- Save LDRmin, LDRmax to file
     # http://stackoverflow.com/questions/4675728/redirect-stdout-to-a-file-in-python
     with open('output_files\LDR_min_max_' + LID + '.dat', 'w') as f:
         with redirect_stdout(f):
             print(LID)
             print("LDRtrue, LDRmin, LDRmax")
             for i in range(len(LDRrange)):
                 print("{0:7.4f},{1:7.4f},{2:7.4f}".format(LDRrange[i], LDRmin[i], LDRmax[i]))
     '''
     # --- Plot K over LDRCal
     fig3 = plt.figure()
     plt.plot(LDRCal0+aLDRCal*dLDRCal/nLDRCal,aX[4,:], linewidth=2.0, color='b')
     plt.xlabel('LDRCal', fontsize=18)
     plt.ylabel('K', fontsize=14)
     plt.title(LID, fontsize=18)
     plt.show()
     plt.close
     '''
 # Additional plot routines ======>
 '''
 #******************************************************************************
 # 1. Plot LDRcorrected - LDR(measured Icross/Iparallel)
 LDRa = np.arange(1.,100.)*0.005
 LDRCorra = np.arange(1.,100.)
 if Y == - 1.: LDRa = 1./LDRa
 LDRCorra = (1./Eta*LDRa*(GT+HT)-(GR+HR))/((GR-HR)-1./Eta*LDRa*(GT-HT))
 if Y == - 1.: LDRa = 1./LDRa
 #
 #fig = plt.figure()
 plt.plot(LDRa,LDRCorra-LDRa)
 plt.plot([0.,0.5],[0.,0.5])
 plt.suptitle('LDRcorrected - LDR(measured Icross/Iparallel)', fontsize=16)
 plt.xlabel('LDR', fontsize=18)
 plt.ylabel('LDRCorr - LDR', fontsize=16)
 #plt.savefig('test.png')
 #
 '''
 '''
 #******************************************************************************
 # 2. Plot LDRsim (simulated measurements without corrections = Icross/Iparallel) over LDRtrue
 LDRa = np.arange(1.,100.)*0.005
 LDRsima = np.arange(1.,100.)
 atruea = (1.-LDRa)/(1+LDRa)
 Ita = TiT*TiO*IinL*(GT+atruea*HT)
 Ira = TiR*TiO*IinL*(GR+atruea*HR)
 LDRsima = Ira/Ita  # simulated uncorrected LDR with Y from input file
 if Y == -1.: LDRsima = 1./LDRsima
 #
 #fig = plt.figure()
 plt.plot(LDRa,LDRsima)
 plt.plot([0.,0.5],[0.,0.5])
 plt.suptitle('LDRsim (simulated measurements without corrections = Icross/Iparallel) over LDRtrue', fontsize=10)
 plt.xlabel('LDRtrue', fontsize=18)
 plt.ylabel('LDRsim', fontsize=16)
 #plt.savefig('test.png')
 #
 '''

Mercurial > public > atmospheric_lidar_ghk / annotate

lidar_correction_ghk.py@28b5510492ba (annotated)

lidar_correction_ghk.py