├── examples ├── pics │ ├── mix0.png │ ├── mix1.png │ ├── mix2.png │ ├── example_traces.png │ ├── rec_artif_shg.png │ └── rec_artif_shg0.png ├── stronglychirpeddouble.py ├── artif_shg.py ├── artif_blind.py └── generate_frog_traces.py ├── froglib ├── __init__.py ├── auxiliary.py ├── plotting.py ├── statistics.py ├── corefunctions.py ├── reconstructionloops.py └── phasemanipulations.py ├── README.md └── LICENSE.txt /examples/pics/mix0.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/xmhk/froglib/HEAD/examples/pics/mix0.png -------------------------------------------------------------------------------- /examples/pics/mix1.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/xmhk/froglib/HEAD/examples/pics/mix1.png -------------------------------------------------------------------------------- /examples/pics/mix2.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/xmhk/froglib/HEAD/examples/pics/mix2.png -------------------------------------------------------------------------------- /examples/pics/example_traces.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/xmhk/froglib/HEAD/examples/pics/example_traces.png -------------------------------------------------------------------------------- /examples/pics/rec_artif_shg.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/xmhk/froglib/HEAD/examples/pics/rec_artif_shg.png -------------------------------------------------------------------------------- /examples/pics/rec_artif_shg0.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/xmhk/froglib/HEAD/examples/pics/rec_artif_shg0.png -------------------------------------------------------------------------------- /examples/stronglychirpeddouble.py: -------------------------------------------------------------------------------- 1 | """ 2 | This file is part of froglib, which allows the creation 3 | and reconstruction of FROG traces. 4 | 5 | froglib is free software: you can redistribute it and/or modify 6 | it under the terms of the GNU General Public License as published by 7 | the Free Software Foundation, either version 3 of the License, or 8 | (at your option) any later version. 9 | 10 | froglib is distributed in the hope that it will be useful, 11 | but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | GNU General Public License for more details. 14 | 15 | You should have received a copy of the GNU General Public License 16 | along with froglib. If not, see . 17 | 18 | Contributors: 19 | 20 | Christoph Mahnke, 2018 21 | 22 | """ 23 | 24 | import os, sys 25 | sys.path.append(os.path._getfullpathname("../")) 26 | 27 | import numpy as np 28 | from matplotlib import pyplot as plt 29 | from froglib import * 30 | 31 | 32 | M = np.loadtxt("example_data/stronglychirpeddouble.dat") 33 | Mexp = np.sqrt(M) 34 | res = mixfrog(Mexp, startnum=10, plot=True ) 35 | 36 | plt.show() 37 | 38 | 39 | 40 | -------------------------------------------------------------------------------- /froglib/__init__.py: -------------------------------------------------------------------------------- 1 | """ 2 | This file is part of froglib, which allows the creation 3 | and reconstruction of FROG traces. 4 | 5 | froglib is free software: you can redistribute it and/or modify 6 | it under the terms of the GNU General Public License as published by 7 | the Free Software Foundation, either version 3 of the License, or 8 | (at your option) any later version. 9 | 10 | froglib is distributed in the hope that it will be useful, 11 | but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | GNU General Public License for more details. 14 | 15 | You should have received a copy of the GNU General Public License 16 | along with froglib. If not, see . 17 | 18 | Contributors: 19 | 20 | Christoph Mahnke, 2018 21 | 22 | """ 23 | 24 | 25 | from .corefunctions import frogtr, pcgpstep 26 | from .reconstructionloops import simplerec, mixfrog 27 | from .statistics import deviationtau, calc_average 28 | from .auxiliary import flip, shift_center 29 | 30 | from .phasemanipulations import remove_relative_phase_offset 31 | from .phasemanipulations import remove_shg_freq_ambi 32 | from .phasemanipulations import remove_blind_freq_ambi 33 | from .phasemanipulations import specshift_to_ref 34 | 35 | from .plotting import compare_frog, simplerecresult 36 | -------------------------------------------------------------------------------- /examples/artif_shg.py: -------------------------------------------------------------------------------- 1 | """ 2 | This file is part of froglib, which allows the creation 3 | and reconstruction of FROG traces. 4 | 5 | froglib is free software: you can redistribute it and/or modify 6 | it under the terms of the GNU General Public License as published by 7 | the Free Software Foundation, either version 3 of the License, or 8 | (at your option) any later version. 9 | 10 | froglib is distributed in the hope that it will be useful, 11 | but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | GNU General Public License for more details. 14 | 15 | You should have received a copy of the GNU General Public License 16 | along with froglib. If not, see . 17 | 18 | Contributors: 19 | 20 | Christoph Mahnke, 2018 21 | 22 | """ 23 | 24 | import os, sys 25 | sys.path.append(os.path._getfullpathname("../")) 26 | 27 | import numpy as np 28 | from matplotlib import pyplot as plt 29 | from froglib import * 30 | 31 | # generate signal 32 | tmax = 7 33 | N = 128 34 | tvec = np.linspace(-tmax, tmax, N) 35 | deltat = 0.5 36 | freqoff = 1.2 37 | #two gaussians of different height and width, different freqs 38 | field = 0.5 * np.exp( - (tvec-deltat)**2) - np.exp( - (tvec+deltat)**2/0.5**2) * np.exp(1.0j * freqoff * tvec) 39 | 40 | # generate artifical trace (SHG) 41 | Mexp = np.abs(frogtr(field, field, mode='shg')) 42 | 43 | # use a simple loop of the PCGP algorithm 44 | res = simplerec(Mexp, iterations=150) 45 | 46 | # show result 47 | simplerecresult(Mexp, res) 48 | plt.show() 49 | 50 | 51 | 52 | -------------------------------------------------------------------------------- /examples/artif_blind.py: -------------------------------------------------------------------------------- 1 | """ 2 | This file is part of froglib, which allows the creation 3 | and reconstruction of FROG traces. 4 | 5 | froglib is free software: you can redistribute it and/or modify 6 | it under the terms of the GNU General Public License as published by 7 | the Free Software Foundation, either version 3 of the License, or 8 | (at your option) any later version. 9 | 10 | froglib is distributed in the hope that it will be useful, 11 | but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | GNU General Public License for more details. 14 | 15 | You should have received a copy of the GNU General Public License 16 | along with froglib. If not, see . 17 | 18 | Contributors: 19 | 20 | Christoph Mahnke, 2018 21 | 22 | """ 23 | 24 | import os, sys 25 | sys.path.append(os.path._getfullpathname("../")) 26 | 27 | import numpy as np 28 | from matplotlib import pyplot as plt 29 | from froglib import * 30 | 31 | 32 | tmax = 7 33 | N = 128 34 | 35 | tvec = np.linspace(-tmax, tmax, N) 36 | 37 | deltat = 0.5 38 | freqoff = 1.2 39 | 40 | # two gaussians of different height and width, different freqs 41 | # chirped gaussian as gate pulse 42 | 43 | field = 0.5 * np.exp( - (tvec-deltat)**2) - np.exp( - (tvec+deltat)**2/0.5**2) * np.exp(1.0j * freqoff * tvec) 44 | gate= np.exp(-tvec**2/0.16) * np.exp(-1.3j * tvec**2) 45 | 46 | Mexp = np.abs(frogtr(field, gate, mode='blind')) 47 | 48 | 49 | res = simplerec(Mexp, iterations=50, mode='blind') 50 | 51 | # show result 52 | 53 | simplerecresult(Mexp, res) 54 | 55 | plt.show() 56 | 57 | 58 | 59 | -------------------------------------------------------------------------------- /examples/generate_frog_traces.py: -------------------------------------------------------------------------------- 1 | """ 2 | This file is part of froglib, which allows the creation 3 | and reconstruction of FROG traces. 4 | 5 | froglib is free software: you can redistribute it and/or modify 6 | it under the terms of the GNU General Public License as published by 7 | the Free Software Foundation, either version 3 of the License, or 8 | (at your option) any later version. 9 | 10 | froglib is distributed in the hope that it will be useful, 11 | but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | GNU General Public License for more details. 14 | 15 | You should have received a copy of the GNU General Public License 16 | along with froglib. If not, see . 17 | 18 | Contributors: 19 | 20 | Christoph Mahnke, 2018 21 | 22 | """ 23 | 24 | import os, sys 25 | sys.path.append(os.path._getfullpathname("../")) 26 | 27 | import numpy as np 28 | from matplotlib import pyplot as plt 29 | import matplotlib 30 | from froglib import * 31 | 32 | tvec = np.linspace(-8,8, 128) 33 | #double pulse 34 | t0=0.4 35 | deltat = 0.7 36 | signal1 = np.exp(-((tvec+deltat/2)/t0)**2) - np.exp(-((tvec-deltat/2)/t0)**2) * np.exp((-(tvec-deltat/2)/t0 * -1j)) 37 | signal2 = 1./np.cosh(tvec) * np.exp(1.0j * (0.6 * tvec + 0.5 * tvec**2)) 38 | 39 | # generate traces 40 | 41 | F1 = frogtr(signal1, signal1, mode='shg') 42 | F2 = frogtr(signal2, signal2, mode='shg') 43 | F3 = frogtr(signal1, signal2, mode='blind') 44 | 45 | # plot traces 46 | 47 | spp = matplotlib.figure.SubplotParams(wspace=0.5) 48 | plt.figure(figsize=(7,3), subplotpars=spp) 49 | ax1= plt.subplot(131);plt.title("double gaussian, SHG") 50 | plt.imshow(np.abs(F1)**2) 51 | ax2= plt.subplot(132);plt.title("sech, SHG") 52 | plt.imshow(np.abs(F2)**2) 53 | ax3=plt.subplot(133);plt.title("double gaussian - sech,\nBLIND") 54 | plt.imshow(np.abs(F3)**2) 55 | 56 | for ax in [ax1,ax2,ax3]: 57 | ax.set_xlabel("time") 58 | ax.set_ylabel("freq") 59 | plt.show() -------------------------------------------------------------------------------- /froglib/auxiliary.py: -------------------------------------------------------------------------------- 1 | """ 2 | This file is part of froglib, which allows the creation 3 | and reconstruction of FROG traces. 4 | 5 | froglib is free software: you can redistribute it and/or modify 6 | it under the terms of the GNU General Public License as published by 7 | the Free Software Foundation, either version 3 of the License, or 8 | (at your option) any later version. 9 | 10 | froglib is distributed in the hope that it will be useful, 11 | but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | GNU General Public License for more details. 14 | 15 | You should have received a copy of the GNU General Public License 16 | along with froglib. If not, see . 17 | 18 | Contributors: 19 | 20 | Christoph Mahnke, 2018 21 | 22 | """ 23 | 24 | 25 | import numpy as np 26 | 27 | def flip(v): 28 | """Flips (reverses) a vector v. 29 | 30 | Arguments: 31 | 32 | v : vector 33 | 34 | Returns: 35 | 36 | v2 : reversed vector 37 | 38 | """ 39 | v2 = [x for x in v] 40 | v2.reverse() 41 | return np.array(v2) 42 | 43 | 44 | 45 | def shift_center(field, eps05=5e-2): 46 | """Shift some field to the center of the time window, with respect to energy. 47 | 48 | This function shifts (rotates) some field to be centered in the time window, 49 | with respect to energy. 50 | 51 | Arguments: 52 | 53 | field : input field 54 | 55 | Optional arguments: 56 | 57 | eps05 : defines how the center of the field is determined. 58 | The function search for the field array element which 59 | fulfills (cumulated energy) = | 0.5 - eps05 | x total energy. 60 | 61 | Returns: 62 | 63 | shiftfield : shifted version of the field 64 | 65 | """ 66 | pp = np.abs(field) ** 2 67 | cs = np.cumsum(pp) 68 | rel = cs / np.sum(pp) 69 | aa = np.nonzero(np.multiply(rel > 0.5 - eps05, rel < 0.5 + eps05))[0] 70 | ll = len(field) 71 | shift = 0 72 | if len(aa) > 0: 73 | shift = int(ll / 2 - np.round(np.mean(aa))) 74 | return np.roll(field, shift) -------------------------------------------------------------------------------- /froglib/plotting.py: -------------------------------------------------------------------------------- 1 | """ 2 | This file is part of froglib, which allows the creation 3 | and reconstruction of FROG traces. 4 | 5 | froglib is free software: you can redistribute it and/or modify 6 | it under the terms of the GNU General Public License as published by 7 | the Free Software Foundation, either version 3 of the License, or 8 | (at your option) any later version. 9 | 10 | froglib is distributed in the hope that it will be useful, 11 | but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | GNU General Public License for more details. 14 | 15 | You should have received a copy of the GNU General Public License 16 | along with froglib. If not, see . 17 | 18 | Contributors: 19 | 20 | Christoph Mahnke, 2018 21 | 22 | """ 23 | 24 | 25 | from matplotlib import pyplot as plt 26 | import numpy as np 27 | from .corefunctions import frogtr 28 | from .phasemanipulations import remove_shg_freq_ambi, remove_blind_freq_ambi 29 | 30 | def compare_frog(mexp, pulse, gpulse, mode='shg', 31 | fixshg_ambi=True, 32 | fixblind_ambi=True): 33 | nn = len(pulse) 34 | mres = frogtr(pulse, gpulse, mode=mode) 35 | i1 = np.abs(mexp) ** 2 / np.sum(np.sum(np.abs(mexp) ** 2)) 36 | i2 = np.abs(mres) ** 2 / np.sum(np.sum(np.abs(mres) ** 2)) 37 | ferr = np.sqrt(1 / nn ** 2 * np.sum(np.sum(np.abs(i1 - i2) ** 2))) 38 | if mode=='shg' and fixshg_ambi: 39 | pulse = remove_shg_freq_ambi(pulse) 40 | gpulse = remove_shg_freq_ambi(gpulse) 41 | if mode=='blind' and fixblind_ambi: 42 | pulse, gpulse = remove_blind_freq_ambi(pulse, gpulse ) 43 | 44 | plt.figure() 45 | plt.subplot(221) 46 | plt.imshow(i1) 47 | plt.xlabel("time") 48 | plt.ylabel("freq") 49 | plt.title("exp") 50 | plt.colorbar() 51 | plt.tight_layout() 52 | plt.subplot(222) 53 | ts = "rec, err = %.2e"%ferr 54 | plt.title(ts) 55 | plt.imshow(i2) 56 | plt.colorbar() 57 | plt.xlabel("time") 58 | plt.ylabel("freq") 59 | plt.tight_layout() 60 | plt.subplot(223) 61 | plt.imshow(i1 - i2) 62 | plt.xlabel("time") 63 | plt.ylabel("freq") 64 | plt.title("difference") 65 | plt.colorbar() 66 | plt.tight_layout() 67 | plt.subplot(224) 68 | plt.plot(np.abs(pulse), c='r', dashes=(3, 1), label='S') 69 | plt.plot(np.abs(gpulse), c='b', dashes=(3, 1), label='G') 70 | plt.legend(loc=0) 71 | plt.ylabel("amplitude") 72 | plt.xlabel("time") 73 | plt.twinx() 74 | plt.plot(np.unwrap(np.angle(pulse)), c='r') 75 | plt.plot(np.unwrap(np.angle(gpulse)), c='b') 76 | 77 | plt.ylabel("phase") 78 | plt.tight_layout() 79 | 80 | def simplerecresult(M, rd): 81 | plt.figure(figsize=(5.5, 1.5)) 82 | plt.semilogy(rd['errors']) 83 | plt.xlabel("iteration no") 84 | plt.ylabel("error") 85 | ts = "min error = %s"%rd['minerror'] 86 | plt.title(ts) 87 | plt.tight_layout() 88 | compare_frog(M, rd['min_sp'], rd['min_gp'], mode=rd['mode']) -------------------------------------------------------------------------------- /froglib/statistics.py: -------------------------------------------------------------------------------- 1 | """ 2 | This file is part of froglib, which allows the creation 3 | and reconstruction of FROG traces. 4 | 5 | froglib is free software: you can redistribute it and/or modify 6 | it under the terms of the GNU General Public License as published by 7 | the Free Software Foundation, either version 3 of the License, or 8 | (at your option) any later version. 9 | 10 | froglib is distributed in the hope that it will be useful, 11 | but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | GNU General Public License for more details. 14 | 15 | You should have received a copy of the GNU General Public License 16 | along with froglib. If not, see . 17 | 18 | Contributors: 19 | 20 | Christoph Mahnke, 2018 21 | 22 | """ 23 | 24 | 25 | import numpy as np 26 | 27 | def deviationtau(n): 28 | """Return the prefactor for error margins of n-point sample. 29 | 30 | Depending on the length of some series of measurements, the error 31 | margin is calculated by taking the standard deviation times a prefactor 32 | tau(n) / sqrt (n). 33 | 34 | error = tau(n) / sqrt (n) x standard_deviation 35 | 36 | This function calculates tau(n) / sqrt (n) and returns it. 37 | 38 | Arguments: 39 | 40 | n : number of samples 41 | 42 | Returns: 43 | 44 | prefactor 45 | 46 | """ 47 | if n<=2: 48 | n = 2 49 | P = [12.706, 4.303, 3.182, 2.776, 2.571, 2.447, 2.365, 2.306, 2.262, 50 | 2.228, 2.201, 2.179, 2.160, 2.145, 2.131, 2.120, 2.110, 2.101, 51 | 2.093, 2.086, 2.080, 2.074, 2.069, 2.064, 2.060, 2.056, 2.052, 52 | 2.048, 2.045, 2.042] 53 | if n > 31: 54 | return 2.0 / np.sqrt(n) 55 | else: 56 | return P[n - 2] / np.sqrt(n) 57 | 58 | 59 | def calc_average(fieldlist): 60 | """Calculates the averages and errors for a list of fields. 61 | 62 | Arguments: 63 | 64 | fieldlist: list of input fields 65 | 66 | Returns: 67 | 68 | rdict: dictionary containing the values: 69 | 70 | field_mean : mean field (complex) 71 | 72 | re_mean : mean of the real part 73 | 74 | re_error : error for the real part 75 | 76 | im_mean : mean of the imag part 77 | 78 | im_error : error for the imag part 79 | 80 | amp_mean : mean amplitude of the field (real) 81 | 82 | amp_error : error for the amp_mean 83 | 84 | phase_mean : mean of the phase 85 | 86 | phase_error : error for the phase. 87 | 88 | """ 89 | Mfieldlist = np.array(fieldlist) 90 | n2 = int(len(fieldlist[0]) / 2) 91 | # real part 92 | mre = np.mean(np.real(Mfieldlist), axis=0) 93 | stdre = np.std(np.real(Mfieldlist), axis=0) 94 | errorre = deviationtau(len(fieldlist)) * stdre 95 | # imag part 96 | mim = np.mean(np.imag(Mfieldlist), axis=0) 97 | stdim = np.std(np.imag(Mfieldlist), axis=0) 98 | errorim = deviationtau(len(fieldlist)) * stdim 99 | # abs 100 | meanfield = mre + 1.0j * mim 101 | # phase 102 | phase = np.unwrap(np.angle(meanfield)) 103 | phase = phase - phase[n2] 104 | errorabs = np.abs(mre / np.sqrt(mre ** 2 + mim ** 2) * errorre) \ 105 | + np.abs(mim / np.sqrt(mre ** 2 + mim ** 2) * errorim) 106 | errorphase = np.abs(mim / ((1.0 + mim ** 2 / mre ** 2) * mre ** 2) * errorre) \ 107 | + np.abs(mim / ((1.0 + mim ** 2 / mre ** 2) * mre ** 2) * errorim) 108 | rd = {} 109 | rd['field_mean'] = meanfield 110 | rd['re_mean'] = mre 111 | rd['re_error'] = errorre 112 | rd['im_mean'] = mim 113 | rd['im_error'] = errorim 114 | rd['amp_mean'] = np.abs(meanfield) 115 | rd['amp_error'] = errorabs 116 | rd['phase_mean'] = phase 117 | rd['phase_error'] = errorphase 118 | 119 | return rd -------------------------------------------------------------------------------- /froglib/corefunctions.py: -------------------------------------------------------------------------------- 1 | """ 2 | This file is part of froglib, which allows the creation 3 | and reconstruction of FROG traces. 4 | 5 | froglib is free software: you can redistribute it and/or modify 6 | it under the terms of the GNU General Public License as published by 7 | the Free Software Foundation, either version 3 of the License, or 8 | (at your option) any later version. 9 | 10 | froglib is distributed in the hope that it will be useful, 11 | but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | GNU General Public License for more details. 14 | 15 | You should have received a copy of the GNU General Public License 16 | along with froglib. If not, see . 17 | 18 | Contributors: 19 | 20 | Christoph Mahnke, 2018 21 | 22 | """ 23 | 24 | import numpy as np 25 | 26 | def gaussianrandomphase(n): 27 | """Return a gaussian pulse with random phase. 28 | 29 | Arguments: 30 | 31 | n : length of desired gaussian pulse array 32 | 33 | Returns: 34 | 35 | field : gaussian pulse with random phase 36 | 37 | """ 38 | tvec = np.arange(n) - int(n / 2) 39 | p = np.exp(-tvec ** 2 / (n / 16) ** 2) * np.exp(2.0j * np.pi * np.random.rand(n)) 40 | #p = np.random.rand(n) * np.exp(2.0j * np.pi * np.random.rand(n)) 41 | return p 42 | 43 | def frogtr(field1, field2, mode='shg'): 44 | """Calculate the Frog Trace of given field(s). 45 | 46 | Arguments: 47 | 48 | field1, field2 : input fields 49 | 50 | Optional Arguments: 51 | 52 | mode : determines whether to calculate the SHG or the Blind Frog trace. 53 | 54 | 'shg'=SHG trace 55 | 'blind'=Blind Frog trace 56 | 57 | Returns: 58 | 59 | frogtrace : Field of the frog trace, which in general is complex. 60 | To compare with some experimental (intensity) trace, 61 | the absolute value squared of Frog trace has to be taken. 62 | 63 | 64 | """ 65 | nn = len(field1) 66 | n2 = int(nn / 2) 67 | if mode == 'shg': 68 | ap = np.outer(field1, field2) + np.outer(field2, field1) # Axis: time-time 69 | elif mode == 'blind': 70 | ap = np.outer(field1, field2) 71 | m1 = np.zeros(np.shape(ap), dtype=np.complex128) 72 | m2 = np.zeros(np.shape(ap), dtype=np.complex128) 73 | for i in range(n2 - 1, -n2, -1): 74 | m1[i + n2, :] = np.roll(ap[i + n2, :], -i) 75 | m1 = np.transpose(m1) 76 | for i in range(nn): 77 | m2[i, :] = np.roll(np.fft.fft(np.roll(m1[i, :], +n2)), -n2) # time-freq 78 | m2 = np.transpose(m2) # freq - time 79 | m2 = m2 / np.max(np.max(np.abs(m2))) 80 | return m2 81 | 82 | 83 | def pcgpstep(mexp, pulse, gatepulse, mode='shg', svd='full'): 84 | """Make a step in the pcgp algorithm. 85 | 86 | This function implements the PCGP Algorithm as describe in Rick Trebino's Book: 87 | 88 | Trebino, Rick. Frequency-resolved optical gating: the measurement of 89 | ultrashort laser pulses. Springer Science & Business Media, 2012. 90 | 91 | Arguments: 92 | 93 | mexp: amplitude represenation of the experimental FROG trace, e.g. 94 | the square root of the measured intensity. 95 | 96 | pulse: input pulse to use as signal. When pulse==None, a gaussian with 97 | random phase is used. 98 | 99 | gatepulse: input pulse to use as gate. When pulse==None, a gaussian with 100 | random phase is used. 101 | 102 | Optional arguments: 103 | 104 | mode: can either be 'shg' or 'blind'. Determines the kind of Frog trace to calculate. 105 | 106 | svd: can either be 'full' or 'power'. When 'full' is used, the singular value decomposition 107 | of numpy is used. For 'power', the (faster) 'power method' is used. 108 | 109 | Returns: 110 | 111 | pulse, gatepulse : iterated fields for signal and gate 112 | 113 | ferr : Frog error for the reconstructed trace 114 | 115 | """ 116 | if pulse is None: 117 | nn = np.shape(mexp)[0] 118 | pulse = gaussianrandomphase(nn) 119 | if gatepulse is None: 120 | nn = np.shape(mexp)[0] 121 | gatepulse = gaussianrandomphase(nn) 122 | nn = len(pulse) 123 | n2 = int(nn / 2) 124 | m2 = frogtr(pulse, gatepulse, mode=mode) 125 | i1 = np.abs(mexp) ** 2 / np.sum(np.sum(np.abs(mexp) ** 2)) 126 | i2 = np.abs(m2) ** 2 / np.sum(np.sum(np.abs(m2) ** 2)) 127 | ferr = np.sqrt(1 / nn ** 2 * np.sum(np.sum(np.abs(i1 - i2) ** 2))) 128 | 129 | m3 = np.abs(mexp) * np.exp(1.0j * np.angle(m2)) 130 | m3 = np.transpose(m3) # zeit - freq 131 | m4 = np.zeros(np.shape(m2), dtype=np.complex128) 132 | m5 = np.zeros(np.shape(m2), dtype=np.complex128) 133 | 134 | for i in range(nn): 135 | m4[i, :] = np.roll(np.fft.ifft(np.roll(m3[i, :], -n2)), n2) 136 | for i in range(n2 - 1, -n2, -1): 137 | m5[i + n2, :] = np.roll(m4[:, i + n2], i) # time-time 138 | if svd=='full': 139 | # full SVD 140 | u, w, v = np.linalg.svd(m5) 141 | pulse = u[:, 0] 142 | gatepulse = v[0, :] 143 | else: 144 | # power method 145 | pulse = np.dot(np.dot(m5, np.transpose(m5)), pulse) 146 | gatepulse = np.dot(np.dot(np.transpose(m5), m5), gatepulse) 147 | pulse = pulse / np.sqrt( np.sum( np.abs(pulse)**2)) 148 | gatepulse = gatepulse / np.sqrt(np.sum(np.abs(gatepulse) ** 2)) 149 | return pulse, gatepulse, ferr -------------------------------------------------------------------------------- /froglib/reconstructionloops.py: -------------------------------------------------------------------------------- 1 | """ 2 | This file is part of froglib, which allows the creation 3 | and reconstruction of FROG traces. 4 | 5 | froglib is free software: you can redistribute it and/or modify 6 | it under the terms of the GNU General Public License as published by 7 | the Free Software Foundation, either version 3 of the License, or 8 | (at your option) any later version. 9 | 10 | froglib is distributed in the hope that it will be useful, 11 | but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | GNU General Public License for more details. 14 | 15 | You should have received a copy of the GNU General Public License 16 | along with froglib. If not, see . 17 | 18 | Contributors: 19 | 20 | Christoph Mahnke, 2018 21 | 22 | """ 23 | 24 | 25 | from .corefunctions import pcgpstep 26 | import numpy as np 27 | from matplotlib import pyplot as plt 28 | from .plotting import simplerecresult 29 | 30 | 31 | 32 | def simplerec(mexp, iterations=10, mode='shg', pulse=None, gatepulse=None, svd='full'): 33 | """Simple reconstruction loop for Frog traces. 34 | 35 | Arguments: 36 | 37 | mexp : amplitude represenation of the experimental FROG trace, e.g. 38 | the square root of the measured intensity. 39 | 40 | Optional Arguments: 41 | 42 | iterations : number of PCGP steps to iterate (default = 10) 43 | 44 | mode : may be 'shg' or 'blind' (default = 'shg') 45 | 46 | pulse : when given, this pulse will be feed into the PCGP loop (default = None) 47 | 48 | gatepulse : when given, this gatepulse will be feed into the PCGP loop (default = None) 49 | 50 | svd : method to calculate the singular value decomposition. 'full' : use numpy's SVD, 51 | 'power' : use the power method. 52 | 53 | Returns: 54 | 55 | rdict : dictionary holding the values: 56 | 57 | errors : Array holding Frog error for each iteration 58 | 59 | gp, sp : Arrays with signal and gate fields for each iteration 60 | 61 | minerror : minimal Frog error that occured during iterations 62 | 63 | min_sp, min_gp : signal and gate pulses for minimal Frog error 64 | 65 | mode : mode used ('shg' or 'blind') 66 | 67 | exp : experimental trace (amplitude) 68 | 69 | """ 70 | 71 | errors = [] 72 | sps = [] 73 | gps = [] 74 | for jj in range(iterations): 75 | pulse, gatepulse, frogerr = pcgpstep(mexp, pulse, gatepulse, mode=mode, svd=svd) 76 | errors.append(frogerr) 77 | sps.append(pulse) 78 | gps.append(gatepulse) 79 | # if not(extspec is None): # use external spec as constraint? (not yet) 80 | # nn = len(pulse); n2 = int(nn/2) 81 | # PPS = np.roll(np.fft.fft(np.roll(pulse,n2)), n2) 82 | # pulse = np.roll( np.fft.ifft(np.roll(np.abs(extspec[0]) * np.exp(1.0j * np.angle(PPS)),n2)), n2) 83 | # GPS = np.roll(np.fft.fft(np.roll(gatepulse,n2)), n2) 84 | # gatepulse = np.roll( np.fft.ifft( np.roll( np.abs(extspec[1]) * np.exp(1.0j * np.angle(GPS)), n2)), n2) 85 | rd = {'errors': errors, 'sp': sps, 'gp': gps, 'exp': mexp} 86 | minerr = np.min(rd['errors']) 87 | indx = np.nonzero(minerr == rd['errors'])[0][0] 88 | rd['minerror'] = minerr 89 | rd['min_sp'] = rd['sp'][indx] 90 | rd['min_gp'] = rd['gp'][indx] 91 | rd['mode']=mode 92 | return rd 93 | 94 | 95 | 96 | def mixfrog(mexp, startnum=3, startite=20, itestep2=100, plot=False): 97 | """Try different reconstructions, return the best. 98 | 99 | This algorithm makes a number of different attempts to reconstruct 100 | a trace, both with 'shg' and 'blind' mode. 101 | 102 | The best result (minimal Frog error) is iterated further. 103 | 104 | Arguments: 105 | 106 | mexp : experimental Frog trace (amplitude) 107 | 108 | Optional arguments: 109 | 110 | startnum : number of attempts for each 'shg' and 'blind' mode 111 | 112 | startite : number of iterations to perform for each mode 113 | 114 | itestep2 : number of iterations for the best field 115 | 116 | plot : whether to plot some results for this mode. 117 | 118 | Returns: 119 | 120 | rdict : dictionary holding the values: 121 | 122 | errors : Array holding Frog error for each iteration 123 | 124 | gp, sp : Arrays with signal and gate fields for each iteration 125 | 126 | minerror : minimal Frog error that occured during iterations 127 | 128 | min_sp, min_gp : signal and gate pulses for minimal Frog error 129 | 130 | mode : mode used ('shg' or 'blind') 131 | 132 | exp : experimental trace (amplitude) 133 | 134 | """ 135 | 136 | errors = [] 137 | pp = [] 138 | gp = [] 139 | for i in range(startnum): 140 | rd = simplerec(mexp, iterations=startite, mode='shg') 141 | errors.append(rd['minerror']) 142 | pp.append(rd['min_sp']) 143 | gp.append(rd['min_gp']) 144 | for i in range(startnum): 145 | rd = simplerec(mexp, iterations=startite, mode='blind') 146 | errors.append(rd['minerror']) 147 | pp.append(rd['min_sp']) 148 | gp.append(rd['min_gp']) 149 | 150 | minerr = np.min(errors) 151 | iindx = np.nonzero(np.array(errors) == np.min(errors))[0][0] 152 | if iindx < startnum: 153 | mode = 'shg' 154 | else: 155 | mode = 'blind' 156 | 157 | rd = simplerec(mexp, pulse=pp[iindx], gatepulse=gp[iindx], mode=mode, 158 | iterations=itestep2) 159 | if plot: 160 | plt.figure(figsize=(5,2)) 161 | plt.plot(errors, 'o') 162 | plt.axvline(x=startnum-1, lw=0.8, c='0.0', dashes=(5,1)) 163 | plt.xlabel("Round no") 164 | plt.ylabel("Frog error") 165 | simplerecresult(mexp, rd) 166 | return rd 167 | 168 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # froglib 2 | 3 | A library to reconstruct the complex optical field of short optical pulses from FROG 4 | (Frequency Resolved Optical Gating[1]) traces. 5 | 6 | For a comprehensive overview on the FROG technique, see: 7 | ``` 8 | Trebino, Rick. Frequency-resolved optical gating: the measurement of ultrashort laser pulses. 9 | Springer Science & Business Media, 2012. 10 | ``` 11 | ### What does froglib provide? 12 | 13 | - generate artificial FROG traces for Second Harmonic Generation (SHG) and Blind FROG setup 14 | - basic implementation of the PCGP (Principle Components Generalized 15 | Projection) algorithm 16 | - basic reconstruction loops 17 | - basic functions to remove simple ambiguities 18 | - tools to calculate the field with errorbars from a list of reconstructed fields 19 | 20 | ### What DOESN'T it provide? 21 | 22 | - A full-feature, ready-to-use end user program. In general, several unforeseeable things may happen 23 | when reconstructing a FROG trace. Even simple ambiguities are sometimes hard to detect automatically. 24 | Reconstruction sometimes tends to stick at traces with small Frog errors, which for the human inspector 25 | are clearly different from the experimental traces. In general, human interaction and judgement is unavoidable. 26 | 27 | - Automatic calibration. Time and frequency grid of a FROG trace have to be choosen according to the Fourier 28 | relation. Possibly, measure traces have to be stretched accordingly before starting reconstruction. 29 | All calculations in froglib are done in normalized units (pixel). 30 | 31 | 32 | ## Usage 33 | 34 | ### generate FROG traces: **frogtr** 35 | ![example frog traces](examples/pics/example_traces.png) 36 | ``` 37 | import numpy as np 38 | from matplotlib import pyplot as plt 39 | import matplotlib 40 | from froglib import * 41 | 42 | tvec = np.linspace(-8,8, 128) 43 | #double pulse 44 | t0=0.4 45 | deltat = 0.7 46 | signal1 = np.exp(-((tvec+deltat/2)/t0)**2) - np.exp(-((tvec-deltat/2)/t0)**2) * np.exp((-(tvec-deltat/2)/t0 * -1j)) 47 | signal2 = 1./np.cosh(tvec) * np.exp(1.0j * (0.6 * tvec + 0.5 * tvec**2)) 48 | 49 | # generate traces 50 | 51 | F1 = frogtr(signal1, signal1, mode='shg') 52 | F2 = frogtr(signal2, signal2, mode='shg') 53 | F3 = frogtr(signal1, signal2, mode='blind') 54 | 55 | # plot traces 56 | 57 | spp = matplotlib.figure.SubplotParams(wspace=0.5) 58 | plt.figure(figsize=(7,3), subplotpars=spp) 59 | ax1= plt.subplot(131);plt.title("double gaussian, SHG") 60 | plt.imshow(np.abs(F1)**2) 61 | ax2= plt.subplot(132);plt.title("sech, SHG") 62 | plt.imshow(np.abs(F2)**2) 63 | ax3=plt.subplot(133);plt.title("double gaussian - sech,\nBLIND") 64 | plt.imshow(np.abs(F3)**2) 65 | 66 | for ax in [ax1,ax2,ax3]: 67 | ax.set_xlabel("time") 68 | ax.set_ylabel("freq") 69 | ``` 70 | 71 | 72 | 73 | 74 | 75 | 76 | ### simple, single reconstruction: **simplerec** 77 | ![example reconstruction error](examples/pics/rec_artif_shg0.png) 78 | ![example reconstruction](examples/pics/rec_artif_shg.png) 79 | ``` 80 | import numpy as np 81 | from matplotlib import pyplot as plt 82 | from froglib import * 83 | 84 | # generate signal 85 | tmax = 7 86 | N = 128 87 | tvec = np.linspace(-tmax, tmax, N) 88 | deltat = 0.5 89 | freqoff = 1.2 90 | #two gaussians of different height and width, different freqs 91 | field = 0.5 * np.exp( - (tvec-deltat)**2) - np.exp( - (tvec+deltat)**2/0.5**2) * np.exp(1.0j * freqoff * tvec) 92 | 93 | # generate artifical trace (SHG) 94 | Mexp = np.abs(frogtr(field, field, mode='shg')) 95 | 96 | # use a simple loop of the PCGP algorithm 97 | res = simplerec(Mexp, iterations=150) 98 | 99 | # show result 100 | simplerecresult(Mexp, res) 101 | plt.show() 102 | ``` 103 | 104 | The result of the reconstruction is stored in the dictionary *res*: 105 | 106 | ``` 107 | (keys) : (values) 108 | errors : Array holding Frog error for each iteration 109 | gp, sp : Arrays with signal and gate fields for each iteration 110 | minerror : minimal Frog error that occured during iterations 111 | min_sp, min_gp : signal and gate pulses for minimal Frog error 112 | mode : mode used ('shg' or 'blind') 113 | exp : experimental trace (amplitude) 114 | ``` 115 | 116 | 117 | ### more advanced reconstruction loop: mixfrog 118 | 119 | The basic idea behind this is to make several attempts to reconstruct a trace. 120 | Each attempt initially is only iterated some steps. Then, the best 'candidate' is 121 | chosen and iterated fully. 122 | Both SHG and Blind FROG reconstructions are attempted. Usually, due to the fact that 123 | experimental SHG FROG traces show a slight asymmetric shape, be it due to noise or misalignment, 124 | the Blind part will give better result. 125 | 126 | When SHG traces are reconstructed with in 'blind' mode, both reconstructed signal and gate pulse 127 | will look very similar albeit phase/time ambiguities. 128 | 129 | For more information, see 130 | 131 | ``` 132 | Hause, A., et al. "Reliable multiple-pulse reconstruction from second-harmonic-generation 133 | frequency-resolved optical gating spectrograms." JOSA B 32.5 (2015): 868-877. 134 | ``` 135 | 136 | ![error for different attempts](examples/pics/mix0.png) 137 | ![error for different attempts](examples/pics/mix1.png) 138 | ![error for different attempts](examples/pics/mix2.png) 139 | ``` 140 | import numpy as np 141 | from matplotlib import pyplot as plt 142 | from froglib import * 143 | 144 | 145 | M = np.loadtxt("example_data/stronglychirpeddouble.dat") 146 | Mexp = np.sqrt(M) 147 | res = mixfrog(Mexp, startnum=10, plot=True ) 148 | 149 | plt.show() 150 | ``` 151 | 152 | 153 | ## License 154 | 155 | froglib is free software: you can redistribute it and/or modify 156 | it under the terms of the GNU General Public License as published by 157 | the Free Software Foundation, either version 3 of the License, or 158 | (at your option) any later version. 159 | 160 | froglib is distributed in the hope that it will be useful, 161 | but WITHOUT ANY WARRANTY; without even the implied warranty of 162 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 163 | GNU General Public License for more details. 164 | 165 | You should have received a copy of the GNU General Public License 166 | along with froglib. If not, see . 167 | 168 | Contributors: 169 | 170 | * Christoph Mahnke, 2018 (chmhnk_at_googlemail_dot_com) -------------------------------------------------------------------------------- /froglib/phasemanipulations.py: -------------------------------------------------------------------------------- 1 | """ 2 | This file is part of froglib, which allows the creation 3 | and reconstruction of FROG traces. 4 | 5 | froglib is free software: you can redistribute it and/or modify 6 | it under the terms of the GNU General Public License as published by 7 | the Free Software Foundation, either version 3 of the License, or 8 | (at your option) any later version. 9 | 10 | froglib is distributed in the hope that it will be useful, 11 | but WITHOUT ANY WARRANTY; without even the implied warranty of 12 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 13 | GNU General Public License for more details. 14 | 15 | You should have received a copy of the GNU General Public License 16 | along with froglib. If not, see . 17 | 18 | Contributors: 19 | 20 | Christoph Mahnke, 2018 21 | 22 | """ 23 | 24 | import numpy as np 25 | 26 | def remove_relative_phase_offset(field1, field2, border=6, 27 | intermediate_steps=50, 28 | magnitudes=np.linspace(0, 4, 5)): 29 | """Remove the arbitrary phase differences between two fields (linear+offset). 30 | 31 | The relative phases for two fields in the context of Frog traces can differ by some 32 | arbitrary offsets: the first one is the constant offset, the second one is the slope 33 | of the phase in the spectral domain (which corresponds to the temporal position). 34 | This algorithm removes these two for the second input field with respect to the first one. 35 | It varies the spectral phase (offset + linear component) and tries to find the 36 | best overlap. 37 | 38 | Arguments: 39 | 40 | field1 : reference field 41 | 42 | field2 : field whose phase shall be adjusted; 43 | 44 | Optional arguments: 45 | 46 | border : Numerical value for the phases to be varied in between 47 | 48 | intermediate_steps : number of intermediate steps for each magnitude 49 | 50 | magnitudes: np.array or list of powers of 10. Phase offsets and slopes 51 | as border * 10 **(-magnitudes) are tried and refines successively. 52 | 53 | Returns: 54 | 55 | field3 : field2 with adjusted phase. 56 | 57 | """ 58 | nn = len(field1) 59 | n2 = int(nn / 2.0) 60 | xv = np.arange(nn) - n2 61 | testSP1 = np.roll(np.fft.fft(np.roll(field1, n2)), n2) 62 | testSP2 = np.roll(np.fft.fft(np.roll(field2, n2)), n2) 63 | NN = intermediate_steps 64 | MM = np.zeros((NN, NN)) 65 | PosNullX = 0 66 | PosNullY = 0 67 | for magnitude in magnitudes: 68 | jjv = np.linspace(-border * 10 ** -magnitude, border * 10 ** -magnitude, NN)\ 69 | + PosNullX 70 | kkv = np.linspace(-border * 10 ** -magnitude, border * 10 ** -magnitude, NN)\ 71 | + PosNullY 72 | for j, jj in enumerate(jjv): 73 | for k, kk in enumerate(kkv): 74 | MM[j, k] = np.sum( 75 | (np.imag(testSP1) - np.imag(testSP2 \ 76 | * np.exp(1.0j * (xv * jj + kk)))) ** 2 77 | * (np.real(testSP1) - np.real(testSP2 \ 78 | * np.exp(1.0j * (xv * jj + kk)))) ** 2 79 | ) 80 | minindex = np.nonzero(MM == np.min(np.min(MM))) 81 | PosNullX = jjv[minindex[0][0]] 82 | PosNullY = kkv[minindex[1][0]] 83 | 84 | field3 = np.roll( 85 | np.fft.ifft( 86 | np.roll( 87 | testSP2 * np.exp(1.0j * (PosNullX * xv + PosNullY)) 88 | , n2) 89 | ), n2) 90 | return field3 91 | 92 | 93 | def remove_shg_freq_ambi(pulse): 94 | """Test and remove the shg frequency ambiguity (spectral shift by n/2). 95 | 96 | During reconstruction of SHG Frog, a common ambiguity occuring is a field shifted by 97 | half of the window in the spectral domain. As it gives the same (often correct) Frog 98 | trace as the unshifted field, a physically valid field can be constructed by shifting 99 | the spectrum back to the center of the frequency domain. 100 | 101 | Arguments: 102 | 103 | pulse : pulse field 104 | 105 | Returns: 106 | 107 | pulse2 : shifted pulse field 108 | 109 | """ 110 | l = len(pulse) 111 | l2 = int(l / 2) 112 | tests = np.exp(- ((np.arange(l) - l2) / (l / 4)) ** 6) 113 | pulsspeksh = np.fft.ifft(np.fft.fftshift(np.fft.fft(pulse))) 114 | normal = np.sum(np.abs(np.multiply(tests, np.fft.fftshift(np.fft.fft(pulse))))) 115 | shifted = np.sum(np.abs(np.multiply(tests, np.fft.fftshift(np.fft.fft(pulsspeksh))))) 116 | if normal > shifted: 117 | return pulse 118 | else: 119 | return pulsspeksh 120 | 121 | 122 | 123 | def remove_blind_freq_ambi(pulse, gpulse, inter_steps=200, check_shg_ambi=True): 124 | """Experimental: remove blind frog frequency ambiguity.""" 125 | errors = [] 126 | for i in range(inter_steps): 127 | ll = len(pulse) 128 | xv = np.arange(ll) - int(ll / 2) 129 | dom = np.pi / inter_steps * 2 * i 130 | sps = np.fft.fftshift(np.abs(np.fft.fft(pulse * np.exp(1.0j * dom * xv)))) 131 | spg = np.fft.fftshift(np.abs(np.fft.fft(gpulse * np.exp(-1.0j * dom * xv)))) 132 | errors.append(np.sum(np.abs(sps - spg) ** 2)) 133 | minerr = np.min(errors) 134 | ii = np.nonzero(minerr == errors)[0][0] 135 | dom = np.pi / inter_steps * 2 * ii 136 | pulse = pulse * np.exp(1.0j * dom * xv) 137 | gpulse = gpulse * np.exp(-1.0j * dom * xv) 138 | if check_shg_ambi: 139 | pulse = remove_shg_freq_ambi(pulse) 140 | gpulse = remove_shg_freq_ambi(gpulse) 141 | return pulse, gpulse 142 | 143 | 144 | 145 | def specshift_to_ref(referencepulse, pulse, inter_steps=200): 146 | """Shift spectrum of some pulse for maximum overlap with reference pulse spectrum. 147 | 148 | Input: 149 | 150 | referencepulse : reference 151 | 152 | pulse : pulse whose spectrum shall be shifted 153 | 154 | Optional Arguments: 155 | 156 | inter_steps : number of intermediate steps to try 157 | 158 | """ 159 | errors = [] 160 | for i in range(inter_steps): 161 | ll = len(referencepulse) 162 | xv = np.arange(ll) - int(ll / 2) 163 | dom = np.pi / inter_steps * 2 * i 164 | sps = np.fft.fftshift(np.abs(np.fft.fft(referencepulse))) 165 | spg = np.fft.fftshift(np.abs(np.fft.fft(pulse * np.exp(-1.0j * dom * xv)))) 166 | errors.append(np.sum(np.abs(sps - spg) ** 2)) 167 | minerr = np.min(errors) 168 | ii = np.nonzero(minerr == errors)[0][0] 169 | dom = np.pi / inter_steps * 2 * ii 170 | pulse = pulse * np.exp(-1.0j * dom * xv) 171 | return pulse -------------------------------------------------------------------------------- /LICENSE.txt: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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No Surrender of Others' Freedom. 541 | 542 | If conditions are imposed on you (whether by court order, agreement or 543 | otherwise) that contradict the conditions of this License, they do not 544 | excuse you from the conditions of this License. If you cannot convey a 545 | covered work so as to satisfy simultaneously your obligations under this 546 | License and any other pertinent obligations, then as a consequence you may 547 | not convey it at all. For example, if you agree to terms that obligate you 548 | to collect a royalty for further conveying from those to whom you convey 549 | the Program, the only way you could satisfy both those terms and this 550 | License would be to refrain entirely from conveying the Program. 551 | 552 | 13. Use with the GNU Affero General Public License. 553 | 554 | Notwithstanding any other provision of this License, you have 555 | permission to link or combine any covered work with a work licensed 556 | under version 3 of the GNU Affero General Public License into a single 557 | combined work, and to convey the resulting work. The terms of this 558 | License will continue to apply to the part which is the covered work, 559 | but the special requirements of the GNU Affero General Public License, 560 | section 13, concerning interaction through a network will apply to the 561 | combination as such. 562 | 563 | 14. Revised Versions of this License. 564 | 565 | The Free Software Foundation may publish revised and/or new versions of 566 | the GNU General Public License from time to time. Such new versions will 567 | be similar in spirit to the present version, but may differ in detail to 568 | address new problems or concerns. 569 | 570 | Each version is given a distinguishing version number. If the 571 | Program specifies that a certain numbered version of the GNU General 572 | Public License "or any later version" applies to it, you have the 573 | option of following the terms and conditions either of that numbered 574 | version or of any later version published by the Free Software 575 | Foundation. If the Program does not specify a version number of the 576 | GNU General Public License, you may choose any version ever published 577 | by the Free Software Foundation. 578 | 579 | If the Program specifies that a proxy can decide which future 580 | versions of the GNU General Public License can be used, that proxy's 581 | public statement of acceptance of a version permanently authorizes you 582 | to choose that version for the Program. 583 | 584 | Later license versions may give you additional or different 585 | permissions. However, no additional obligations are imposed on any 586 | author or copyright holder as a result of your choosing to follow a 587 | later version. 588 | 589 | 15. Disclaimer of Warranty. 590 | 591 | THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY 592 | APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT 593 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY 594 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, 595 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 596 | PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM 597 | IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF 598 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 599 | 600 | 16. Limitation of Liability. 601 | 602 | IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING 603 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS 604 | THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY 605 | GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE 606 | USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF 607 | DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD 608 | PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), 609 | EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF 610 | SUCH DAMAGES. 611 | 612 | 17. Interpretation of Sections 15 and 16. 613 | 614 | If the disclaimer of warranty and limitation of liability provided 615 | above cannot be given local legal effect according to their terms, 616 | reviewing courts shall apply local law that most closely approximates 617 | an absolute waiver of all civil liability in connection with the 618 | Program, unless a warranty or assumption of liability accompanies a 619 | copy of the Program in return for a fee. 620 | 621 | END OF TERMS AND CONDITIONS 622 | 623 | How to Apply These Terms to Your New Programs 624 | 625 | If you develop a new program, and you want it to be of the greatest 626 | possible use to the public, the best way to achieve this is to make it 627 | free software which everyone can redistribute and change under these terms. 628 | 629 | To do so, attach the following notices to the program. It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | 635 | Copyright (C) 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . --------------------------------------------------------------------------------