000601075 001__ 601075 000601075 005__ 20250715170835.0 000601075 0247_ $$2doi$$a10.3390/photochem4010005 000601075 0247_ $$2datacite_doi$$a10.3204/PUBDB-2024-00101 000601075 0247_ $$2altmetric$$aaltmetric:161262765 000601075 0247_ $$2WOS$$aWOS:001268541300001 000601075 0247_ $$2openalex$$aopenalex:W4391383739 000601075 037__ $$aPUBDB-2024-00101 000601075 041__ $$aEnglish 000601075 082__ $$a540 000601075 1001_ $$0P:(DE-H253)PIP1084521$$aTikhonov, Denis$$b0$$eCorresponding author 000601075 245__ $$aInverse problems in pump-probe spectroscopy 000601075 260__ $$aBasel, Switzerland$$bMDPI$$c2024 000601075 3367_ $$2DRIVER$$aarticle 000601075 3367_ $$2DataCite$$aOutput Types/Journal article 000601075 3367_ $$0PUB:(DE-HGF)16$$2PUB:(DE-HGF)$$aJournal Article$$bjournal$$mjournal$$s1738232675_3824113 000601075 3367_ $$2BibTeX$$aARTICLE 000601075 3367_ $$2ORCID$$aJOURNAL_ARTICLE 000601075 3367_ $$00$$2EndNote$$aJournal Article 000601075 520__ $$aUltrafast pump-probe spectroscopic studies allow for deep insights into the mechanisms and timescales of photophysical and photochemical processes. Extracting valuable information from these studies, such as reactive intermediates’ lifetimes and coherent oscillation frequencies, is an example of the inverse problems of chemical kinetics. This article describes a consistent approach for solving this inverse problem that avoids the common obstacles of simple least-squares fitting that can lead to unreliable results. The presented approach is based on the regularized Markov Chain Monte Carlo sampling for the strongly nonlinear parameters, allowing for a straightforward solution of the ill-posed nonlinear inverse problem. The software to implement the described fitting routine is introduced and the numerical examples of its application are given. We will also touch on criticalexperimental parameters, such as the temporal overlap of pulses and cross-correlation time and their connection to the minimal reachable time resolution. 000601075 536__ $$0G:(DE-HGF)POF4-631$$a631 - Matter – Dynamics, Mechanisms and Control (POF4-631)$$cPOF4-631$$fPOF IV$$x0 000601075 536__ $$0G:(DE-H253)F-20191568$$aFS-Proposal: F-20191568 (F-20191568)$$cF-20191568$$x1 000601075 542__ $$2Crossref$$i2024-01-31$$uhttps://creativecommons.org/licenses/by/4.0/ 000601075 588__ $$aDataset connected to CrossRef, Journals: bib-pubdb1.desy.de 000601075 693__ $$0EXP:(DE-H253)F-BL1-20150101$$1EXP:(DE-H253)FLASH-20150101$$6EXP:(DE-H253)F-BL1-20150101$$aFLASH$$fFLASH Beamline BL1$$x0 000601075 7001_ $$0P:(DE-H253)PIP1088985$$aGarg, Diksha$$b1 000601075 7001_ $$0P:(DE-H253)PIP1013514$$aSchnell, Melanie$$b2$$eCorresponding author 000601075 77318 $$2Crossref$$3journal-article$$a10.3390/photochem4010005$$bMDPI AG$$d2024-01-31$$n1$$p57-110$$tPhotochem$$v4$$x2673-7256$$y2024 000601075 773__ $$0PERI:(DE-600)3136471-8$$a10.3390/photochem4010005$$gVol. 4, no. 1, p. 57 - 110$$n1$$p57-110$$tPhotochem$$v4$$x2673-7256$$y2024 000601075 8564_ $$uhttps://bib-pubdb1.desy.de/record/601075/files/HTML-Approval_of_scientific_publication.html 000601075 8564_ $$uhttps://bib-pubdb1.desy.de/record/601075/files/PDF-Approval_of_scientific_publication.pdf 000601075 8564_ $$uhttps://bib-pubdb1.desy.de/record/601075/files/published%20version_%20inverse%20problems%20in%20pumpo-probe.pdf$$yOpenAccess 000601075 8564_ $$uhttps://bib-pubdb1.desy.de/record/601075/files/published%20version_%20inverse%20problems%20in%20pumpo-probe.pdf?subformat=pdfa$$xpdfa$$yOpenAccess 000601075 909CO $$ooai:bib-pubdb1.desy.de:601075$$pdnbdelivery$$pdriver$$pVDB$$popen_access$$popenaire 000601075 9101_ $$0I:(DE-588b)2008985-5$$6P:(DE-H253)PIP1084521$$aDeutsches Elektronen-Synchrotron$$b0$$kDESY 000601075 9101_ $$0I:(DE-588b)2008985-5$$6P:(DE-H253)PIP1088985$$aDeutsches Elektronen-Synchrotron$$b1$$kDESY 000601075 9101_ $$0I:(DE-588b)2008985-5$$6P:(DE-H253)PIP1013514$$aDeutsches Elektronen-Synchrotron$$b2$$kDESY 000601075 9131_ $$0G:(DE-HGF)POF4-631$$1G:(DE-HGF)POF4-630$$2G:(DE-HGF)POF4-600$$3G:(DE-HGF)POF4$$4G:(DE-HGF)POF$$aDE-HGF$$bForschungsbereich Materie$$lVon Materie zu Materialien und Leben$$vMatter – Dynamics, Mechanisms and Control$$x0 000601075 9141_ $$y2024 000601075 915__ $$0StatID:(DE-HGF)0200$$2StatID$$aDBCoverage$$bSCOPUS$$d2025-01-08 000601075 915__ $$0LIC:(DE-HGF)CCBY4$$2HGFVOC$$aCreative Commons Attribution CC BY 4.0 000601075 915__ $$0StatID:(DE-HGF)0112$$2StatID$$aWoS$$bEmerging Sources Citation Index$$d2025-01-08 000601075 915__ $$0StatID:(DE-HGF)0501$$2StatID$$aDBCoverage$$bDOAJ Seal$$d2023-03-15T23:54:11Z 000601075 915__ $$0StatID:(DE-HGF)0500$$2StatID$$aDBCoverage$$bDOAJ$$d2023-03-15T23:54:11Z 000601075 915__ $$0StatID:(DE-HGF)0700$$2StatID$$aFees$$d2025-01-08 000601075 915__ $$0StatID:(DE-HGF)0150$$2StatID$$aDBCoverage$$bWeb of Science Core Collection$$d2025-01-08 000601075 915__ $$0StatID:(DE-HGF)0510$$2StatID$$aOpenAccess 000601075 915__ $$0StatID:(DE-HGF)0030$$2StatID$$aPeer Review$$bDOAJ : Anonymous peer review$$d2023-03-15T23:54:11Z 000601075 915__ $$0StatID:(DE-HGF)0561$$2StatID$$aArticle Processing Charges$$d2025-01-08 000601075 915__ $$0StatID:(DE-HGF)0300$$2StatID$$aDBCoverage$$bMedline$$d2025-01-08 000601075 915__ $$0StatID:(DE-HGF)0199$$2StatID$$aDBCoverage$$bClarivate Analytics Master Journal List$$d2025-01-08 000601075 9201_ $$0I:(DE-H253)FS-SMP-20171124$$kFS-SMP$$lSpectroscopy of molecular processes$$x0 000601075 980__ $$ajournal 000601075 980__ $$aVDB 000601075 980__ $$aUNRESTRICTED 000601075 980__ $$aI:(DE-H253)FS-SMP-20171124 000601075 9801_ $$aFullTexts 000601075 999C5 $$1Zewail$$2Crossref$$9-- missing cx lookup --$$a10.1002/1521-3773(20000804)39:15<2586::AID-ANIE2586>3.0.CO;2-O$$p2586 -$$tAngew. Chem. Int. Ed.$$v39$$y2000 000601075 999C5 $$1Young$$2Crossref$$9-- missing cx lookup --$$a10.1088/1361-6455/aa9735$$p032003 -$$tJ. Phys. At. Mol. Opt. Phys.$$v51$$y2018 000601075 999C5 $$1Zettergren$$2Crossref$$oZettergren 2021$$y2021 000601075 999C5 $$1Hertel$$2Crossref$$9-- missing cx lookup --$$a10.1088/0034-4885/69/6/R06$$p1897 -$$tRep. Prog. Phys.$$v69$$y2006 000601075 999C5 $$1Scutelnic$$2Crossref$$9-- missing cx lookup --$$a10.1038/s41467-021-25045-0$$p5003 -$$tNat. Commun.$$v12$$y2021 000601075 999C5 $$1Lee$$2Crossref$$9-- missing cx lookup --$$a10.1038/s41467-021-26193-z$$p6107 -$$tNat. Commun.$$v12$$y2021 000601075 999C5 $$1Garg$$2Crossref$$9-- missing cx lookup --$$a10.3389/fphy.2022.880793$$p880793 -$$tFront. Phys.$$v10$$y2022 000601075 999C5 $$1Calegari$$2Crossref$$9-- missing cx lookup --$$a10.1126/science.1254061$$p336 -$$tScience$$v346$$y2014 000601075 999C5 $$1Wolf$$2Crossref$$9-- missing cx lookup --$$a10.1039/D0FD00112K$$p555 -$$tFaraday Discuss.$$v228$$y2021 000601075 999C5 $$1Onvlee$$2Crossref$$9-- missing cx lookup --$$a10.1038/s41467-022-33901-w$$p7462 -$$tNat. Commun.$$v13$$y2022 000601075 999C5 $$1Brixner$$2Crossref$$9-- missing cx lookup --$$a10.1002/anie.202102901$$p18867 -$$tAngew. Chem. Int. Ed.$$v60$$y2021 000601075 999C5 $$2Crossref$$uPress, W.H., Teukolsky, S.A., Vetterling, W.T., and Flannery, B.P. (2007). Numerical Recipes 3rd Edition: The Art of Scientific Computing, Cambridge University Press. [3rd ed.]. 000601075 999C5 $$1Mosegaard$$2Crossref$$9-- missing cx lookup --$$a10.1029/94JB03097$$p12431 -$$tJ. Geophys. Res. Solid Earth$$v100$$y1995 000601075 999C5 $$2Crossref$$9-- missing cx lookup --$$a10.1146/annurev-statistics-031017-100108$$uBingham, D., Butler, T., and Estep, D. (2024). Inverse Problems for Physics-Based Process Models. Annu. Rev. Stat. Its Appl., 11. 000601075 999C5 $$1Tikhonov$$2Crossref$$oTikhonov 1963$$y1963 000601075 999C5 $$2Crossref$$9-- missing cx lookup --$$a10.1007/978-94-017-5167-4$$uTikhonov, A., Leonov, A., and Yagola, A. (1998). Nonlinear Ill-Posed Problems, Chapman & Hall. 000601075 999C5 $$1Hoerl$$2Crossref$$9-- missing cx lookup --$$a10.1080/00401706.1970.10488634$$p55 -$$tTechnometrics$$v12$$y1970 000601075 999C5 $$1Pedersen$$2Crossref$$9-- missing cx lookup --$$a10.1080/00268979609482552$$p1455 -$$tMol. Phys.$$v89$$y1996 000601075 999C5 $$1Hadamard$$2Crossref$$oHadamard 1902$$y1902 000601075 999C5 $$1Tikhonov$$2Crossref$$9-- missing cx lookup --$$a10.1016/j.molstruc.2016.05.090$$p20 -$$tJ. Mol. Struct.$$v1132$$y2017 000601075 999C5 $$1Hestenes$$2Crossref$$9-- missing cx lookup --$$a10.6028/jres.049.044$$p409 -$$tJ. Res. Natl. Bur. Stand.$$v49$$y1952 000601075 999C5 $$1Powell$$2Crossref$$9-- missing cx lookup --$$a10.1093/comjnl/7.2.155$$p155 -$$tComput. J.$$v7$$y1964 000601075 999C5 $$1Tibshirani$$2Crossref$$9-- missing cx lookup --$$a10.1111/j.2517-6161.1996.tb02080.x$$p267 -$$tJ. R. Stat. Soc. Ser. (Methodol.)$$v58$$y1996 000601075 999C5 $$1Santosa$$2Crossref$$9-- missing cx lookup --$$a10.1137/0907087$$p1307 -$$tSIAM J. Sci. Stat. Comput.$$v7$$y1986 000601075 999C5 $$1Bauer$$2Crossref$$9-- missing cx lookup --$$a10.1016/j.matcom.2011.01.016$$p1795 -$$tMath. Comput. Simul.$$v81$$y2011 000601075 999C5 $$1Chiu$$2Crossref$$9-- missing cx lookup --$$a10.1016/0022-2860(79)80066-6$$p185 -$$tJ. Mol. Struct.$$v54$$y1979 000601075 999C5 $$1Holub$$2Crossref$$9-- missing cx lookup --$$a10.1002/chem.201805145$$p2313 -$$tChem.—Eur. J.$$v25$$y2019 000601075 999C5 $$1Vishnevskiy$$2Crossref$$9-- missing cx lookup --$$a10.1021/acs.inorgchem.5b02102$$p11868 -$$tInorg. Chem.$$v54$$y2015 000601075 999C5 $$1Metropolis$$2Crossref$$9-- missing cx lookup --$$a10.1063/1.1699114$$p1087 -$$tJ. Chem. Phys.$$v21$$y2004 000601075 999C5 $$1Hastings$$2Crossref$$9-- missing cx lookup --$$a10.1093/biomet/57.1.97$$p97 -$$tBiometrika$$v57$$y1970 000601075 999C5 $$1Rosenbluth$$2Crossref$$9-- missing cx lookup --$$a10.1063/1.1632112$$p22 -$$tAIP Conf. Proc.$$v690$$y2003 000601075 999C5 $$1Snellenburg$$2Crossref$$9-- missing cx lookup --$$a10.18637/jss.v049.i03$$p1 -$$tJ. Stat. Softw.$$v49$$y2012 000601075 999C5 $$1Pascher$$2Crossref$$9-- missing cx lookup --$$a10.1021/acs.jpca.2c00907$$p4087 -$$tJ. Phys. Chem.$$v126$$y2022 000601075 999C5 $$1Arecchi$$2Crossref$$9-- missing cx lookup --$$a10.1109/JQE.1965.1072212$$p169 -$$tIEEE J. Quantum Electron.$$v1$$y1965 000601075 999C5 $$1Lindh$$2Crossref$$9-- missing cx lookup --$$a10.1021/acs.jpca.3c06983$$p10210 -$$tJ. Phys. Chem.$$v127$$y2023 000601075 999C5 $$1Mengele$$2Crossref$$9-- missing cx lookup --$$a10.1002/chem.202201931$$pe202201931 -$$tChem.—Eur. J.$$v28$$y2022 000601075 999C5 $$1Shchatsinin$$2Crossref$$9-- missing cx lookup --$$a10.1063/1.3026734$$p204308 -$$tJ. Chem. Phys.$$v129$$y2008 000601075 999C5 $$1Larsen$$2Crossref$$9-- missing cx lookup --$$a10.1016/j.bbabio.2004.04.011$$p82 -$$tBiochim. Biophys. Acta (BBA)-Bioenerg.$$v1657$$y2004 000601075 999C5 $$2Crossref$$uConnors, K. (1990). Chemical Kinetics: The Study of Reaction Rates in Solution, VCH Publishers, Inc. 000601075 999C5 $$2Crossref$$uAtkins, P., and Paula, J. (2008). Atkins’ Physical Chemistry, Oxford University Press. 000601075 999C5 $$1Rivas$$2Crossref$$9-- missing cx lookup --$$a10.1364/OPTICA.454920$$p429 -$$tOptica$$v9$$y2022 000601075 999C5 $$1Debnath$$2Crossref$$9-- missing cx lookup --$$a10.1038/s41467-019-10989-1$$p2944 -$$tNat. Commun.$$v10$$y2019 000601075 999C5 $$2Crossref$$9-- missing cx lookup --$$a10.1093/hesc/9780199541423.001.0001$$uAtkins, P., and Friedman, R. (2011). Molecular Quantum Mechanics, OUP Oxford. 000601075 999C5 $$1Manzano$$2Crossref$$9-- missing cx lookup --$$a10.1063/1.5115323$$p025106 -$$tAIP Adv.$$v10$$y2020 000601075 999C5 $$1Tikhonov$$2Crossref$$9-- missing cx lookup --$$a10.1126/sciadv.ade0311$$peade0311 -$$tSci. Adv.$$v8$$y2022 000601075 999C5 $$1Sun$$2Crossref$$9-- missing cx lookup --$$a10.1038/s41467-023-36653-3$$p934 -$$tNat. Commun.$$v14$$y2023 000601075 999C5 $$1Hatano$$2Crossref$$9-- missing cx lookup --$$a10.1080/00268976.2019.1593535$$p2121 -$$tMol. Phys.$$v117$$y2019 000601075 999C5 $$1Schulz$$2Crossref$$9-- missing cx lookup --$$a10.1038/ncomms6938$$p5938 -$$tNat. Commun.$$v6$$y2015 000601075 999C5 $$1Savelyev$$2Crossref$$9-- missing cx lookup --$$a10.1088/1367-2630/aa652d$$p043009 -$$tNew J. Phys.$$v19$$y2017 000601075 999C5 $$2Crossref$$9-- missing cx lookup --$$a10.1364/CLEO_SI.2019.STu4E.4$$uSchirmel, N., Alisauskas, S., Huülsenbusch, T., Manschwetus, B., Mohr, C., Winkelmann, L., Große-Wortmann, U., Zheng, J., Lang, T., and Hartl, I. (2019, January 5–10). Long-Term Stabilization of Temporal and Spectral Drifts of a Burst-Mode OPCPA System. Proceedings of the Conference on Lasers and Electro-Optics, San Jose, CA, USA. 000601075 999C5 $$1Lambropoulos$$2Crossref$$9-- missing cx lookup --$$a10.1016/S0065-2199(08)60043-3$$p87 -$$tAdv. At. Mol. Phys.$$v12$$y1976 000601075 999C5 $$1Kheifets$$2Crossref$$9-- missing cx lookup --$$a10.1088/1361-6455/acb188$$p022001 -$$tJ. Phys. At. Mol. Opt. Phys.$$v56$$y2023 000601075 999C5 $$1Virtanen$$2Crossref$$9-- missing cx lookup --$$a10.1038/s41592-019-0686-2$$p261 -$$tNat. Methods$$v17$$y2020 000601075 999C5 $$2Crossref$$uChopra, P. (2022). Astrochemically Relevant Polycyclic Aromatic Hydrocarbons Investigated Using Ultrafast Pump-Probe Spectroscopy and Near-Edge X-ray Absorption Fine Structure Spectroscopy. [Ph.D. Thesis, Christian-Albrechts-Universität zu Kiel]. 000601075 999C5 $$2Crossref$$uGarg, D. (2023). Electronic Structure and Ultrafast Fragmentation Dynamics of Polycyclic Aromatic Hydrocarbons. [Ph.D. Thesis, Universität Hamburg]. 000601075 999C5 $$1Douguet$$2Crossref$$9-- missing cx lookup --$$a10.1103/PhysRevA.95.013407$$p013407 -$$tPhys. Rev. A$$v95$$y2017 000601075 999C5 $$1Epp$$2Crossref$$9-- missing cx lookup --$$a10.1016/j.nima.2009.12.053$$p483 -$$tNucl. Instruments Methods Phys. Res. Sect. Accel. Spectrom. Detect. Assoc. Equip.$$v614$$y2010 000601075 999C5 $$1Erk$$2Crossref$$9-- missing cx lookup --$$a10.1107/S1600577518008585$$p1529 -$$tJ. Synchrotron. Radiat.$$v25$$y2018 000601075 999C5 $$2Crossref$$9-- missing cx lookup --$$a10.1007/978-3-319-04507-8$$uJaeschke, E., Khan, S., Schneider, J.R., and Hastings, J.B. (2014). Synchrotron Light Sources and Free-Electron Lasers: Accelerator Physics, Instrumentation and Science Applications, Springer International Publishing. 000601075 999C5 $$1Beye$$2Crossref$$9-- missing cx lookup --$$a10.1140/epjp/s13360-023-03814-8$$p193 -$$tEur. Phys. J. Plus$$v138$$y2023 000601075 999C5 $$1Garcia$$2Crossref$$9-- missing cx lookup --$$a10.1364/JOSA.55.000654$$p654 -$$tJ. Opt. Soc. Am.$$v55$$y1965 000601075 999C5 $$1Martin$$2Crossref$$9-- missing cx lookup --$$a10.1103/PhysRevA.36.3575$$p3575 -$$tPhys. Rev. A$$v36$$y1987 000601075 999C5 $$2Crossref$$uWilliams, T., and Kelley, C. (2020, January 20). Gnuplot 5.4: An Interactive Plotting Program. Available online: http://www.gnuplot.info. 000601075 999C5 $$1LEVENBERG$$2Crossref$$9-- missing cx lookup --$$a10.1090/qam/10666$$p164 -$$tQ. Appl. Math.$$v2$$y1944 000601075 999C5 $$1Marquardt$$2Crossref$$9-- missing cx lookup --$$a10.1137/0111030$$p431 -$$tJ. Soc. Ind. Appl. Math.$$v11$$y1963 000601075 999C5 $$1Akaike$$2Crossref$$9-- missing cx lookup --$$a10.1109/TAC.1974.1100705$$p716 -$$tIEEE Trans. Autom. Control$$v19$$y1974 000601075 999C5 $$2Crossref$$9-- missing cx lookup --$$a10.1007/BF00651344$$p387 -$$tAstrophys. Space Sci.$$v4$$y1969 000601075 999C5 $$1Tikhonov$$2Crossref$$9-- missing cx lookup --$$a10.1063/5.0168417$$p174101 -$$tJ. Chem. Phys.$$v159$$y2023 000601075 999C5 $$2Crossref$$9-- missing cx lookup --$$a10.1007/978-3-662-22574-5$$uShapiro, S.L. (1977). Ultrashort Light Pulses: Picosecond Techniques and Applications, Springer. 000601075 999C5 $$1Vardeny$$2Crossref$$9-- missing cx lookup --$$a10.1016/0030-4018(81)90231-5$$p396 -$$tOpt. Commun.$$v39$$y1981 000601075 999C5 $$1Lebedev$$2Crossref$$9-- missing cx lookup --$$a10.1134/1.1884668$$p272 -$$tJ. Exp. Theor. Phys.$$v100$$y2005 000601075 999C5 $$1Rhodes$$2Crossref$$9-- missing cx lookup --$$a10.1002/lpor.201200102$$p557 -$$tLaser Photonics Rev.$$v7$$y2013 000601075 999C5 $$2Crossref$$u(2024, January 18). SciPy: Open Source Scientific Tools for Python. Available online: http://www.scipy.org/. 000601075 999C5 $$1Weigand$$2Crossref$$9-- missing cx lookup --$$a10.1007/s43630-023-00460-y$$p2413 -$$tPhotochem. Photobiol. Sci.$$v22$$y2023 000601075 999C5 $$1Niklas$$2Crossref$$9-- missing cx lookup --$$a10.1016/S0006-3495(03)74804-8$$p3899 -$$tBiophys. J.$$v85$$y2003 000601075 999C5 $$1Croce$$2Crossref$$9-- missing cx lookup --$$a10.1016/S0006-3495(01)76069-9$$p901 -$$tBiophys. J.$$v80$$y2001 000601075 999C5 $$1Holzwarth$$2Crossref$$9-- missing cx lookup --$$a10.1529/biophysj.105.059824$$p552 -$$tBiophys. J.$$v90$$y2006 000601075 999C5 $$1Zurek$$2Crossref$$9-- missing cx lookup --$$a10.1063/1.881293$$p36 -$$tPhys. Today$$v44$$y1991 000601075 999C5 $$1Zurek$$2Crossref$$oZurek 2002$$y2002