Forschungszentrum Karlsruhe Technik und Umwelt. LINEFIT concept. Problem: Transition from measured transmission spectrum to ILS.
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1 LINEFI concept Poblem: anston om measued tansmsson spectum to ILS tansmsson esponse [cm] wae numbe [cm - ] wae numbe [cm - ] Necessay steps: alculaton o adated spectum Deconoluton o ILS Dect deconoluton s unsatsactoy due to compaable wdth o ILS and sgnatues n the adated spectum and due to pesence o nose. Soluton: Intoduce a model o the ILS and do a t o model paametes. Fo optmal econstucton use sucent numbe o paametes and appopate (physcally motated egulasaton constant.
2 ILS paametesaton used by LINEFI.0 deal eal Expement o thought: Inteeogam o puely monochomatc souce sgnal opd [cm] he deal (e coected nteeogam shows pue cosne oscllaton embedded n a snc-shaped enelope. he actual (e coected nteeogam shows deatng modulaton and e oentaton: Repesentaton by complex modulaton ecency (Note ambguty: Lnea e eo equalent to sht n spectal doman. LINEFI smple ILS model paametes: Lnea declne o modulaton ecency, constant e eo LINEFI extended ILS model paametes:
3 omplex modulaton ecency at 0 equdstant postons along optcal path deence. Regulasaton constants ae: ssume constant e eo, assume constant modulaton ecency. LINEFI8: Use dened constants possble! ddtonal paametes to be tted LINEFI handles seeal MWs at the same tme to deduce a common ILS. Each MW should contan a sngle, solated lne. Fo each MW thee ae two (up to ou addtonal t paametes: Inddual spectal sht o compensate o mpeect calbaton o spectal abscssa and mpeect spectoscopc data Inddual gas column o compensate o eo n gas tempeatue and mpeect spectoscopc data LINEFI8: Inddual scale and slope o tansmsson spectum o compensate o eos n the pepaaton o tansmsson spectum (Note: aeul adustment by hand usng a wde spectal wndow s an accuate method. I you pee to do ont t o these quanttes usng LINEFI, choose MW wde than n case o ILS eteal alone, at least 0. cm -.
4 he eteal pocedue Fo each paamete to be adusted, LINEFI calculates a deate (geneally constucted numecally. he deate specta buld up the Jakoban. he lneased poblem s soled, seeal teatons ae needed to nd the nal soluton (numbe o teatons set by use. Reteal n case o smple paamete set Numbe o paametes: n MW ( n MW Poblem s well-posed, no addtonal constants needed,, = ( ( calc Reteal n case o extended paamete set Numbe o paametes: 40 n MW ( n MW Poblem s ll-posed, egulasaton constants needed, = ( ((, mod,mod,mod,, calc cost uncton calc mod,mod mod, LINEFI8: calc = (, eg mod,,,,,,, (( eg
5 = opeato o deaton, : Opeato o st deate, / : path dependent weght o each constant. ost uncton: calc, mod ( mod eg mod,, ( eg Sgncance o esults Measued spectal lnes and ILS ae o compaable wdth. heeoe esults a educed sblty o detals n the modulaton ecency and e oentaton at lage OPD. he sgncance o the eteed paamete ecto s epesented by the aeagng kenels. eg = Ken n K = ( mod mod mod he column n o the aeagng kenel matx K depcts the esponse o the eteed paamete ecto to the aaton o the model paamete n. kenel esponse N O lne aound 00 cm opd [cm]
6 Note: Detals n modulaton and e beyond the lmt accessble by gas cell measuements ae hadly detectable n atmosphec obseatons also. heeoe, ths s no panul lmtaton o cell measuements. lso ead LINEFI kenels the othe way ound: Useul esolng powe o measung atmosphec lnes (compaable Dopple wdth, compaable SNR can be estmated om the kenels.
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