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Is it “common practice in Fourier transform spectroscopy to multiply the measured interferogram by an apodizing function”? If so, why?



The Next CEO of Stack OverflowWhy the magnitude of dipole moment influences on FTIR % transmittance?In infrared spectroscopy, why is there no C=C reading for E alkenes?What equipment is used for two-dimensional IR spectroscopy and how can the molecular structure of a compound be resolved?Why does nitrous oxide have 300 times the global warming potential of CO2?What do s, m, w, m-w, and w-s mean in the context of infrared spectroscopy?rovibrational spectroscopy: why do intensities of rotational lines increase with J?In vibrational spectroscopy, what affect do overtones have on the spectra?Determination of Urea and Hydrogen Peroxide in Cow Milk by ATR-FTIR(Attenuated total reflection-Fourier Transform Infrared Spectroscopy)Is there a detailed explanation as to why polarity of a molecule affects the absorption intensity of IR radiation?Why is the Infrared spectrum usually drawn using transmittance rather than absorbance?










1












$begingroup$


The recent paper in Nature Independent confirmation of a methane spike on Mars and a source region east of Gale Crater is interesting and the basis is a reanalysis of 2013 data taken by a X spectrometer about the Mars Express spacecraft in orbit around Mars looking down at the Martian atmosphere.



The paper itself is paywalled but the supplemental data describes the reanalysis in great detail.




The Planetary Fourier Spectrometer [38] (PFS) on Mars Express 37 is a double-pendulum infrared Fourier spectrometer optimized for atmospheric studies. It has two distinct spectral channels operating simultaneously and covering the wavenumber range between 200–2000 cm−1 (Long Wavelength Channel, hereafter LWC) and 2000–8300 cm−1 (Short Wavelength Channel, hereafter SWC). Both channels have a sampling step of 1 cm−1 and a spectral resolution of ~1.3 cm−1, when no apodization function is applied, and ~1.8 cm−1 when a Hamming function is applied to the measured interferograms (as in the case of the present work).




Key to the process is an understanding of how the raw data is preprocessed using a Hamming apodization function before spectral fitting.




Step 1: Hamming apodization function is applied to PFS interferograms. It is common practice in Fourier transform spectroscopy to multiply the measured interferogram by an apodizing function in order to reduce the amount of ringing present in the resulting instrumental line shape [77]. This reduces the spectral resolution a bit (from 1.3 cm-1 to 1.8 cm-1 in the case of PFS [78]), but also reduces the instrumental noise and the magnitude of the side-lobes in the instrumental line shape, which are a direct result of the finite maximum optical difference in the measured interferograms [79]. The Hamming function H is defined as H(δ/L) = 0.54+0.46cos(πδ/L), where δ is the optical path difference out to a maximum value of L.



  1. Davis, S. P., Abrams, M. C. & Brault, J. W., Fourier Transform Spectrometry, Academic Press (2001).

  2. Giuranna, M., et al., Calibration of the Planetary Fourier Spectrometer short wavelength channel. Planet. Space Sci. 53 (10), 975–991 (2005).

  3. Naylor, D.A. & Tahic, M. K., Apodizing functions for Fourier transform spectroscopy. J. Opt. Soc. Am. A 24, 3644–3648 (2007).



I was surprised to read that raw data is filtered before fitting to spectroscopic models in order to extract concentrations. I'm not an FTIRer, but I would have instead expected that all instrumental errors would be included in the fitted theoretical spectra generation and that the raw data would be fit in its pristine, unaltered form. After all, the only thing you really know for sure when fitting is that the data is the data, it's what you actually measured. Everything else is speculation.



QUESTION: Assuming that the block quote is right and it is indeed "common practice in Fourier transform spectroscopy to multiply the measured interferogram by an apodizing function in order to reduce the amount of ringing present in the resulting instrumental line shape" why is this considered "safe" to do? Why aren't all instrumental effects incorporated into the fitting function allowing for the raw data to be fit directly instead?




The spectra in question, from Independent confirmation of a methane spike on Mars and a source region east of Gale Crater:



enter image description here










share|improve this question









$endgroup$
















    1












    $begingroup$


    The recent paper in Nature Independent confirmation of a methane spike on Mars and a source region east of Gale Crater is interesting and the basis is a reanalysis of 2013 data taken by a X spectrometer about the Mars Express spacecraft in orbit around Mars looking down at the Martian atmosphere.



    The paper itself is paywalled but the supplemental data describes the reanalysis in great detail.




    The Planetary Fourier Spectrometer [38] (PFS) on Mars Express 37 is a double-pendulum infrared Fourier spectrometer optimized for atmospheric studies. It has two distinct spectral channels operating simultaneously and covering the wavenumber range between 200–2000 cm−1 (Long Wavelength Channel, hereafter LWC) and 2000–8300 cm−1 (Short Wavelength Channel, hereafter SWC). Both channels have a sampling step of 1 cm−1 and a spectral resolution of ~1.3 cm−1, when no apodization function is applied, and ~1.8 cm−1 when a Hamming function is applied to the measured interferograms (as in the case of the present work).




    Key to the process is an understanding of how the raw data is preprocessed using a Hamming apodization function before spectral fitting.




    Step 1: Hamming apodization function is applied to PFS interferograms. It is common practice in Fourier transform spectroscopy to multiply the measured interferogram by an apodizing function in order to reduce the amount of ringing present in the resulting instrumental line shape [77]. This reduces the spectral resolution a bit (from 1.3 cm-1 to 1.8 cm-1 in the case of PFS [78]), but also reduces the instrumental noise and the magnitude of the side-lobes in the instrumental line shape, which are a direct result of the finite maximum optical difference in the measured interferograms [79]. The Hamming function H is defined as H(δ/L) = 0.54+0.46cos(πδ/L), where δ is the optical path difference out to a maximum value of L.



    1. Davis, S. P., Abrams, M. C. & Brault, J. W., Fourier Transform Spectrometry, Academic Press (2001).

    2. Giuranna, M., et al., Calibration of the Planetary Fourier Spectrometer short wavelength channel. Planet. Space Sci. 53 (10), 975–991 (2005).

    3. Naylor, D.A. & Tahic, M. K., Apodizing functions for Fourier transform spectroscopy. J. Opt. Soc. Am. A 24, 3644–3648 (2007).



    I was surprised to read that raw data is filtered before fitting to spectroscopic models in order to extract concentrations. I'm not an FTIRer, but I would have instead expected that all instrumental errors would be included in the fitted theoretical spectra generation and that the raw data would be fit in its pristine, unaltered form. After all, the only thing you really know for sure when fitting is that the data is the data, it's what you actually measured. Everything else is speculation.



    QUESTION: Assuming that the block quote is right and it is indeed "common practice in Fourier transform spectroscopy to multiply the measured interferogram by an apodizing function in order to reduce the amount of ringing present in the resulting instrumental line shape" why is this considered "safe" to do? Why aren't all instrumental effects incorporated into the fitting function allowing for the raw data to be fit directly instead?




    The spectra in question, from Independent confirmation of a methane spike on Mars and a source region east of Gale Crater:



    enter image description here










    share|improve this question









    $endgroup$














      1












      1








      1





      $begingroup$


      The recent paper in Nature Independent confirmation of a methane spike on Mars and a source region east of Gale Crater is interesting and the basis is a reanalysis of 2013 data taken by a X spectrometer about the Mars Express spacecraft in orbit around Mars looking down at the Martian atmosphere.



      The paper itself is paywalled but the supplemental data describes the reanalysis in great detail.




      The Planetary Fourier Spectrometer [38] (PFS) on Mars Express 37 is a double-pendulum infrared Fourier spectrometer optimized for atmospheric studies. It has two distinct spectral channels operating simultaneously and covering the wavenumber range between 200–2000 cm−1 (Long Wavelength Channel, hereafter LWC) and 2000–8300 cm−1 (Short Wavelength Channel, hereafter SWC). Both channels have a sampling step of 1 cm−1 and a spectral resolution of ~1.3 cm−1, when no apodization function is applied, and ~1.8 cm−1 when a Hamming function is applied to the measured interferograms (as in the case of the present work).




      Key to the process is an understanding of how the raw data is preprocessed using a Hamming apodization function before spectral fitting.




      Step 1: Hamming apodization function is applied to PFS interferograms. It is common practice in Fourier transform spectroscopy to multiply the measured interferogram by an apodizing function in order to reduce the amount of ringing present in the resulting instrumental line shape [77]. This reduces the spectral resolution a bit (from 1.3 cm-1 to 1.8 cm-1 in the case of PFS [78]), but also reduces the instrumental noise and the magnitude of the side-lobes in the instrumental line shape, which are a direct result of the finite maximum optical difference in the measured interferograms [79]. The Hamming function H is defined as H(δ/L) = 0.54+0.46cos(πδ/L), where δ is the optical path difference out to a maximum value of L.



      1. Davis, S. P., Abrams, M. C. & Brault, J. W., Fourier Transform Spectrometry, Academic Press (2001).

      2. Giuranna, M., et al., Calibration of the Planetary Fourier Spectrometer short wavelength channel. Planet. Space Sci. 53 (10), 975–991 (2005).

      3. Naylor, D.A. & Tahic, M. K., Apodizing functions for Fourier transform spectroscopy. J. Opt. Soc. Am. A 24, 3644–3648 (2007).



      I was surprised to read that raw data is filtered before fitting to spectroscopic models in order to extract concentrations. I'm not an FTIRer, but I would have instead expected that all instrumental errors would be included in the fitted theoretical spectra generation and that the raw data would be fit in its pristine, unaltered form. After all, the only thing you really know for sure when fitting is that the data is the data, it's what you actually measured. Everything else is speculation.



      QUESTION: Assuming that the block quote is right and it is indeed "common practice in Fourier transform spectroscopy to multiply the measured interferogram by an apodizing function in order to reduce the amount of ringing present in the resulting instrumental line shape" why is this considered "safe" to do? Why aren't all instrumental effects incorporated into the fitting function allowing for the raw data to be fit directly instead?




      The spectra in question, from Independent confirmation of a methane spike on Mars and a source region east of Gale Crater:



      enter image description here










      share|improve this question









      $endgroup$




      The recent paper in Nature Independent confirmation of a methane spike on Mars and a source region east of Gale Crater is interesting and the basis is a reanalysis of 2013 data taken by a X spectrometer about the Mars Express spacecraft in orbit around Mars looking down at the Martian atmosphere.



      The paper itself is paywalled but the supplemental data describes the reanalysis in great detail.




      The Planetary Fourier Spectrometer [38] (PFS) on Mars Express 37 is a double-pendulum infrared Fourier spectrometer optimized for atmospheric studies. It has two distinct spectral channels operating simultaneously and covering the wavenumber range between 200–2000 cm−1 (Long Wavelength Channel, hereafter LWC) and 2000–8300 cm−1 (Short Wavelength Channel, hereafter SWC). Both channels have a sampling step of 1 cm−1 and a spectral resolution of ~1.3 cm−1, when no apodization function is applied, and ~1.8 cm−1 when a Hamming function is applied to the measured interferograms (as in the case of the present work).




      Key to the process is an understanding of how the raw data is preprocessed using a Hamming apodization function before spectral fitting.




      Step 1: Hamming apodization function is applied to PFS interferograms. It is common practice in Fourier transform spectroscopy to multiply the measured interferogram by an apodizing function in order to reduce the amount of ringing present in the resulting instrumental line shape [77]. This reduces the spectral resolution a bit (from 1.3 cm-1 to 1.8 cm-1 in the case of PFS [78]), but also reduces the instrumental noise and the magnitude of the side-lobes in the instrumental line shape, which are a direct result of the finite maximum optical difference in the measured interferograms [79]. The Hamming function H is defined as H(δ/L) = 0.54+0.46cos(πδ/L), where δ is the optical path difference out to a maximum value of L.



      1. Davis, S. P., Abrams, M. C. & Brault, J. W., Fourier Transform Spectrometry, Academic Press (2001).

      2. Giuranna, M., et al., Calibration of the Planetary Fourier Spectrometer short wavelength channel. Planet. Space Sci. 53 (10), 975–991 (2005).

      3. Naylor, D.A. & Tahic, M. K., Apodizing functions for Fourier transform spectroscopy. J. Opt. Soc. Am. A 24, 3644–3648 (2007).



      I was surprised to read that raw data is filtered before fitting to spectroscopic models in order to extract concentrations. I'm not an FTIRer, but I would have instead expected that all instrumental errors would be included in the fitted theoretical spectra generation and that the raw data would be fit in its pristine, unaltered form. After all, the only thing you really know for sure when fitting is that the data is the data, it's what you actually measured. Everything else is speculation.



      QUESTION: Assuming that the block quote is right and it is indeed "common practice in Fourier transform spectroscopy to multiply the measured interferogram by an apodizing function in order to reduce the amount of ringing present in the resulting instrumental line shape" why is this considered "safe" to do? Why aren't all instrumental effects incorporated into the fitting function allowing for the raw data to be fit directly instead?




      The spectra in question, from Independent confirmation of a methane spike on Mars and a source region east of Gale Crater:



      enter image description here







      ir-spectroscopy






      share|improve this question













      share|improve this question











      share|improve this question




      share|improve this question










      asked 3 hours ago









      uhohuhoh

      1,761840




      1,761840




















          1 Answer
          1






          active

          oldest

          votes


















          2












          $begingroup$

          You usually post interesting questions, which appear to be deceptively simple yet they are very challenging. Modern day data acquisition and signal processing is so complicated that it is almost like a black-box. It is amusing when I ask electrical engineers some signal processing questions, they don't know the answers and when I ask mathematicians it is too much applied mathematics for them. I am not an FTIR expert either but as an analytical chemist, I can add some remarks. I think apodization is routinely done in order to decrease noise and oscillations when you do an inverse transform. If you do some mathematical operations in the frequency domain, when you do the inverse transform, the level of noise is crazily high. Of course, when you are looking at very small signals do not wish to have noise.



          In general, sometimes I need to fit functions to the data to peak shaped functions. I always get a better fit once I digitally filter the data and fit later (moving average, Savitsky Golay, Hamming in the time domain and so on.) Noise is the biggest enemy of any analytical chemist or a spectroscopist.



          With any smoothing process, either in the frequency domain or in the time domain, you tend to loose resolution. There is always a sweet spot for digital filtering or if you have heard the story of Goldilocks who entered the house of three bears..."When she had finished the porridge Goldilocks felt tired and went to find somewhere to sit down. The first chair she found was too big, the second chair was still too big, but the third chair felt just right." The same rule of thumb goes for digital filtering. Too little is useless, too much you loose all resolution and just the right filtering gives you the best signal to noise ratio.






          share|improve this answer









          $endgroup$








          • 1




            $begingroup$
            As an ex organic chemist, I can confirm that using the Hamming function to apodise the data before fft is common, and I can also confirm we all just nod our heads and smile when the NMR technician explains why this is the case.
            $endgroup$
            – Ingolifs
            24 mins ago











          Your Answer





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          active

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          active

          oldest

          votes









          2












          $begingroup$

          You usually post interesting questions, which appear to be deceptively simple yet they are very challenging. Modern day data acquisition and signal processing is so complicated that it is almost like a black-box. It is amusing when I ask electrical engineers some signal processing questions, they don't know the answers and when I ask mathematicians it is too much applied mathematics for them. I am not an FTIR expert either but as an analytical chemist, I can add some remarks. I think apodization is routinely done in order to decrease noise and oscillations when you do an inverse transform. If you do some mathematical operations in the frequency domain, when you do the inverse transform, the level of noise is crazily high. Of course, when you are looking at very small signals do not wish to have noise.



          In general, sometimes I need to fit functions to the data to peak shaped functions. I always get a better fit once I digitally filter the data and fit later (moving average, Savitsky Golay, Hamming in the time domain and so on.) Noise is the biggest enemy of any analytical chemist or a spectroscopist.



          With any smoothing process, either in the frequency domain or in the time domain, you tend to loose resolution. There is always a sweet spot for digital filtering or if you have heard the story of Goldilocks who entered the house of three bears..."When she had finished the porridge Goldilocks felt tired and went to find somewhere to sit down. The first chair she found was too big, the second chair was still too big, but the third chair felt just right." The same rule of thumb goes for digital filtering. Too little is useless, too much you loose all resolution and just the right filtering gives you the best signal to noise ratio.






          share|improve this answer









          $endgroup$








          • 1




            $begingroup$
            As an ex organic chemist, I can confirm that using the Hamming function to apodise the data before fft is common, and I can also confirm we all just nod our heads and smile when the NMR technician explains why this is the case.
            $endgroup$
            – Ingolifs
            24 mins ago















          2












          $begingroup$

          You usually post interesting questions, which appear to be deceptively simple yet they are very challenging. Modern day data acquisition and signal processing is so complicated that it is almost like a black-box. It is amusing when I ask electrical engineers some signal processing questions, they don't know the answers and when I ask mathematicians it is too much applied mathematics for them. I am not an FTIR expert either but as an analytical chemist, I can add some remarks. I think apodization is routinely done in order to decrease noise and oscillations when you do an inverse transform. If you do some mathematical operations in the frequency domain, when you do the inverse transform, the level of noise is crazily high. Of course, when you are looking at very small signals do not wish to have noise.



          In general, sometimes I need to fit functions to the data to peak shaped functions. I always get a better fit once I digitally filter the data and fit later (moving average, Savitsky Golay, Hamming in the time domain and so on.) Noise is the biggest enemy of any analytical chemist or a spectroscopist.



          With any smoothing process, either in the frequency domain or in the time domain, you tend to loose resolution. There is always a sweet spot for digital filtering or if you have heard the story of Goldilocks who entered the house of three bears..."When she had finished the porridge Goldilocks felt tired and went to find somewhere to sit down. The first chair she found was too big, the second chair was still too big, but the third chair felt just right." The same rule of thumb goes for digital filtering. Too little is useless, too much you loose all resolution and just the right filtering gives you the best signal to noise ratio.






          share|improve this answer









          $endgroup$








          • 1




            $begingroup$
            As an ex organic chemist, I can confirm that using the Hamming function to apodise the data before fft is common, and I can also confirm we all just nod our heads and smile when the NMR technician explains why this is the case.
            $endgroup$
            – Ingolifs
            24 mins ago













          2












          2








          2





          $begingroup$

          You usually post interesting questions, which appear to be deceptively simple yet they are very challenging. Modern day data acquisition and signal processing is so complicated that it is almost like a black-box. It is amusing when I ask electrical engineers some signal processing questions, they don't know the answers and when I ask mathematicians it is too much applied mathematics for them. I am not an FTIR expert either but as an analytical chemist, I can add some remarks. I think apodization is routinely done in order to decrease noise and oscillations when you do an inverse transform. If you do some mathematical operations in the frequency domain, when you do the inverse transform, the level of noise is crazily high. Of course, when you are looking at very small signals do not wish to have noise.



          In general, sometimes I need to fit functions to the data to peak shaped functions. I always get a better fit once I digitally filter the data and fit later (moving average, Savitsky Golay, Hamming in the time domain and so on.) Noise is the biggest enemy of any analytical chemist or a spectroscopist.



          With any smoothing process, either in the frequency domain or in the time domain, you tend to loose resolution. There is always a sweet spot for digital filtering or if you have heard the story of Goldilocks who entered the house of three bears..."When she had finished the porridge Goldilocks felt tired and went to find somewhere to sit down. The first chair she found was too big, the second chair was still too big, but the third chair felt just right." The same rule of thumb goes for digital filtering. Too little is useless, too much you loose all resolution and just the right filtering gives you the best signal to noise ratio.






          share|improve this answer









          $endgroup$



          You usually post interesting questions, which appear to be deceptively simple yet they are very challenging. Modern day data acquisition and signal processing is so complicated that it is almost like a black-box. It is amusing when I ask electrical engineers some signal processing questions, they don't know the answers and when I ask mathematicians it is too much applied mathematics for them. I am not an FTIR expert either but as an analytical chemist, I can add some remarks. I think apodization is routinely done in order to decrease noise and oscillations when you do an inverse transform. If you do some mathematical operations in the frequency domain, when you do the inverse transform, the level of noise is crazily high. Of course, when you are looking at very small signals do not wish to have noise.



          In general, sometimes I need to fit functions to the data to peak shaped functions. I always get a better fit once I digitally filter the data and fit later (moving average, Savitsky Golay, Hamming in the time domain and so on.) Noise is the biggest enemy of any analytical chemist or a spectroscopist.



          With any smoothing process, either in the frequency domain or in the time domain, you tend to loose resolution. There is always a sweet spot for digital filtering or if you have heard the story of Goldilocks who entered the house of three bears..."When she had finished the porridge Goldilocks felt tired and went to find somewhere to sit down. The first chair she found was too big, the second chair was still too big, but the third chair felt just right." The same rule of thumb goes for digital filtering. Too little is useless, too much you loose all resolution and just the right filtering gives you the best signal to noise ratio.







          share|improve this answer












          share|improve this answer



          share|improve this answer










          answered 33 mins ago









          M. FarooqM. Farooq

          1,142110




          1,142110







          • 1




            $begingroup$
            As an ex organic chemist, I can confirm that using the Hamming function to apodise the data before fft is common, and I can also confirm we all just nod our heads and smile when the NMR technician explains why this is the case.
            $endgroup$
            – Ingolifs
            24 mins ago












          • 1




            $begingroup$
            As an ex organic chemist, I can confirm that using the Hamming function to apodise the data before fft is common, and I can also confirm we all just nod our heads and smile when the NMR technician explains why this is the case.
            $endgroup$
            – Ingolifs
            24 mins ago







          1




          1




          $begingroup$
          As an ex organic chemist, I can confirm that using the Hamming function to apodise the data before fft is common, and I can also confirm we all just nod our heads and smile when the NMR technician explains why this is the case.
          $endgroup$
          – Ingolifs
          24 mins ago




          $begingroup$
          As an ex organic chemist, I can confirm that using the Hamming function to apodise the data before fft is common, and I can also confirm we all just nod our heads and smile when the NMR technician explains why this is the case.
          $endgroup$
          – Ingolifs
          24 mins ago

















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