Abstract

We devised a novel two-step reference scheme that can greatly suppress the additive and convolutional noises in heterodyne nonlinear spectroscopy. To optimally remove additive noise, we fully utilized the spectral correlation in multi-channel reference data through a linear combination and regression algorithm. Using our pump-probe 2D IR spectrometer, we demonstrated that our scheme can improve the signal-to-noise ratio by 10-30 times and reach the noise floor of the signal detector. The new algorithm is guaranteed to reduce noise, enables the use of unmatched reference detectors, and does not introduce baseline shift or signal distortion. This scheme is applicable to many heterodyne spectroscopic techniques.

© 2017 Optical Society of America

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References

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2016 (3)

2015 (3)

K. Röttger, S. Wang, F. Renth, J. Bahrenburg, and F. Temps, “A femtosecond pump–probe spectrometer for dynamics in transmissive polymer films,” Appl. Phys. B 118(2), 185–193 (2015).

L. A. Bizimana, J. Brazard, W. P. Carbery, T. Gellen, and D. B. Turner, “Resolving molecular vibronic structure using high-sensitivity two-dimensional electronic spectroscopy,” J. Chem. Phys. 143(16), 164203 (2015).
[PubMed]

J. Brazard, L. A. Bizimana, and D. B. Turner, “Accurate convergence of transient-absorption spectra using pulsed lasers,” Rev. Sci. Instrum. 86(5), 053106 (2015).
[PubMed]

2014 (3)

2013 (1)

2012 (1)

G. Auböck, C. Consani, R. Monni, A. Cannizzo, F. van Mourik, and M. Chergui, “Femtosecond pump/supercontinuum-probe setup with 20 kHz repetition rate,” Rev. Sci. Instrum. 83(9), 093105 (2012).
[PubMed]

2011 (1)

C. A. Werley, S. M. Teo, and K. A. Nelson, “Pulsed laser noise analysis and pump-probe signal detection with a data acquisition card,” Rev. Sci. Instrum. 82(12), 123108 (2011).
[PubMed]

2010 (1)

A. L. Dobryakov, S. A. Kovalenko, A. Weigel, J. L. Pérez-Lustres, J. Lange, A. Müller, and N. P. Ernsting, “Femtosecond pump/supercontinuum-probe spectroscopy: Optimized setup and signal analysis for single-shot spectral referencing,” Rev. Sci. Instrum. 81(11), 113106 (2010).
[PubMed]

2009 (1)

U. Megerle, I. Pugliesi, C. Schriever, C. F. Sailer, and E. Riedle, “Sub-50 fs broadband absorption spectroscopy with tunable excitation: putting the analysis of ultrafast molecular dynamics on solid ground,” Appl. Phys. B 96(2), 215–231 (2009).

2008 (1)

C. Schriever, S. Lochbrunner, E. Riedle, and D. J. Nesbitt, “Ultrasensitive ultraviolet-visible 20 fs absorption spectroscopy of low vapor pressure molecules in the gas phase,” Rev. Sci. Instrum. 79(1), 013107 (2008).
[PubMed]

2007 (2)

D. Polli, L. Lüer, and G. Cerullo, “High-time-resolution pump-probe system with broadband detection for the study of time-domain vibrational dynamics,” Rev. Sci. Instrum. 78(10), 103108 (2007).
[PubMed]

K. E. H. Anderson, S. L. Sewall, R. R. Cooney, and P. Kambhampati, “Noise analysis and noise reduction methods in kilohertz pump-probe experiments,” Rev. Sci. Instrum. 78(7), 073101 (2007).
[PubMed]

2006 (2)

S. Sul, D. Karaiskaj, Y. Jiang, and N.-H. Ge, “Conformations of N-Acetyl-L-Prolinamide by Two-Dimensional Infrared Spectroscopy,” J. Phys. Chem. B 110(40), 19891–19905 (2006).
[PubMed]

S.-H. Shim, D. B. Strasfeld, and M. T. Zanni, “Generation and characterization of phase and amplitude shaped femtosecond mid-IR pulses,” Opt. Express 14(26), 13120–13130 (2006).
[PubMed]

2004 (1)

D. W. McCamant, P. Kukura, S. Yoon, and R. A. Mathies, “Femtosecond broadband stimulated Raman spectroscopy: Apparatus and methods,” Rev. Sci. Instrum. 75(11), 4971–4980 (2004).
[PubMed]

2000 (1)

1999 (1)

Y.-q. Li, D. Guzun, and M. Xiao, “Sub-Shot-Noise-Limited Optical Heterodyne Detection Using an Amplitude-Squeezed Local Oscillator,” Phys. Rev. Lett. 82(26), 5225–5228 (1999).

1995 (1)

1994 (1)

1993 (1)

J. A. Moon, “Optimization of signal‐to‐noise ratios in pump‐probe spectroscopy,” Rev. Sci. Instrum. 64(7), 1775–1778 (1993).

1983 (1)

Abbas, G. L.

Allison, T. K.

Anderson, K. E. H.

K. E. H. Anderson, S. L. Sewall, R. R. Cooney, and P. Kambhampati, “Noise analysis and noise reduction methods in kilohertz pump-probe experiments,” Rev. Sci. Instrum. 78(7), 073101 (2007).
[PubMed]

Arpin, P. C.

S. D. McClure, D. B. Turner, P. C. Arpin, T. Mirkovic, and G. D. Scholes, “Coherent Oscillations in the PC577 Cryptophyte Antenna Occur in the Excited Electronic State,” J. Phys. Chem. B 118(5), 1296–1308 (2014).
[PubMed]

Auböck, G.

G. Auböck, C. Consani, R. Monni, A. Cannizzo, F. van Mourik, and M. Chergui, “Femtosecond pump/supercontinuum-probe setup with 20 kHz repetition rate,” Rev. Sci. Instrum. 83(9), 093105 (2012).
[PubMed]

Bahrenburg, J.

K. Röttger, S. Wang, F. Renth, J. Bahrenburg, and F. Temps, “A femtosecond pump–probe spectrometer for dynamics in transmissive polymer films,” Appl. Phys. B 118(2), 185–193 (2015).

Barber, J.

Bizimana, L. A.

J. Brazard, L. A. Bizimana, and D. B. Turner, “Accurate convergence of transient-absorption spectra using pulsed lasers,” Rev. Sci. Instrum. 86(5), 053106 (2015).
[PubMed]

L. A. Bizimana, J. Brazard, W. P. Carbery, T. Gellen, and D. B. Turner, “Resolving molecular vibronic structure using high-sensitivity two-dimensional electronic spectroscopy,” J. Chem. Phys. 143(16), 164203 (2015).
[PubMed]

Blair, A. F.

Bradler, M.

Brazard, J.

L. A. Bizimana, J. Brazard, W. P. Carbery, T. Gellen, and D. B. Turner, “Resolving molecular vibronic structure using high-sensitivity two-dimensional electronic spectroscopy,” J. Chem. Phys. 143(16), 164203 (2015).
[PubMed]

J. Brazard, L. A. Bizimana, and D. B. Turner, “Accurate convergence of transient-absorption spectra using pulsed lasers,” Rev. Sci. Instrum. 86(5), 053106 (2015).
[PubMed]

Brixner, T.

Brown, S.

Cannizzo, A.

G. Auböck, C. Consani, R. Monni, A. Cannizzo, F. van Mourik, and M. Chergui, “Femtosecond pump/supercontinuum-probe setup with 20 kHz repetition rate,” Rev. Sci. Instrum. 83(9), 093105 (2012).
[PubMed]

Carbery, W. P.

L. A. Bizimana, J. Brazard, W. P. Carbery, T. Gellen, and D. B. Turner, “Resolving molecular vibronic structure using high-sensitivity two-dimensional electronic spectroscopy,” J. Chem. Phys. 143(16), 164203 (2015).
[PubMed]

Cerullo, G.

D. Polli, L. Lüer, and G. Cerullo, “High-time-resolution pump-probe system with broadband detection for the study of time-domain vibrational dynamics,” Rev. Sci. Instrum. 78(10), 103108 (2007).
[PubMed]

Chan, V. W. S.

Chen, Y.

Chergui, M.

G. Auböck, C. Consani, R. Monni, A. Cannizzo, F. van Mourik, and M. Chergui, “Femtosecond pump/supercontinuum-probe setup with 20 kHz repetition rate,” Rev. Sci. Instrum. 83(9), 093105 (2012).
[PubMed]

Consani, C.

G. Auböck, C. Consani, R. Monni, A. Cannizzo, F. van Mourik, and M. Chergui, “Femtosecond pump/supercontinuum-probe setup with 20 kHz repetition rate,” Rev. Sci. Instrum. 83(9), 093105 (2012).
[PubMed]

Cooney, R. R.

K. E. H. Anderson, S. L. Sewall, R. R. Cooney, and P. Kambhampati, “Noise analysis and noise reduction methods in kilohertz pump-probe experiments,” Rev. Sci. Instrum. 78(7), 073101 (2007).
[PubMed]

Dobryakov, A. L.

A. L. Dobryakov, S. A. Kovalenko, A. Weigel, J. L. Pérez-Lustres, J. Lange, A. Müller, and N. P. Ernsting, “Femtosecond pump/supercontinuum-probe spectroscopy: Optimized setup and signal analysis for single-shot spectral referencing,” Rev. Sci. Instrum. 81(11), 113106 (2010).
[PubMed]

Eck, R.

Eklund, E. C.

Ernsting, N. P.

A. L. Dobryakov, S. A. Kovalenko, A. Weigel, J. L. Pérez-Lustres, J. Lange, A. Müller, and N. P. Ernsting, “Femtosecond pump/supercontinuum-probe spectroscopy: Optimized setup and signal analysis for single-shot spectral referencing,” Rev. Sci. Instrum. 81(11), 113106 (2010).
[PubMed]

Ge, N.-H.

S. Sul, D. Karaiskaj, Y. Jiang, and N.-H. Ge, “Conformations of N-Acetyl-L-Prolinamide by Two-Dimensional Infrared Spectroscopy,” J. Phys. Chem. B 110(40), 19891–19905 (2006).
[PubMed]

Gellen, T.

L. A. Bizimana, J. Brazard, W. P. Carbery, T. Gellen, and D. B. Turner, “Resolving molecular vibronic structure using high-sensitivity two-dimensional electronic spectroscopy,” J. Chem. Phys. 143(16), 164203 (2015).
[PubMed]

Gerrity, M.

Ghosh, A.

Guzun, D.

Y.-q. Li, D. Guzun, and M. Xiao, “Sub-Shot-Noise-Limited Optical Heterodyne Detection Using an Amplitude-Squeezed Local Oscillator,” Phys. Rev. Lett. 82(26), 5225–5228 (1999).

Hamm, P.

Holmes, J. F.

Jiang, Y.

S. Sul, D. Karaiskaj, Y. Jiang, and N.-H. Ge, “Conformations of N-Acetyl-L-Prolinamide by Two-Dimensional Infrared Spectroscopy,” J. Phys. Chem. B 110(40), 19891–19905 (2006).
[PubMed]

Kaindl, R. A.

Kambhampati, P.

K. E. H. Anderson, S. L. Sewall, R. R. Cooney, and P. Kambhampati, “Noise analysis and noise reduction methods in kilohertz pump-probe experiments,” Rev. Sci. Instrum. 78(7), 073101 (2007).
[PubMed]

Kanal, F.

Karaiskaj, D.

S. Sul, D. Karaiskaj, Y. Jiang, and N.-H. Ge, “Conformations of N-Acetyl-L-Prolinamide by Two-Dimensional Infrared Spectroscopy,” J. Phys. Chem. B 110(40), 19891–19905 (2006).
[PubMed]

Kaucikas, M.

Keiber, S.

Kovalenko, S. A.

A. L. Dobryakov, S. A. Kovalenko, A. Weigel, J. L. Pérez-Lustres, J. Lange, A. Müller, and N. P. Ernsting, “Femtosecond pump/supercontinuum-probe spectroscopy: Optimized setup and signal analysis for single-shot spectral referencing,” Rev. Sci. Instrum. 81(11), 113106 (2010).
[PubMed]

Krummel, A. T.

Kukura, P.

D. W. McCamant, P. Kukura, S. Yoon, and R. A. Mathies, “Femtosecond broadband stimulated Raman spectroscopy: Apparatus and methods,” Rev. Sci. Instrum. 75(11), 4971–4980 (2004).
[PubMed]

Lange, J.

A. L. Dobryakov, S. A. Kovalenko, A. Weigel, J. L. Pérez-Lustres, J. Lange, A. Müller, and N. P. Ernsting, “Femtosecond pump/supercontinuum-probe spectroscopy: Optimized setup and signal analysis for single-shot spectral referencing,” Rev. Sci. Instrum. 81(11), 113106 (2010).
[PubMed]

Li, Y.-q.

Y.-q. Li, D. Guzun, and M. Xiao, “Sub-Shot-Noise-Limited Optical Heterodyne Detection Using an Amplitude-Squeezed Local Oscillator,” Phys. Rev. Lett. 82(26), 5225–5228 (1999).

Lochbrunner, S.

C. Schriever, S. Lochbrunner, E. Riedle, and D. J. Nesbitt, “Ultrasensitive ultraviolet-visible 20 fs absorption spectroscopy of low vapor pressure molecules in the gas phase,” Rev. Sci. Instrum. 79(1), 013107 (2008).
[PubMed]

Lüer, L.

D. Polli, L. Lüer, and G. Cerullo, “High-time-resolution pump-probe system with broadband detection for the study of time-domain vibrational dynamics,” Rev. Sci. Instrum. 78(10), 103108 (2007).
[PubMed]

Luther, B. M.

Mathies, R. A.

D. W. McCamant, P. Kukura, S. Yoon, and R. A. Mathies, “Femtosecond broadband stimulated Raman spectroscopy: Apparatus and methods,” Rev. Sci. Instrum. 75(11), 4971–4980 (2004).
[PubMed]

McCamant, D. W.

D. W. McCamant, P. Kukura, S. Yoon, and R. A. Mathies, “Femtosecond broadband stimulated Raman spectroscopy: Apparatus and methods,” Rev. Sci. Instrum. 75(11), 4971–4980 (2004).
[PubMed]

McClure, S. D.

S. D. McClure, D. B. Turner, P. C. Arpin, T. Mirkovic, and G. D. Scholes, “Coherent Oscillations in the PC577 Cryptophyte Antenna Occur in the Excited Electronic State,” J. Phys. Chem. B 118(5), 1296–1308 (2014).
[PubMed]

Megerle, U.

U. Megerle, I. Pugliesi, C. Schriever, C. F. Sailer, and E. Riedle, “Sub-50 fs broadband absorption spectroscopy with tunable excitation: putting the analysis of ultrafast molecular dynamics on solid ground,” Appl. Phys. B 96(2), 215–231 (2009).

Mirkovic, T.

S. D. McClure, D. B. Turner, P. C. Arpin, T. Mirkovic, and G. D. Scholes, “Coherent Oscillations in the PC577 Cryptophyte Antenna Occur in the Excited Electronic State,” J. Phys. Chem. B 118(5), 1296–1308 (2014).
[PubMed]

Monni, R.

G. Auböck, C. Consani, R. Monni, A. Cannizzo, F. van Mourik, and M. Chergui, “Femtosecond pump/supercontinuum-probe setup with 20 kHz repetition rate,” Rev. Sci. Instrum. 83(9), 093105 (2012).
[PubMed]

Moon, J. A.

J. A. Moon, “Optimization of signal‐to‐noise ratios in pump‐probe spectroscopy,” Rev. Sci. Instrum. 64(7), 1775–1778 (1993).

Müller, A.

A. L. Dobryakov, S. A. Kovalenko, A. Weigel, J. L. Pérez-Lustres, J. Lange, A. Müller, and N. P. Ernsting, “Femtosecond pump/supercontinuum-probe spectroscopy: Optimized setup and signal analysis for single-shot spectral referencing,” Rev. Sci. Instrum. 81(11), 113106 (2010).
[PubMed]

Nelson, K. A.

C. A. Werley, S. M. Teo, and K. A. Nelson, “Pulsed laser noise analysis and pump-probe signal detection with a data acquisition card,” Rev. Sci. Instrum. 82(12), 123108 (2011).
[PubMed]

Nesbitt, D. J.

C. Schriever, S. Lochbrunner, E. Riedle, and D. J. Nesbitt, “Ultrasensitive ultraviolet-visible 20 fs absorption spectroscopy of low vapor pressure molecules in the gas phase,” Rev. Sci. Instrum. 79(1), 013107 (2008).
[PubMed]

Ostrander, J. S.

Oudenhoven, T. A.

Pérez-Lustres, J. L.

A. L. Dobryakov, S. A. Kovalenko, A. Weigel, J. L. Pérez-Lustres, J. Lange, A. Müller, and N. P. Ernsting, “Femtosecond pump/supercontinuum-probe spectroscopy: Optimized setup and signal analysis for single-shot spectral referencing,” Rev. Sci. Instrum. 81(11), 113106 (2010).
[PubMed]

Polli, D.

D. Polli, L. Lüer, and G. Cerullo, “High-time-resolution pump-probe system with broadband detection for the study of time-domain vibrational dynamics,” Rev. Sci. Instrum. 78(10), 103108 (2007).
[PubMed]

Pugliesi, I.

U. Megerle, I. Pugliesi, C. Schriever, C. F. Sailer, and E. Riedle, “Sub-50 fs broadband absorption spectroscopy with tunable excitation: putting the analysis of ultrafast molecular dynamics on solid ground,” Appl. Phys. B 96(2), 215–231 (2009).

Rask, B. J.

Reber, M. A. R.

Renth, F.

K. Röttger, S. Wang, F. Renth, J. Bahrenburg, and F. Temps, “A femtosecond pump–probe spectrometer for dynamics in transmissive polymer films,” Appl. Phys. B 118(2), 185–193 (2015).

Riedle, E.

M. Bradler and E. Riedle, “Temporal and spectral correlations in bulk continua and improved use in transient spectroscopy,” J. Opt. Soc. Am. B 31(7), 1465–1475 (2014).

U. Megerle, I. Pugliesi, C. Schriever, C. F. Sailer, and E. Riedle, “Sub-50 fs broadband absorption spectroscopy with tunable excitation: putting the analysis of ultrafast molecular dynamics on solid ground,” Appl. Phys. B 96(2), 215–231 (2009).

C. Schriever, S. Lochbrunner, E. Riedle, and D. J. Nesbitt, “Ultrasensitive ultraviolet-visible 20 fs absorption spectroscopy of low vapor pressure molecules in the gas phase,” Rev. Sci. Instrum. 79(1), 013107 (2008).
[PubMed]

Röttger, K.

K. Röttger, S. Wang, F. Renth, J. Bahrenburg, and F. Temps, “A femtosecond pump–probe spectrometer for dynamics in transmissive polymer films,” Appl. Phys. B 118(2), 185–193 (2015).

Sailer, C. F.

U. Megerle, I. Pugliesi, C. Schriever, C. F. Sailer, and E. Riedle, “Sub-50 fs broadband absorption spectroscopy with tunable excitation: putting the analysis of ultrafast molecular dynamics on solid ground,” Appl. Phys. B 96(2), 215–231 (2009).

Scholes, G. D.

S. D. McClure, D. B. Turner, P. C. Arpin, T. Mirkovic, and G. D. Scholes, “Coherent Oscillations in the PC577 Cryptophyte Antenna Occur in the Excited Electronic State,” J. Phys. Chem. B 118(5), 1296–1308 (2014).
[PubMed]

Schriever, C.

U. Megerle, I. Pugliesi, C. Schriever, C. F. Sailer, and E. Riedle, “Sub-50 fs broadband absorption spectroscopy with tunable excitation: putting the analysis of ultrafast molecular dynamics on solid ground,” Appl. Phys. B 96(2), 215–231 (2009).

C. Schriever, S. Lochbrunner, E. Riedle, and D. J. Nesbitt, “Ultrasensitive ultraviolet-visible 20 fs absorption spectroscopy of low vapor pressure molecules in the gas phase,” Rev. Sci. Instrum. 79(1), 013107 (2008).
[PubMed]

Serrano, A. L.

Sewall, S. L.

K. E. H. Anderson, S. L. Sewall, R. R. Cooney, and P. Kambhampati, “Noise analysis and noise reduction methods in kilohertz pump-probe experiments,” Rev. Sci. Instrum. 78(7), 073101 (2007).
[PubMed]

Shim, S.-H.

Stenger, J.

Strasfeld, D. B.

Sul, S.

S. Sul, D. Karaiskaj, Y. Jiang, and N.-H. Ge, “Conformations of N-Acetyl-L-Prolinamide by Two-Dimensional Infrared Spectroscopy,” J. Phys. Chem. B 110(40), 19891–19905 (2006).
[PubMed]

Temps, F.

K. Röttger, S. Wang, F. Renth, J. Bahrenburg, and F. Temps, “A femtosecond pump–probe spectrometer for dynamics in transmissive polymer films,” Appl. Phys. B 118(2), 185–193 (2015).

Teo, S. M.

C. A. Werley, S. M. Teo, and K. A. Nelson, “Pulsed laser noise analysis and pump-probe signal detection with a data acquisition card,” Rev. Sci. Instrum. 82(12), 123108 (2011).
[PubMed]

Tracy, K. M.

Turner, D. B.

J. Brazard, L. A. Bizimana, and D. B. Turner, “Accurate convergence of transient-absorption spectra using pulsed lasers,” Rev. Sci. Instrum. 86(5), 053106 (2015).
[PubMed]

L. A. Bizimana, J. Brazard, W. P. Carbery, T. Gellen, and D. B. Turner, “Resolving molecular vibronic structure using high-sensitivity two-dimensional electronic spectroscopy,” J. Chem. Phys. 143(16), 164203 (2015).
[PubMed]

S. D. McClure, D. B. Turner, P. C. Arpin, T. Mirkovic, and G. D. Scholes, “Coherent Oscillations in the PC577 Cryptophyte Antenna Occur in the Excited Electronic State,” J. Phys. Chem. B 118(5), 1296–1308 (2014).
[PubMed]

van Mourik, F.

G. Auböck, C. Consani, R. Monni, A. Cannizzo, F. van Mourik, and M. Chergui, “Femtosecond pump/supercontinuum-probe setup with 20 kHz repetition rate,” Rev. Sci. Instrum. 83(9), 093105 (2012).
[PubMed]

Van Thor, J. J.

Wang, S.

K. Röttger, S. Wang, F. Renth, J. Bahrenburg, and F. Temps, “A femtosecond pump–probe spectrometer for dynamics in transmissive polymer films,” Appl. Phys. B 118(2), 185–193 (2015).

Weigel, A.

A. L. Dobryakov, S. A. Kovalenko, A. Weigel, J. L. Pérez-Lustres, J. Lange, A. Müller, and N. P. Ernsting, “Femtosecond pump/supercontinuum-probe spectroscopy: Optimized setup and signal analysis for single-shot spectral referencing,” Rev. Sci. Instrum. 81(11), 113106 (2010).
[PubMed]

Werley, C. A.

C. A. Werley, S. M. Teo, and K. A. Nelson, “Pulsed laser noise analysis and pump-probe signal detection with a data acquisition card,” Rev. Sci. Instrum. 82(12), 123108 (2011).
[PubMed]

Wiemann, S.

Xiao, M.

Y.-q. Li, D. Guzun, and M. Xiao, “Sub-Shot-Noise-Limited Optical Heterodyne Detection Using an Amplitude-Squeezed Local Oscillator,” Phys. Rev. Lett. 82(26), 5225–5228 (1999).

Yee, T. K.

Yoon, S.

D. W. McCamant, P. Kukura, S. Yoon, and R. A. Mathies, “Femtosecond broadband stimulated Raman spectroscopy: Apparatus and methods,” Rev. Sci. Instrum. 75(11), 4971–4980 (2004).
[PubMed]

Zanni, M. T.

Zinth, W.

Zurek, M.

Appl. Opt. (1)

Appl. Phys. B (2)

U. Megerle, I. Pugliesi, C. Schriever, C. F. Sailer, and E. Riedle, “Sub-50 fs broadband absorption spectroscopy with tunable excitation: putting the analysis of ultrafast molecular dynamics on solid ground,” Appl. Phys. B 96(2), 215–231 (2009).

K. Röttger, S. Wang, F. Renth, J. Bahrenburg, and F. Temps, “A femtosecond pump–probe spectrometer for dynamics in transmissive polymer films,” Appl. Phys. B 118(2), 185–193 (2015).

J. Chem. Phys. (1)

L. A. Bizimana, J. Brazard, W. P. Carbery, T. Gellen, and D. B. Turner, “Resolving molecular vibronic structure using high-sensitivity two-dimensional electronic spectroscopy,” J. Chem. Phys. 143(16), 164203 (2015).
[PubMed]

J. Opt. Soc. Am. B (1)

J. Phys. Chem. B (2)

S. D. McClure, D. B. Turner, P. C. Arpin, T. Mirkovic, and G. D. Scholes, “Coherent Oscillations in the PC577 Cryptophyte Antenna Occur in the Excited Electronic State,” J. Phys. Chem. B 118(5), 1296–1308 (2014).
[PubMed]

S. Sul, D. Karaiskaj, Y. Jiang, and N.-H. Ge, “Conformations of N-Acetyl-L-Prolinamide by Two-Dimensional Infrared Spectroscopy,” J. Phys. Chem. B 110(40), 19891–19905 (2006).
[PubMed]

Opt. Express (4)

Opt. Lett. (4)

Optica (1)

Phys. Rev. Lett. (1)

Y.-q. Li, D. Guzun, and M. Xiao, “Sub-Shot-Noise-Limited Optical Heterodyne Detection Using an Amplitude-Squeezed Local Oscillator,” Phys. Rev. Lett. 82(26), 5225–5228 (1999).

Rev. Sci. Instrum. (9)

D. Polli, L. Lüer, and G. Cerullo, “High-time-resolution pump-probe system with broadband detection for the study of time-domain vibrational dynamics,” Rev. Sci. Instrum. 78(10), 103108 (2007).
[PubMed]

K. E. H. Anderson, S. L. Sewall, R. R. Cooney, and P. Kambhampati, “Noise analysis and noise reduction methods in kilohertz pump-probe experiments,” Rev. Sci. Instrum. 78(7), 073101 (2007).
[PubMed]

A. L. Dobryakov, S. A. Kovalenko, A. Weigel, J. L. Pérez-Lustres, J. Lange, A. Müller, and N. P. Ernsting, “Femtosecond pump/supercontinuum-probe spectroscopy: Optimized setup and signal analysis for single-shot spectral referencing,” Rev. Sci. Instrum. 81(11), 113106 (2010).
[PubMed]

D. W. McCamant, P. Kukura, S. Yoon, and R. A. Mathies, “Femtosecond broadband stimulated Raman spectroscopy: Apparatus and methods,” Rev. Sci. Instrum. 75(11), 4971–4980 (2004).
[PubMed]

G. Auböck, C. Consani, R. Monni, A. Cannizzo, F. van Mourik, and M. Chergui, “Femtosecond pump/supercontinuum-probe setup with 20 kHz repetition rate,” Rev. Sci. Instrum. 83(9), 093105 (2012).
[PubMed]

J. Brazard, L. A. Bizimana, and D. B. Turner, “Accurate convergence of transient-absorption spectra using pulsed lasers,” Rev. Sci. Instrum. 86(5), 053106 (2015).
[PubMed]

J. A. Moon, “Optimization of signal‐to‐noise ratios in pump‐probe spectroscopy,” Rev. Sci. Instrum. 64(7), 1775–1778 (1993).

C. A. Werley, S. M. Teo, and K. A. Nelson, “Pulsed laser noise analysis and pump-probe signal detection with a data acquisition card,” Rev. Sci. Instrum. 82(12), 123108 (2011).
[PubMed]

C. Schriever, S. Lochbrunner, E. Riedle, and D. J. Nesbitt, “Ultrasensitive ultraviolet-visible 20 fs absorption spectroscopy of low vapor pressure molecules in the gas phase,” Rev. Sci. Instrum. 79(1), 013107 (2008).
[PubMed]

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Figures (9)

Fig. 1
Fig. 1

Schematic of our pump-probe 2D IR setup. OPA: optical parametric amplifier; DFG: difference frequency generation; BS: beam splitter; WGP: wire grid polarizer. CM: concave mirror. G: grating. Two spectrographs are unmatched to demonstrate the performance of our reference scheme.

Fig. 2
Fig. 2

Statistical properties of noise before and after multi-channel referencing. The three rows are δ I LO , Δ I LO , and Δ K (see Section 3.2) from top to bottom. The four columns are the time trajectories, histograms, autocorrelations, and amplitude spectra from left to right.

Fig. 3
Fig. 3

(a) Spectral correlation of Δ I between pixels within the signal array (top) and between the signal and reference arrays (bottom). (b) Scatter plot of a trajectory with 10K data points to show the relationship between the 29th signal pixel and the 29th physical or virtual reference pixels. The left column is for the single-channel method in Eq. (13). The right column is for the multi-channel method in Eq. (16). The coefficient b and column vector β 29   were optimized based on Eq. (14) and (17), respectively. The black line in the top row is y = x , which is the best linear least-squares fit of the data. (c) Performance of different reference methods as measured by σ ( Δ K ) . The blue circles, orange squares, and red triangles show the results from the conventional ratiometric, our single-channel and multi-channel reference method, respectively. The green diamonds show the total noise floor in the conventional methods, and the black dashed line shows the detector noise of the signal array only. Raw data statistics are shown in Fig. 9.

Fig. 4
Fig. 4

(a) Convergence of the q factor as a function of the number of blank shots. Red is for the fully-aggregated case, and blue is for the fully-dispersed case. (b) Long-term stability of the q factor as a function of time. Red is using a fixed B estimated from a single data set, whereas blue is using B refreshed on-the-fly.

Fig. 5
Fig. 5

(a) Traces of the τ scan in a 2D IR experiment of NMA-d/D2O. Performance of multi-channel referencing (red) compared with conventional ratiometric referencing (blue) and no referencing (green). Convolutional noise is not removed yet. (b) The correlation coefficient between Δ I LO and I LO ' (blue square) and between Δ K   and I ^ LO * (red circle).

Fig. 6
Fig. 6

(a) Residual noise after referencing with a 32-pixel array (blue circles), an unmatched 64-pixel array (red triangles), and a combined 96-pixel array composed of the 32- and 64-pixel array (green squares). The detector noise of the signal array is shown as the dashed line in both panels. Because the detector noises of our signal and reference arrays were partially correlated, some pixels on the green-square curve show residual noise slightly below the detector noise. (b) Dependence of residual noise on the number of reference pixels (indicated in the legend). The number of reference pixels was reduced from 32 to 8, 4, 2, and 1 by digitally binning over 4, 8, 16, and 32 adjacent pixels, respectively, and re-calculating B for each case. The blue-circle curve in (a) and (b) are the same as the red-triangle curve in Fig. 3(c).

Fig. 7
Fig. 7

Effect of detector SNR on referencing performance. The legend indicates the multiples ( l) of noise included. (a) Adding detector noise to the signal array; (b) adding detector noise to the reference array. Because the original data already contains one part of detector noise, the added detector noise is scaled by ( l 2 1 ) 1 / 2 . (c) Adding photon shot noise to the signal array; and (d) adding photon shot noise to the reference array.

Fig. 8
Fig. 8

Characteristics of one pixel from our MCT arrays. The detector has adjustable gain settings corresponding to different full-well capacities. (a) Calibration curves for detector responsivity. (b) Relative SNR as a function of detector outputs. Red (blue) is for high (low) gain where the response is linear (nonlinear).

Fig. 9
Fig. 9

σ ( Δ I )   with the light off (a) and with the light on (b), and the mean spectrum (c) for the two rows of the 2 × 32 MCT array. Blue circles are for the signal array and red squares are for the reference array. (d) Correlation coefficients between the corresponding signal and reference pixels. The blue crosses are for corr ( Δ I LO , Δ I Ref ) , and green circles are for corr ( δ I LO , δ I Ref ) .

Equations (24)

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I tot = ( E LO + E Sig ) 2 = I LO + I Sig + 2 E LO E Sig
Δ I tot = ( E LO * + E Sig * ) 2 ( E LO ) 2 Δ I LO + χ ( 3 ) I LO * I Pu *
Δ I tot = ( E LO * + E Sig * ) 2 ( E LO E Sig ) 2 Δ I LO + χ ( 3 ) ( I LO * I Pu * + I LO I Pu )
I LO I Pu = I ¯ LO I ¯ Pu ( 1 + δ I LO I ¯ LO ) ( 1 + δ I Pu I ¯ Pu )
Δ I tot I ¯ LO = ΔO D e ¯ + Δ I LO I ¯ LO + ΔO D e ¯ ( δ I LO * I ¯ LO + δ I Pu * I ¯ Pu + δ I LO * I ¯ LO δ I Pu * I ¯ Pu )
σ ( Δ I LO ) 2 ( N LO + N r 2 + D t ) + ( N LO p 2 ) 2
J (   I ¯ LO + d LO ) + δ I LO (   I ¯ Ref + d Ref ) + δ I Ref (   I ¯ Ref + d Ref ) k LO + ( δ I LO k LO k Ref δ I Ref )
Δ J = J * J = Δ I LO k LO k Ref Δ I Ref
var ( Δ J ) k Ref = 0 , var ( Δ J ) k LO = 0
k LO k Ref = cov ( Δ I LO , Δ I Ref ) var ( Δ I Ref ) = R σ ( Δ I LO ) σ ( Δ I Ref )
var min ( Δ J ) = ( 1 R 2 ) var ( Δ I LO )
K I LO b I Ref
Δ K = Δ I LO b Δ I Ref
b = cov ( Δ I LO , Δ I Ref ) var ( Δ I Ref ) = R σ ( Δ I LO ) σ ( Δ I Ref )
var min ( Δ K ) = ( 1 R 2 ) var ( Δ I LO )
Δ K ( i ) = Δ I LO ( i ) Δ I Ref β i
β i = Δ I Ref T Δ I Ref 1 Δ I Ref T Δ I LO ( i )
B = Δ I Ref T Δ I Ref 1 Δ I Ref T Δ I LO = cov ( Δ I Ref ) 1 cov ( Δ I Ref , Δ I LO )
var min ( Δ K ( i ) ) var ( Δ I LO ( i ) ) = 1 cov ( Δ I LO ( i ) , Δ I Ref ) cov ( Δ I Ref ) 1 cov ( Δ I Ref , Δ I LO ( i ) ) var ( Δ I LO ( i ) )
q =   σ ( Δ K ) based on the estimated B from blank shots σ ( Δ K ) based on the optimal B from all shots
S Δ I tot Δ I Ref B
S ( i ) = Δ K ( i ) + χ ( 3 ) I LO * I Pu * ( i )
I ^ LO * I LO + Δ I Ref B
I ^ LO * I tot * + I tot + Δ I Ref B 2 , I ^ LO I tot * + I tot Δ I Ref B 2

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