Abstract

Multi-excitation Raman spectroscopy filters out Raman signals from a fluorescent background by sequentially using multiple excitation frequencies. The filtering method exploits the shift of the Raman spectra with excitation frequency and the static response of the fluorescent background. This technique builds upon previous work which used two slightly shifted excitations, Shifted Excitation Raman Difference Spectroscopy (SERDS), in order to filter the Raman signal. An Expectation-Maximization algorithm is used to estimate the Raman and fluorescence signals from multiple spectra acquired with slightly shifted excitation frequencies. In both simulation and experiment, the efficacy of the algorithm increases with the number of excitation frequencies even when holding the total excitation energy constant, such that the signal to noise ratio is inversely proportional to the number of excitation frequencies. In situations where the intense fluorescence causes significant shot noise compared to the weak Raman signals, the multi-excitation approach is more effective than non-iterative techniques such as polynomial background subtraction.

©2008 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]

2007 (2)

E. F. Y. Hom, F. Marchis, T. K. Lee, S. Haase, D. A. Agard, and J.W. Sedat, “AIDA: an adaptive image deconvolution algorithm with application to multi-frame and three-dimensional data,” J. Opt. Soc. Am. A  24, 1580–1600 (2007).
[Crossref]

I. Osticioli, A. Zoppi, and E. M. Castellucci, “Shift-excitation Raman difference spectroscopydifference deconvolution method for the luminescence background rejection from Raman spectra of solid samples,” Appl. Spectrosc. 61, 839–844 (2007).
[Crossref] [PubMed]

2006 (3)

2005 (2)

2004 (2)

D. R. Fuhrmann, C. Preza, J. A. O’Sullivan, D. L. Snyder, and W. Smith, “Spectrum estimation from quantumlimited interferograms,” IEEE Trans. Signal Process 52, 950–961 (2004).
[Crossref]

E. Kolaczyk and R. Nowak, “Multiscale likelihood analysis and complexity penalized estimation,” Annals of Stat. 32, 500–527 (2004).
[Crossref]

2003 (1)

2002 (2)

J. Zhao, M. M. Carrabba, and F. S. Allen, “Automated fluorescence rejection using shifted excitation Raman difference spectroscopy,” Appl. Spectrosc. 56, 834–845 (2002).
[Crossref]

P. Matousek, M. Towrie, and A.W. Parker, “Fluorescence background suppression in Raman spectroscopy using combined Kerr gated and shifted excitation Raman difference techniques,” J. Raman Spectrosc. 33, 238–242 (2002).
[Crossref]

2000 (1)

R. Nowak and E. Kolaczyk, “A multiscale statistical framework for Poisson inverse problems,” IEEE Trans Inf. Theory 46, 1811–1825 (2000).
[Crossref]

1999 (1)

1998 (2)

S. E. J. Bell, E. Bourguignon, and A. Dennis, “Analysis of luminescent samples using subtracted shifted Raman spectroscopy,” Analyst 123, 1729–1734 (1998).
[Crossref]

S. E. Bialkowski, “Overcoming the multiplex disadvantage by using maximum-likelihood inversion,” Appl. Spectrosc. 52, 591–598 (1998).
[Crossref]

1996 (1)

M. Lang, H. Guo, J. E. Odegard, C. S. Burrus, and R. O. Wells, “Noise reduction using an undecimated discrete wavelet transform,” IEEE Signal Process Lett. 3, 10–12 (1996).
[Crossref]

1995 (1)

1992 (1)

1982 (1)

L. A. Shepp and Y. Vardi, “Maximum likelihood reconstructions for emission tomography,” IEEE Trans. Med. Imaging MI-1, 113122 (1982).

1974 (1)

L. B. Lucy, “An iterative technique for the rectification of observed distributions,” Astron. J. 79, 745754 (1974).
[Crossref]

1972 (2)

W. H. Richardson, “Bayesian-based iterative method of image restoration,” J. Opt. Soc. Am. 62, 5559 (1972).
[Crossref]

P. P. Yaney, “Reduction of fluorescence background in Raman spectra by the pulsed Raman technique,” J. Opt. Soc. Am. 62, 1297–1303 (1972).
[Crossref]

1950 (1)

M. Kasha, “Characterization of electronic transitions in complex molecules,” Discuss. Faraday Soc. 9, 14–19 (1950).
[Crossref]

1928 (1)

C. V. Raman, “A new radiation,” Indian J. Phys. 2, 387 (1928).

Agard, D. A.

E. F. Y. Hom, F. Marchis, T. K. Lee, S. Haase, D. A. Agard, and J.W. Sedat, “AIDA: an adaptive image deconvolution algorithm with application to multi-frame and three-dimensional data,” J. Opt. Soc. Am. A  24, 1580–1600 (2007).
[Crossref]

Allen, F. S.

Bell, S. E. J.

S. E. J. Bell, E. Bourguignon, and A. Dennis, “Analysis of luminescent samples using subtracted shifted Raman spectroscopy,” Analyst 123, 1729–1734 (1998).
[Crossref]

Bialkowski, S. E.

Bourguignon, E.

S. E. J. Bell, E. Bourguignon, and A. Dennis, “Analysis of luminescent samples using subtracted shifted Raman spectroscopy,” Analyst 123, 1729–1734 (1998).
[Crossref]

Brady, D. J.

Brown, C.W.

J. R. Ferraro, K. Nakamoto, and C.W. Brown, Introductory Raman Spectroscopy, 2nd Ed. (Academic Press, San Diego, Cal., 2003).

Burrus, C. S.

M. Lang, H. Guo, J. E. Odegard, C. S. Burrus, and R. O. Wells, “Noise reduction using an undecimated discrete wavelet transform,” IEEE Signal Process Lett. 3, 10–12 (1996).
[Crossref]

Carrabba, M. M.

Castellucci, E. M.

Cherepy, N. J.

Dennis, A.

S. E. J. Bell, E. Bourguignon, and A. Dennis, “Analysis of luminescent samples using subtracted shifted Raman spectroscopy,” Analyst 123, 1729–1734 (1998).
[Crossref]

Erbert, G.

M. Maiwald, G. Erbert, A. Klehr, H. D. Kronfeldt, H. Schmidt, B. Sumpf, and G. Trnkle, “Rapid shifted excitation Raman difference spectroscopy with a distributed feedback diode laser emitting at 785 nm,” Appl. Phys. B  85, 509–512 (2006).
[Crossref]

Ferraro, J. R.

J. R. Ferraro, K. Nakamoto, and C.W. Brown, Introductory Raman Spectroscopy, 2nd Ed. (Academic Press, San Diego, Cal., 2003).

Fuhrmann, D. R.

D. R. Fuhrmann, C. Preza, J. A. O’Sullivan, D. L. Snyder, and W. Smith, “Spectrum estimation from quantumlimited interferograms,” IEEE Trans. Signal Process 52, 950–961 (2004).
[Crossref]

Gehm, M. E.

Guo, H.

M. Lang, H. Guo, J. E. Odegard, C. S. Burrus, and R. O. Wells, “Noise reduction using an undecimated discrete wavelet transform,” IEEE Signal Process Lett. 3, 10–12 (1996).
[Crossref]

Haase, S.

E. F. Y. Hom, F. Marchis, T. K. Lee, S. Haase, D. A. Agard, and J.W. Sedat, “AIDA: an adaptive image deconvolution algorithm with application to multi-frame and three-dimensional data,” J. Opt. Soc. Am. A  24, 1580–1600 (2007).
[Crossref]

Hom, E. F. Y.

E. F. Y. Hom, F. Marchis, T. K. Lee, S. Haase, D. A. Agard, and J.W. Sedat, “AIDA: an adaptive image deconvolution algorithm with application to multi-frame and three-dimensional data,” J. Opt. Soc. Am. A  24, 1580–1600 (2007).
[Crossref]

Jannson, P. A.

P. A. Jannson, Deconvolution of Images and Spectra (Academic Press, San Diego, Calif., 1997)

Kasha, M.

M. Kasha, “Characterization of electronic transitions in complex molecules,” Discuss. Faraday Soc. 9, 14–19 (1950).
[Crossref]

Klehr, A.

M. Maiwald, G. Erbert, A. Klehr, H. D. Kronfeldt, H. Schmidt, B. Sumpf, and G. Trnkle, “Rapid shifted excitation Raman difference spectroscopy with a distributed feedback diode laser emitting at 785 nm,” Appl. Phys. B  85, 509–512 (2006).
[Crossref]

Kolaczyk, E.

E. Kolaczyk and R. Nowak, “Multiscale likelihood analysis and complexity penalized estimation,” Annals of Stat. 32, 500–527 (2004).
[Crossref]

R. Nowak and E. Kolaczyk, “A multiscale statistical framework for Poisson inverse problems,” IEEE Trans Inf. Theory 46, 1811–1825 (2000).
[Crossref]

Kronfeldt, H. D.

M. Maiwald, G. Erbert, A. Klehr, H. D. Kronfeldt, H. Schmidt, B. Sumpf, and G. Trnkle, “Rapid shifted excitation Raman difference spectroscopy with a distributed feedback diode laser emitting at 785 nm,” Appl. Phys. B  85, 509–512 (2006).
[Crossref]

Lang, M.

M. Lang, H. Guo, J. E. Odegard, C. S. Burrus, and R. O. Wells, “Noise reduction using an undecimated discrete wavelet transform,” IEEE Signal Process Lett. 3, 10–12 (1996).
[Crossref]

Lee, T. K.

E. F. Y. Hom, F. Marchis, T. K. Lee, S. Haase, D. A. Agard, and J.W. Sedat, “AIDA: an adaptive image deconvolution algorithm with application to multi-frame and three-dimensional data,” J. Opt. Soc. Am. A  24, 1580–1600 (2007).
[Crossref]

Lieber, C. A.

Lieberman, S. H.

Lucy, L. B.

L. B. Lucy, “An iterative technique for the rectification of observed distributions,” Astron. J. 79, 745754 (1974).
[Crossref]

Mahadevan-Jansen, A.

Maiwald, M.

M. Maiwald, G. Erbert, A. Klehr, H. D. Kronfeldt, H. Schmidt, B. Sumpf, and G. Trnkle, “Rapid shifted excitation Raman difference spectroscopy with a distributed feedback diode laser emitting at 785 nm,” Appl. Phys. B  85, 509–512 (2006).
[Crossref]

Marchis, F.

E. F. Y. Hom, F. Marchis, T. K. Lee, S. Haase, D. A. Agard, and J.W. Sedat, “AIDA: an adaptive image deconvolution algorithm with application to multi-frame and three-dimensional data,” J. Opt. Soc. Am. A  24, 1580–1600 (2007).
[Crossref]

Mathies, R. A.

Matousek, P.

McCain, S. T.

Mosier-Boss, S. H.

Nakamoto, K.

J. R. Ferraro, K. Nakamoto, and C.W. Brown, Introductory Raman Spectroscopy, 2nd Ed. (Academic Press, San Diego, Cal., 2003).

Newbery, R.

Nowak, R.

R. Willett and R. Nowak, “Multiscale Poisson intensity and density estimation,” IEEE Trans Inf. Theory 53, 3171–3187 (2005).
[Crossref]

E. Kolaczyk and R. Nowak, “Multiscale likelihood analysis and complexity penalized estimation,” Annals of Stat. 32, 500–527 (2004).
[Crossref]

R. Nowak and E. Kolaczyk, “A multiscale statistical framework for Poisson inverse problems,” IEEE Trans Inf. Theory 46, 1811–1825 (2000).
[Crossref]

R. Willett and R. Nowak, “Fast multiresolution photon-limited image reconstruction,” in Proc. IEEE Int. Sym. Biomedical Imaging - ISBI ’04 (15–18 April, Arlington, VA, USA, 2004).

O’Sullivan, J. A.

D. R. Fuhrmann, C. Preza, J. A. O’Sullivan, D. L. Snyder, and W. Smith, “Spectrum estimation from quantumlimited interferograms,” IEEE Trans. Signal Process 52, 950–961 (2004).
[Crossref]

Odegard, J. E.

M. Lang, H. Guo, J. E. Odegard, C. S. Burrus, and R. O. Wells, “Noise reduction using an undecimated discrete wavelet transform,” IEEE Signal Process Lett. 3, 10–12 (1996).
[Crossref]

Osticioli, I.

Parker, A.

Parker, A. W.

Parker, A.W.

P. Matousek, M. Towrie, and A.W. Parker, “Fluorescence background suppression in Raman spectroscopy using combined Kerr gated and shifted excitation Raman difference techniques,” J. Raman Spectrosc. 33, 238–242 (2002).
[Crossref]

Pitsianis, N. P.

Potulri, P.

Preza, C.

D. R. Fuhrmann, C. Preza, J. A. O’Sullivan, D. L. Snyder, and W. Smith, “Spectrum estimation from quantumlimited interferograms,” IEEE Trans. Signal Process 52, 950–961 (2004).
[Crossref]

Raman, C. V.

C. V. Raman, “A new radiation,” Indian J. Phys. 2, 387 (1928).

Richardson, W. H.

W. H. Richardson, “Bayesian-based iterative method of image restoration,” J. Opt. Soc. Am. 62, 5559 (1972).
[Crossref]

Schmidt, H.

M. Maiwald, G. Erbert, A. Klehr, H. D. Kronfeldt, H. Schmidt, B. Sumpf, and G. Trnkle, “Rapid shifted excitation Raman difference spectroscopy with a distributed feedback diode laser emitting at 785 nm,” Appl. Phys. B  85, 509–512 (2006).
[Crossref]

Sedat, J.W.

E. F. Y. Hom, F. Marchis, T. K. Lee, S. Haase, D. A. Agard, and J.W. Sedat, “AIDA: an adaptive image deconvolution algorithm with application to multi-frame and three-dimensional data,” J. Opt. Soc. Am. A  24, 1580–1600 (2007).
[Crossref]

Shepp, L. A.

L. A. Shepp and Y. Vardi, “Maximum likelihood reconstructions for emission tomography,” IEEE Trans. Med. Imaging MI-1, 113122 (1982).

Shreve, A. P.

Smith, W.

D. R. Fuhrmann, C. Preza, J. A. O’Sullivan, D. L. Snyder, and W. Smith, “Spectrum estimation from quantumlimited interferograms,” IEEE Trans. Signal Process 52, 950–961 (2004).
[Crossref]

Snyder, D. L.

D. R. Fuhrmann, C. Preza, J. A. O’Sullivan, D. L. Snyder, and W. Smith, “Spectrum estimation from quantumlimited interferograms,” IEEE Trans. Signal Process 52, 950–961 (2004).
[Crossref]

Stanley, A.

Sullivan, M. E.

Sumpf, B.

M. Maiwald, G. Erbert, A. Klehr, H. D. Kronfeldt, H. Schmidt, B. Sumpf, and G. Trnkle, “Rapid shifted excitation Raman difference spectroscopy with a distributed feedback diode laser emitting at 785 nm,” Appl. Phys. B  85, 509–512 (2006).
[Crossref]

Towrie, M.

Trnkle, G.

M. Maiwald, G. Erbert, A. Klehr, H. D. Kronfeldt, H. Schmidt, B. Sumpf, and G. Trnkle, “Rapid shifted excitation Raman difference spectroscopy with a distributed feedback diode laser emitting at 785 nm,” Appl. Phys. B  85, 509–512 (2006).
[Crossref]

Vardi, Y.

L. A. Shepp and Y. Vardi, “Maximum likelihood reconstructions for emission tomography,” IEEE Trans. Med. Imaging MI-1, 113122 (1982).

Wang, Y.

Wells, R. O.

M. Lang, H. Guo, J. E. Odegard, C. S. Burrus, and R. O. Wells, “Noise reduction using an undecimated discrete wavelet transform,” IEEE Signal Process Lett. 3, 10–12 (1996).
[Crossref]

Willett, R.

R. Willett and R. Nowak, “Multiscale Poisson intensity and density estimation,” IEEE Trans Inf. Theory 53, 3171–3187 (2005).
[Crossref]

R. Willett, “Multiscale intensity estimation for marked Poisson processes,” in Proc. IEEE Conf. Acoust., Speech, Signal Processing - ICASSP (2007).

R. Willett and R. Nowak, “Fast multiresolution photon-limited image reconstruction,” in Proc. IEEE Int. Sym. Biomedical Imaging - ISBI ’04 (15–18 April, Arlington, VA, USA, 2004).

Yaney, P. P.

Zhao, J.

Zoppi, A.

Analyst (1)

S. E. J. Bell, E. Bourguignon, and A. Dennis, “Analysis of luminescent samples using subtracted shifted Raman spectroscopy,” Analyst 123, 1729–1734 (1998).
[Crossref]

Annals of Stat. (1)

E. Kolaczyk and R. Nowak, “Multiscale likelihood analysis and complexity penalized estimation,” Annals of Stat. 32, 500–527 (2004).
[Crossref]

Appl. Opt. (1)

Appl. Phys. (1)

M. Maiwald, G. Erbert, A. Klehr, H. D. Kronfeldt, H. Schmidt, B. Sumpf, and G. Trnkle, “Rapid shifted excitation Raman difference spectroscopy with a distributed feedback diode laser emitting at 785 nm,” Appl. Phys. B  85, 509–512 (2006).
[Crossref]

Appl. Spectrosc. (9)

I. Osticioli, A. Zoppi, and E. M. Castellucci, “Shift-excitation Raman difference spectroscopydifference deconvolution method for the luminescence background rejection from Raman spectra of solid samples,” Appl. Spectrosc. 61, 839–844 (2007).
[Crossref] [PubMed]

S. T. McCain, M. E. Gehm, Y. Wang, N. P. Pitsianis, and D. J. Brady, “Coded aperture Raman spectroscopy for quantitative measurements of ethanol in a tissue phantom,” Appl. Spectrosc. 60, 663–671 (2006).
[Crossref] [PubMed]

S. E. Bialkowski, “Overcoming the multiplex disadvantage by using maximum-likelihood inversion,” Appl. Spectrosc. 52, 591–598 (1998).
[Crossref]

A. P. Shreve, N. J. Cherepy, and R. A. Mathies, “Effective rejection of fluorescence interference in Raman spectroscopy using a shifted excitation difference technique,” Appl. Spectrosc. 46, 707–711 (1992).
[Crossref]

S. H. Mosier-Boss, S. H. Lieberman, and R. Newbery, “Fluorescence rejection in Raman spectroscopy by shiftedspectra, edge detection, and FFT filtering techniques,” Appl. Spectrosc. 49, 630–638 (1995).
[Crossref]

P. Matousek, M. Towrie, A. Stanley, and A. Parker, “Efficient rejection of fluorescence from Raman spectra using picosecond Kerr gating,” Appl. Spectrosc. 53, 1485–1489 (1999).
[Crossref]

J. Zhao, M. M. Carrabba, and F. S. Allen, “Automated fluorescence rejection using shifted excitation Raman difference spectroscopy,” Appl. Spectrosc. 56, 834–845 (2002).
[Crossref]

C. A. Lieber and A. Mahadevan-Jansen, “Automated method for subtraction of fluorescence from biological Raman spectra,” Appl. Spectrosc. 57, 1363–1367 (2003).
[Crossref] [PubMed]

P. Matousek, M. Towrie, and A. W. Parker, “Simple reconstruction algorithm for shifted excitation Raman difference spectroscopy,” Appl. Spectrosc. 59, 848–851 (2005).
[Crossref] [PubMed]

Astron. J. (1)

L. B. Lucy, “An iterative technique for the rectification of observed distributions,” Astron. J. 79, 745754 (1974).
[Crossref]

Discuss. Faraday Soc. (1)

M. Kasha, “Characterization of electronic transitions in complex molecules,” Discuss. Faraday Soc. 9, 14–19 (1950).
[Crossref]

IEEE Signal Process Lett. (1)

M. Lang, H. Guo, J. E. Odegard, C. S. Burrus, and R. O. Wells, “Noise reduction using an undecimated discrete wavelet transform,” IEEE Signal Process Lett. 3, 10–12 (1996).
[Crossref]

IEEE Trans Inf. Theory (2)

R. Willett and R. Nowak, “Multiscale Poisson intensity and density estimation,” IEEE Trans Inf. Theory 53, 3171–3187 (2005).
[Crossref]

R. Nowak and E. Kolaczyk, “A multiscale statistical framework for Poisson inverse problems,” IEEE Trans Inf. Theory 46, 1811–1825 (2000).
[Crossref]

IEEE Trans. Med. Imaging (1)

L. A. Shepp and Y. Vardi, “Maximum likelihood reconstructions for emission tomography,” IEEE Trans. Med. Imaging MI-1, 113122 (1982).

IEEE Trans. Signal Process (1)

D. R. Fuhrmann, C. Preza, J. A. O’Sullivan, D. L. Snyder, and W. Smith, “Spectrum estimation from quantumlimited interferograms,” IEEE Trans. Signal Process 52, 950–961 (2004).
[Crossref]

Indian J. Phys. (1)

C. V. Raman, “A new radiation,” Indian J. Phys. 2, 387 (1928).

J. Opt. Soc. Am. (3)

W. H. Richardson, “Bayesian-based iterative method of image restoration,” J. Opt. Soc. Am. 62, 5559 (1972).
[Crossref]

P. P. Yaney, “Reduction of fluorescence background in Raman spectra by the pulsed Raman technique,” J. Opt. Soc. Am. 62, 1297–1303 (1972).
[Crossref]

E. F. Y. Hom, F. Marchis, T. K. Lee, S. Haase, D. A. Agard, and J.W. Sedat, “AIDA: an adaptive image deconvolution algorithm with application to multi-frame and three-dimensional data,” J. Opt. Soc. Am. A  24, 1580–1600 (2007).
[Crossref]

J. Raman Spectrosc. (1)

P. Matousek, M. Towrie, and A.W. Parker, “Fluorescence background suppression in Raman spectroscopy using combined Kerr gated and shifted excitation Raman difference techniques,” J. Raman Spectrosc. 33, 238–242 (2002).
[Crossref]

Other (5)

S. L. Rudder, J. C. Connolly, and G. J. Steckman , “Hybrid ECL/DBR wavelength and spectrum stabilized lasers demonstrate high power and narrow spectral linewidth,” in Laser Beam Control and Applications, A. V. Kudryashov, A. H. Paxton, V. S. Ilchenko, A. Giesen, D. Nickel, S. J. Davis, M. C. Heaven, and J. T. Schriempf, eds., Proc. SPIE 6101, pp.112–119 (2006).

P. A. Jannson, Deconvolution of Images and Spectra (Academic Press, San Diego, Calif., 1997)

J. R. Ferraro, K. Nakamoto, and C.W. Brown, Introductory Raman Spectroscopy, 2nd Ed. (Academic Press, San Diego, Cal., 2003).

R. Willett, “Multiscale intensity estimation for marked Poisson processes,” in Proc. IEEE Conf. Acoust., Speech, Signal Processing - ICASSP (2007).

R. Willett and R. Nowak, “Fast multiresolution photon-limited image reconstruction,” in Proc. IEEE Int. Sym. Biomedical Imaging - ISBI ’04 (15–18 April, Arlington, VA, USA, 2004).

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Figures (8)

Fig. 1.
Fig. 1.

One simulated measurement from each of the 2, 4, 8, and 16 frequency simulations (aceg) and corresponding EM reconstructions of the Raman component (bdfg).

Fig. 2.
Fig. 2.

(a) Root-mean-squared error of simulations as a function of number of excitation frequencies used and SNR of observations. The fluorescence signal to Raman signal ratio was 1 and 20 simulations were performed for each case. (b) Root-mean-squared error of simulations as a function of number of excitation frequencies used and SNR of observations. The fluorescence signal to Raman signal ratio was 1000 and 20 simulations were performed for each case. These results highlight the improvement associated with multiple excitation frequencies.

Fig. 3.
Fig. 3.

(a) Laser diodes 1-8 (LD1-8) are fiber-coupled, then pass through mode-mixer (MM) to randomize their spatial distribution. A lens (L1) collimates the light from the fiber, which is then spectrally filtered by a short-pass thin-film filter (F1). A mirror (M1) mounted on a BK7 window reflects the beam towards the sample. A lens (L2) focuses the beam onto the sample, and two lens systems (L2,L3) image the scattered light onto the entrance aperture of the spectrometer. A long-pass filter (F2) blocks the laser light. (b) Photograph of excitation/collection setup.

Fig. 4.
Fig. 4.

Naphthalene Raman spectra collected with each excitation laser.

Fig. 5.
Fig. 5.

Naphthalene Raman spectra corrected for relative shift of each excitation laser.

Fig. 6.
Fig. 6.

(a) Measured spectra with all 8 excitation lasers for solution of 1×10-8 M dye dissolved in ethanol, 50 mW excitation power per laser, 1 second per excitation (b) Measured spectra with all 8 excitation lasers for solution of 1×10-6M dye dissolved in ethanol, 5 mW excitation power per laser, 1 second per excitation

Fig. 7.
Fig. 7.

(a-d) Low concentration dye results, (a)- Polynomial fit background subtraction of spectra from laser 1, (b)- Subtraction of spectra from lasers 1 and 2, (c)- Estimated Raman spectrum from Fourier deconvolution of b, (d)- Pure ethanol measured with one of the excitation lasers (e-h) High concentration dye results, (e)- Polynomial fit background subtraction of spectra from laser 1, (f)- Subtraction of spectra from lasers 1 and 2, (g)- Estimated Raman spectrum from Fourier deconvolution of f, (h)- Pure ethanol measured with one of the excitation lasers

Fig. 8.
Fig. 8.

(a) Low concentration dye EM reconstructions for 2, 4, and 8 excitation lasers, (b) High concentration dye EM reconstructions for 2, 4 and 8 excitation lasers

Equations (21)

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g R = h e ( ν ) S R ( ν ν ) d ν .
g F = h e ( v ) S R ( v ) d v .
g R 1 g R 2 = S R ( v v ) ( δ ( v 1 v ) δ ( v 2 v ) ) d v .
y SERDS Poisson ( S F + S R ( v v 1 ) ) Poisson ( S F + S R ( v v 2 ) ) .
g Rk = h ek ( v ) S R ( v v ) d v ,
g Fk = h ek ( v ) S F ( v ) d v .
g k = g Rk + S F .
g [ g 1 T , g 2 T . . . g K T ] T .
y Poisson ( HS ) ,
H = H F H R 1 H F H Rk
x ̂ t + 1 = S ̂ t × ( H T ( y∙ ( H S ̂ t ) ) )
S ̂ t + 1 = x ̂ t + 1
P ̂ t + 1 arg min P [ log p ( x ̂ t + 1 S ( P ̂ ) ) + pen ( P ̂ ) ]
S ̂ t + 1 S ( P ̂ t + 1 )
p ( x S ( P ̂ ) ) = i = 0 N 1 e S [ i ] S [ i ] x [ i ] x [ i ] !
H ( S F , S R ) = [ S F + S R w , S F + S R w ( w ( n ) + Δ 2 ) , , S F + S R w ( w ( n ) + Δ k ) ]
S R w ( w ( n ) ) = S R ( n ) .
z k = g k w ( w ( n ) - Δ k ) .
H T g 1 g k = [ 1 k k = 1 k g kn , 1 k k = 1 k z kn ] .
y d = H d S R ,
S R = F 1 ( F ( y D ) F ( H d ) ) ,

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