Abstract

A new global analysis algorithm to analyse (hyper-) spectral images is presented. It is based on the phasor representation that has been demonstrated to be very powerful for the analysis of lifetime imaging data. In spectral phasor analysis the fluorescence spectrum of each pixel in the image is Fourier transformed. Next, the real and imaginary components of the first harmonic of the transform are employed as X and Y coordinates in a scatter (spectral phasor) plot. Importantly, the spectral phasor representation allows for rapid (real time) semi-blind spectral unmixing of up to three components in the image. This is demonstrated on slides with fixed cells containing three fluorescent labels. In addition the method is used to analyse autofluorescence of cells in a fresh grass blade. It is shown that the spectral phasor approach is compatible with spectral imaging data recorded with a low number of spectral channels.

© 2012 OSA

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2011

A. N. Bader, A. M. Pena, C. Johan van Voskuilen, J. A. Palero, F. Leroy, A. Colonna, and H. C. Gerritsen, “Fast nonlinear spectral microscopy of in vivo human skin,” Biomed. Opt. Express 2(2), 365–373 (2011).
[CrossRef] [PubMed]

F. Fereidouni, A. Esposito, G. A. Blab, and H. C. Gerritsen, “A modified phasor approach for analyzing time-gated fluorescence lifetime images,” J. Microsc. 244(3), 248–258 (2011).
[CrossRef] [PubMed]

2010

J. Willem Borst and A. J. W. G. Visser, “Fluorescence lifetime imaging microscopy in life sciences,” Meas. Sci. Technol. 21(10), 102002 (2010).
[CrossRef]

2009

R. A. Neher, M. Mitkovski, F. Kirchhoff, E. Neher, F. J. Theis, and A. Zeug, “Blind source separation techniques for the decomposition of multiply labeled fluorescence images,” Biophys. J. 96(9), 3791–3800 (2009).
[CrossRef] [PubMed]

R. Cisek, L. Spencer, N. Prent, D. Zigmantas, G. S. Espie, and V. Barzda, “Optical microscopy in photosynthesis,” Photosynth. Res. 102(2-3), 111–141 (2009).
[CrossRef] [PubMed]

2008

M. A. Digman, V. R. Caiolfa, M. Zamai, and E. Gratton, “The phasor approach to fluorescence lifetime imaging analysis,” Biophys. J. 94(2), L14–L16 (2008).
[CrossRef] [PubMed]

J. A. Palero, G. Latouche, H. S. de Bruijn, A. van der Ploeg van den Heuvel, H. J. Sterenborg, and H. C. Gerritsen, “Design and implementation of a sensitive high-resolution nonlinear spectral imaging microscope,” J. Biomed. Opt. 13(4), 044019 (2008).
[CrossRef] [PubMed]

2006

2005

G. I. Redford and R. M. Clegg, “Polar plot representation for frequency-domain analysis of fluorescence lifetimes,” J. Fluoresc. 15(5), 805–815 (2005).
[CrossRef] [PubMed]

2004

H. Shirakawa and S. Miyazaki, “Blind spectral decomposition of single-cell fluorescence by parallel factor analysis,” Biophys. J. 86(3), 1739–1752 (2004).
[CrossRef] [PubMed]

2003

S. Meyer, A. Cartelat, I. Moya, and Z. G. Cerovic, “UV-induced blue-green and far-red fluorescence along wheat leaves: a potential signature of leaf ageing,” J. Exp. Bot. 54(383), 757–769 (2003).
[CrossRef] [PubMed]

T. Zimmermann, J. Rietdorf, and R. Pepperkok, “Spectral imaging and its applications in live cell microscopy,” FEBS Lett. 546(1), 87–92 (2003).
[CrossRef] [PubMed]

V. E. Centonze, M. Sun, A. Masuda, H. Gerritsen, and B. Herman, “Fluorescence resonance energy transfer imaging microscopy,” Methods Enzymol. 360, 542–560 (2003).
[CrossRef] [PubMed]

2000

P. J. Verveer, A. Squire, and P. I. H. Bastiaens, “Global analysis of fluorescence lifetime imaging microscopy data,” Biophys. J. 78(4), 2127–2137 (2000).
[CrossRef] [PubMed]

1999

P. I. H. Bastiaens and A. Squire, “Fluorescence lifetime imaging microscopy: spatial resolution of biochemical processes in the cell,” Trends Cell Biol. 9(2), 48–52 (1999).
[CrossRef] [PubMed]

1998

C. Buschmann and H. K. Lichtenthaler, “Principles and characteristics of multi-colour fluorescence imaging of plants,” J. Plant Physiol. 152(2-3), 297–314 (1998).
[CrossRef]

1993

E. M. M. Manders, F. J. Verbeek, and J. A. Aten, “Measurement of co-localization of objects in dual-colour confocal images,” J. Microsc. 169(3), 375–382 (1993).
[CrossRef]

1984

D. M. Jameson, E. Gratton, and R. Hall, “The measurement and analysis of heterogeneous emissions by multifrequency phase and modulation fluorometry,” Appl. Spectrosc. Rev. 20(1), 55–106 (1984).
[CrossRef]

Aten, J. A.

E. M. M. Manders, F. J. Verbeek, and J. A. Aten, “Measurement of co-localization of objects in dual-colour confocal images,” J. Microsc. 169(3), 375–382 (1993).
[CrossRef]

Bader, A. N.

Barzda, V.

R. Cisek, L. Spencer, N. Prent, D. Zigmantas, G. S. Espie, and V. Barzda, “Optical microscopy in photosynthesis,” Photosynth. Res. 102(2-3), 111–141 (2009).
[CrossRef] [PubMed]

Bastiaens, P. I. H.

P. J. Verveer, A. Squire, and P. I. H. Bastiaens, “Global analysis of fluorescence lifetime imaging microscopy data,” Biophys. J. 78(4), 2127–2137 (2000).
[CrossRef] [PubMed]

P. I. H. Bastiaens and A. Squire, “Fluorescence lifetime imaging microscopy: spatial resolution of biochemical processes in the cell,” Trends Cell Biol. 9(2), 48–52 (1999).
[CrossRef] [PubMed]

Blab, G. A.

F. Fereidouni, A. Esposito, G. A. Blab, and H. C. Gerritsen, “A modified phasor approach for analyzing time-gated fluorescence lifetime images,” J. Microsc. 244(3), 248–258 (2011).
[CrossRef] [PubMed]

Buschmann, C.

C. Buschmann and H. K. Lichtenthaler, “Principles and characteristics of multi-colour fluorescence imaging of plants,” J. Plant Physiol. 152(2-3), 297–314 (1998).
[CrossRef]

Caiolfa, V. R.

M. A. Digman, V. R. Caiolfa, M. Zamai, and E. Gratton, “The phasor approach to fluorescence lifetime imaging analysis,” Biophys. J. 94(2), L14–L16 (2008).
[CrossRef] [PubMed]

Cartelat, A.

S. Meyer, A. Cartelat, I. Moya, and Z. G. Cerovic, “UV-induced blue-green and far-red fluorescence along wheat leaves: a potential signature of leaf ageing,” J. Exp. Bot. 54(383), 757–769 (2003).
[CrossRef] [PubMed]

Centonze, V. E.

V. E. Centonze, M. Sun, A. Masuda, H. Gerritsen, and B. Herman, “Fluorescence resonance energy transfer imaging microscopy,” Methods Enzymol. 360, 542–560 (2003).
[CrossRef] [PubMed]

Cerovic, Z. G.

S. Meyer, A. Cartelat, I. Moya, and Z. G. Cerovic, “UV-induced blue-green and far-red fluorescence along wheat leaves: a potential signature of leaf ageing,” J. Exp. Bot. 54(383), 757–769 (2003).
[CrossRef] [PubMed]

Cisek, R.

R. Cisek, L. Spencer, N. Prent, D. Zigmantas, G. S. Espie, and V. Barzda, “Optical microscopy in photosynthesis,” Photosynth. Res. 102(2-3), 111–141 (2009).
[CrossRef] [PubMed]

Clegg, R. M.

G. I. Redford and R. M. Clegg, “Polar plot representation for frequency-domain analysis of fluorescence lifetimes,” J. Fluoresc. 15(5), 805–815 (2005).
[CrossRef] [PubMed]

Colonna, A.

de Bruijn, H. S.

J. A. Palero, G. Latouche, H. S. de Bruijn, A. van der Ploeg van den Heuvel, H. J. Sterenborg, and H. C. Gerritsen, “Design and implementation of a sensitive high-resolution nonlinear spectral imaging microscope,” J. Biomed. Opt. 13(4), 044019 (2008).
[CrossRef] [PubMed]

J. A. Palero, H. S. de Bruijn, A. van der Ploeg-van den Heuvel, H. J. C. M. Sterenborg, and H. C. Gerritsen, “In vivo nonlinear spectral imaging in mouse skin,” Opt. Express 14(10), 4395–4402 (2006).
[CrossRef] [PubMed]

Digman, M. A.

M. A. Digman, V. R. Caiolfa, M. Zamai, and E. Gratton, “The phasor approach to fluorescence lifetime imaging analysis,” Biophys. J. 94(2), L14–L16 (2008).
[CrossRef] [PubMed]

Espie, G. S.

R. Cisek, L. Spencer, N. Prent, D. Zigmantas, G. S. Espie, and V. Barzda, “Optical microscopy in photosynthesis,” Photosynth. Res. 102(2-3), 111–141 (2009).
[CrossRef] [PubMed]

Esposito, A.

F. Fereidouni, A. Esposito, G. A. Blab, and H. C. Gerritsen, “A modified phasor approach for analyzing time-gated fluorescence lifetime images,” J. Microsc. 244(3), 248–258 (2011).
[CrossRef] [PubMed]

Fereidouni, F.

F. Fereidouni, A. Esposito, G. A. Blab, and H. C. Gerritsen, “A modified phasor approach for analyzing time-gated fluorescence lifetime images,” J. Microsc. 244(3), 248–258 (2011).
[CrossRef] [PubMed]

Garini, Y.

Y. Garini, I. T. Young, and G. McNamara, “Spectral imaging: principles and applications,” Cytometry A 69A(8), 735–747 (2006).
[CrossRef] [PubMed]

Gerritsen, H.

V. E. Centonze, M. Sun, A. Masuda, H. Gerritsen, and B. Herman, “Fluorescence resonance energy transfer imaging microscopy,” Methods Enzymol. 360, 542–560 (2003).
[CrossRef] [PubMed]

Gerritsen, H. C.

A. N. Bader, A. M. Pena, C. Johan van Voskuilen, J. A. Palero, F. Leroy, A. Colonna, and H. C. Gerritsen, “Fast nonlinear spectral microscopy of in vivo human skin,” Biomed. Opt. Express 2(2), 365–373 (2011).
[CrossRef] [PubMed]

F. Fereidouni, A. Esposito, G. A. Blab, and H. C. Gerritsen, “A modified phasor approach for analyzing time-gated fluorescence lifetime images,” J. Microsc. 244(3), 248–258 (2011).
[CrossRef] [PubMed]

J. A. Palero, G. Latouche, H. S. de Bruijn, A. van der Ploeg van den Heuvel, H. J. Sterenborg, and H. C. Gerritsen, “Design and implementation of a sensitive high-resolution nonlinear spectral imaging microscope,” J. Biomed. Opt. 13(4), 044019 (2008).
[CrossRef] [PubMed]

J. A. Palero, H. S. de Bruijn, A. van der Ploeg-van den Heuvel, H. J. C. M. Sterenborg, and H. C. Gerritsen, “In vivo nonlinear spectral imaging in mouse skin,” Opt. Express 14(10), 4395–4402 (2006).
[CrossRef] [PubMed]

Gratton, E.

M. A. Digman, V. R. Caiolfa, M. Zamai, and E. Gratton, “The phasor approach to fluorescence lifetime imaging analysis,” Biophys. J. 94(2), L14–L16 (2008).
[CrossRef] [PubMed]

D. M. Jameson, E. Gratton, and R. Hall, “The measurement and analysis of heterogeneous emissions by multifrequency phase and modulation fluorometry,” Appl. Spectrosc. Rev. 20(1), 55–106 (1984).
[CrossRef]

Hall, R.

D. M. Jameson, E. Gratton, and R. Hall, “The measurement and analysis of heterogeneous emissions by multifrequency phase and modulation fluorometry,” Appl. Spectrosc. Rev. 20(1), 55–106 (1984).
[CrossRef]

Herman, B.

V. E. Centonze, M. Sun, A. Masuda, H. Gerritsen, and B. Herman, “Fluorescence resonance energy transfer imaging microscopy,” Methods Enzymol. 360, 542–560 (2003).
[CrossRef] [PubMed]

Jameson, D. M.

D. M. Jameson, E. Gratton, and R. Hall, “The measurement and analysis of heterogeneous emissions by multifrequency phase and modulation fluorometry,” Appl. Spectrosc. Rev. 20(1), 55–106 (1984).
[CrossRef]

Johan van Voskuilen, C.

Kirchhoff, F.

R. A. Neher, M. Mitkovski, F. Kirchhoff, E. Neher, F. J. Theis, and A. Zeug, “Blind source separation techniques for the decomposition of multiply labeled fluorescence images,” Biophys. J. 96(9), 3791–3800 (2009).
[CrossRef] [PubMed]

Latouche, G.

J. A. Palero, G. Latouche, H. S. de Bruijn, A. van der Ploeg van den Heuvel, H. J. Sterenborg, and H. C. Gerritsen, “Design and implementation of a sensitive high-resolution nonlinear spectral imaging microscope,” J. Biomed. Opt. 13(4), 044019 (2008).
[CrossRef] [PubMed]

Leroy, F.

Lichtenthaler, H. K.

C. Buschmann and H. K. Lichtenthaler, “Principles and characteristics of multi-colour fluorescence imaging of plants,” J. Plant Physiol. 152(2-3), 297–314 (1998).
[CrossRef]

Manders, E. M. M.

E. M. M. Manders, F. J. Verbeek, and J. A. Aten, “Measurement of co-localization of objects in dual-colour confocal images,” J. Microsc. 169(3), 375–382 (1993).
[CrossRef]

Masuda, A.

V. E. Centonze, M. Sun, A. Masuda, H. Gerritsen, and B. Herman, “Fluorescence resonance energy transfer imaging microscopy,” Methods Enzymol. 360, 542–560 (2003).
[CrossRef] [PubMed]

McNamara, G.

Y. Garini, I. T. Young, and G. McNamara, “Spectral imaging: principles and applications,” Cytometry A 69A(8), 735–747 (2006).
[CrossRef] [PubMed]

Meyer, S.

S. Meyer, A. Cartelat, I. Moya, and Z. G. Cerovic, “UV-induced blue-green and far-red fluorescence along wheat leaves: a potential signature of leaf ageing,” J. Exp. Bot. 54(383), 757–769 (2003).
[CrossRef] [PubMed]

Mitkovski, M.

R. A. Neher, M. Mitkovski, F. Kirchhoff, E. Neher, F. J. Theis, and A. Zeug, “Blind source separation techniques for the decomposition of multiply labeled fluorescence images,” Biophys. J. 96(9), 3791–3800 (2009).
[CrossRef] [PubMed]

Miyazaki, S.

H. Shirakawa and S. Miyazaki, “Blind spectral decomposition of single-cell fluorescence by parallel factor analysis,” Biophys. J. 86(3), 1739–1752 (2004).
[CrossRef] [PubMed]

Moya, I.

S. Meyer, A. Cartelat, I. Moya, and Z. G. Cerovic, “UV-induced blue-green and far-red fluorescence along wheat leaves: a potential signature of leaf ageing,” J. Exp. Bot. 54(383), 757–769 (2003).
[CrossRef] [PubMed]

Neher, E.

R. A. Neher, M. Mitkovski, F. Kirchhoff, E. Neher, F. J. Theis, and A. Zeug, “Blind source separation techniques for the decomposition of multiply labeled fluorescence images,” Biophys. J. 96(9), 3791–3800 (2009).
[CrossRef] [PubMed]

Neher, R. A.

R. A. Neher, M. Mitkovski, F. Kirchhoff, E. Neher, F. J. Theis, and A. Zeug, “Blind source separation techniques for the decomposition of multiply labeled fluorescence images,” Biophys. J. 96(9), 3791–3800 (2009).
[CrossRef] [PubMed]

Palero, J. A.

Pena, A. M.

Pepperkok, R.

T. Zimmermann, J. Rietdorf, and R. Pepperkok, “Spectral imaging and its applications in live cell microscopy,” FEBS Lett. 546(1), 87–92 (2003).
[CrossRef] [PubMed]

Prent, N.

R. Cisek, L. Spencer, N. Prent, D. Zigmantas, G. S. Espie, and V. Barzda, “Optical microscopy in photosynthesis,” Photosynth. Res. 102(2-3), 111–141 (2009).
[CrossRef] [PubMed]

Redford, G. I.

G. I. Redford and R. M. Clegg, “Polar plot representation for frequency-domain analysis of fluorescence lifetimes,” J. Fluoresc. 15(5), 805–815 (2005).
[CrossRef] [PubMed]

Rietdorf, J.

T. Zimmermann, J. Rietdorf, and R. Pepperkok, “Spectral imaging and its applications in live cell microscopy,” FEBS Lett. 546(1), 87–92 (2003).
[CrossRef] [PubMed]

Shirakawa, H.

H. Shirakawa and S. Miyazaki, “Blind spectral decomposition of single-cell fluorescence by parallel factor analysis,” Biophys. J. 86(3), 1739–1752 (2004).
[CrossRef] [PubMed]

Spencer, L.

R. Cisek, L. Spencer, N. Prent, D. Zigmantas, G. S. Espie, and V. Barzda, “Optical microscopy in photosynthesis,” Photosynth. Res. 102(2-3), 111–141 (2009).
[CrossRef] [PubMed]

Squire, A.

P. J. Verveer, A. Squire, and P. I. H. Bastiaens, “Global analysis of fluorescence lifetime imaging microscopy data,” Biophys. J. 78(4), 2127–2137 (2000).
[CrossRef] [PubMed]

P. I. H. Bastiaens and A. Squire, “Fluorescence lifetime imaging microscopy: spatial resolution of biochemical processes in the cell,” Trends Cell Biol. 9(2), 48–52 (1999).
[CrossRef] [PubMed]

Sterenborg, H. J.

J. A. Palero, G. Latouche, H. S. de Bruijn, A. van der Ploeg van den Heuvel, H. J. Sterenborg, and H. C. Gerritsen, “Design and implementation of a sensitive high-resolution nonlinear spectral imaging microscope,” J. Biomed. Opt. 13(4), 044019 (2008).
[CrossRef] [PubMed]

Sterenborg, H. J. C. M.

Sun, M.

V. E. Centonze, M. Sun, A. Masuda, H. Gerritsen, and B. Herman, “Fluorescence resonance energy transfer imaging microscopy,” Methods Enzymol. 360, 542–560 (2003).
[CrossRef] [PubMed]

Theis, F. J.

R. A. Neher, M. Mitkovski, F. Kirchhoff, E. Neher, F. J. Theis, and A. Zeug, “Blind source separation techniques for the decomposition of multiply labeled fluorescence images,” Biophys. J. 96(9), 3791–3800 (2009).
[CrossRef] [PubMed]

van der Ploeg van den Heuvel, A.

J. A. Palero, G. Latouche, H. S. de Bruijn, A. van der Ploeg van den Heuvel, H. J. Sterenborg, and H. C. Gerritsen, “Design and implementation of a sensitive high-resolution nonlinear spectral imaging microscope,” J. Biomed. Opt. 13(4), 044019 (2008).
[CrossRef] [PubMed]

van der Ploeg-van den Heuvel, A.

Verbeek, F. J.

E. M. M. Manders, F. J. Verbeek, and J. A. Aten, “Measurement of co-localization of objects in dual-colour confocal images,” J. Microsc. 169(3), 375–382 (1993).
[CrossRef]

Verveer, P. J.

P. J. Verveer, A. Squire, and P. I. H. Bastiaens, “Global analysis of fluorescence lifetime imaging microscopy data,” Biophys. J. 78(4), 2127–2137 (2000).
[CrossRef] [PubMed]

Visser, A. J. W. G.

J. Willem Borst and A. J. W. G. Visser, “Fluorescence lifetime imaging microscopy in life sciences,” Meas. Sci. Technol. 21(10), 102002 (2010).
[CrossRef]

Willem Borst, J.

J. Willem Borst and A. J. W. G. Visser, “Fluorescence lifetime imaging microscopy in life sciences,” Meas. Sci. Technol. 21(10), 102002 (2010).
[CrossRef]

Young, I. T.

Y. Garini, I. T. Young, and G. McNamara, “Spectral imaging: principles and applications,” Cytometry A 69A(8), 735–747 (2006).
[CrossRef] [PubMed]

Zamai, M.

M. A. Digman, V. R. Caiolfa, M. Zamai, and E. Gratton, “The phasor approach to fluorescence lifetime imaging analysis,” Biophys. J. 94(2), L14–L16 (2008).
[CrossRef] [PubMed]

Zeug, A.

R. A. Neher, M. Mitkovski, F. Kirchhoff, E. Neher, F. J. Theis, and A. Zeug, “Blind source separation techniques for the decomposition of multiply labeled fluorescence images,” Biophys. J. 96(9), 3791–3800 (2009).
[CrossRef] [PubMed]

Zigmantas, D.

R. Cisek, L. Spencer, N. Prent, D. Zigmantas, G. S. Espie, and V. Barzda, “Optical microscopy in photosynthesis,” Photosynth. Res. 102(2-3), 111–141 (2009).
[CrossRef] [PubMed]

Zimmermann, T.

T. Zimmermann, J. Rietdorf, and R. Pepperkok, “Spectral imaging and its applications in live cell microscopy,” FEBS Lett. 546(1), 87–92 (2003).
[CrossRef] [PubMed]

Appl. Spectrosc. Rev.

D. M. Jameson, E. Gratton, and R. Hall, “The measurement and analysis of heterogeneous emissions by multifrequency phase and modulation fluorometry,” Appl. Spectrosc. Rev. 20(1), 55–106 (1984).
[CrossRef]

Biomed. Opt. Express

Biophys. J.

P. J. Verveer, A. Squire, and P. I. H. Bastiaens, “Global analysis of fluorescence lifetime imaging microscopy data,” Biophys. J. 78(4), 2127–2137 (2000).
[CrossRef] [PubMed]

R. A. Neher, M. Mitkovski, F. Kirchhoff, E. Neher, F. J. Theis, and A. Zeug, “Blind source separation techniques for the decomposition of multiply labeled fluorescence images,” Biophys. J. 96(9), 3791–3800 (2009).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

(A) Reference spectral phasor plot showing the positions of Gaussian spectra. The grid covers emission maxima from 370 – 650 nm (the wavelength determines the position on the semicircle, as indicated by its colour) and spectral widths from 500 – 4000 cm−1 (with increasing spectral width, the position in the phasor plot is shifted towards the centre of the circle). As an example, a spectrum and its position in the phasor are shown. (B) The relative intensities α1, α2 and α3 of components A1, A2 and A3 in a pixel can be derived from the phasor.

Fig. 2
Fig. 2

Spectral phasor analysis of solutions of organic dyes Coumarin 120 (A), Rosebengal (B) and Fluorescein (C-D), mixtures of Coumarin 120 and Fluorescein, and a mixture of Coumarin 120, Fluorescein and Rosebengal (F). In each phasor diagram also the average spectrum over the whole image (white line) and of a single pixel is displayed (coloured line). A reference semicircle of Gaussian spectra (370-650 nm, 500 cm−1) and a grey triangle connecting the reference positions of the dyes are indicated in each phasor diagram. We note that positions in the phasor plot are colour coded according to their real RGB colour.

Fig. 3
Fig. 3

Spectral phasor analysis of FluoCells test slides #2 (field of view 80x80µm) A) Spectral phasor plot; for three areas in the phasor plot (indicated by the dashed boxes), the spectra are averaged and displayed together with the average spectrum of the whole image. A solid reference semicircle (370-650 nm, 500 cm−1) and three solid reference lines corresponding to the positions of the emission maxima found from the spectra are shown in the phasor plot. B) Real colour representation of the original image. C-E) Unmixed images of DAPI, BODIPY and Texas Red.

Fig. 4
Fig. 4

Spectral phasor analysis of FluoCells test slides #6 (field of view 50x50µm); A) Spectral phasor plot; for three areas in the phasor plot (indicated by the dashed boxes), the spectra are averaged and displayed together with the average spectrum of the whole image. A solid reference semicircle (370-650 nm, 500 cm−1) and three solid reference lines corresponding to the positions of the emission maxima found from the spectra are shown in the phasor plot. B) Real colour representation of the original image. C-E) Unmixed images of Alexa 488, Alexa 555 and TO-PRO3.

Fig. 5
Fig. 5

Spectral phasor plot of a Grass blade autofluorescence image. For three areas in the phasor plot, the spectra are averaged and displayed (indicated by dashed boxes and spectra) together with the average spectrum of the whole image. A solid reference semicircle of Gaussian spectra (370-650 nm, 500 cm−1) and three solid reference lines of the positions of emission maxima found in the spectra (470 nm, 495 nm and 630 nm) are also shown. The grey triangle connects the reference positions of the dyes, allowing unmixing of the image in the three channels. B) The real colour representation of the autofluorescence image. C-E) The unmixed signals.

Fig. 6
Fig. 6

Spectral analysis of the BPAE cells shown in Fig. 3. (A) Images corresponding to 3 emission filters (top) and total intensity (bottom). (B-D) Spectral phasor diagrams of spectral images with 16, 8 and 4 wavelength channels respectively. The reference phasor grids (top left) cover emission maxima from 370 – 650 nm and spectral widths from 500 – 4000 cm−1. Spectra of regions at the edges of the phasor cloud are included.

Equations (8)

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y nj = n a nk x kj .
y nj = a n1 x 1j + a n2 x 2j + a n3 x 3j .
Y j = A 1 x 1j + A 2 x 2j + A 3 x 3j x 1j + x 2j + x 3j = α 1 A 1 + α 2 A 2 + α 3 A 3 .
A k = n=1 N a nk e i 2π N n .
α k = x k x 1 + x 2 + x 3 ,
Y j = α 1 A 1 + α 2 A 2 +(1( α 1 + α 2 )) A 3 .
Re Y j = α 1 Re A 1 + α 2 Re A 2 +(1( α 1 + α 2 ))Re A 3 , Im Y j = α 1 Im A 1 + α 2 Im A 2 +(1( α 1 + α 2 ))Im A 3 ,
α 1 = Re A 2 ImYReYIm A 2 +Re A 3 Im A 2 Re A 2 Im A 3 +ReYIm A 3 Re A 3 ImY Re A 2 Im A 1 Re A 1 Im A 2 Re A 3 Im A 2 Re A 2 Im A 3 +Re A 1 Im A 3 Re A 3 Im A 1 , α 2 = Re A 3 ImYReYIm A 3 +Re A 1 Im A 3 Re A 3 Im A 1 +ReYIm A 1 Re A 1 ImY Re A 2 Im A 1 Re A 1 Im A 2 Re A 3 Im A 2 Re A 2 Im A 3 +Re A 1 Im A 3 Re A 3 Im A 1 .

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