Abstract

We have analyzed the Fourier-frequency content of spectral power distributions deriving from three types of illuminants (daylight, incandescent, and fluorescent) and the color signals from both biochrome and nonbiochrome surfaces lit by these illuminants. As far as daylight and the incandescent illuminant are concerned, after filtering the signals through parabolic (low-pass) filters in the Fourier-frequency domain and then reconstructing them, we found that most of the spectral information was contained below 0.016 c/nm. When fluorescent illuminants were involved, we were unable to recover either the original illuminants or color signals to any satisfactory degree. We also used the spectral modulation sensitivity function, which is related to the human visual system’s color discrimination thresholds, as a Fourier-frequency filter and obtained consistently less reliable results than with low-pass filtering. We provide comparative results for daylight signals recovered by three different methods. We found reconstructions based on linear models to be the most effective.

© 2003 Optical Society of America

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References

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2003 (2)

M. H. Brill, “A non-PC look at principal components,” Color Res. Appl. 28, 69–71 (2003).
[CrossRef]

J. Romero, J. Hernández-Andrés, J. L. Nieves, J. A. Garcı́a, “Color coordinates of objects with daylight changes,” Color Res. Appl. 28, 25–35 (2003).
[CrossRef]

2001 (4)

M. Thomson, S. Westland, “Colour-imager characterization by parametric fitting of sensor responses,” Color Res. Appl. 26, 442–449 (2001).
[CrossRef]

V. Bonnardel, E. Valero, “Study of colour discrimination with comb-filtered spectra,” Vision Res. 41, 541–548 (2001).
[CrossRef] [PubMed]

G. Finlayson, S. D. Hordley, “Color constancy at a pixel,” J. Opt. Soc. Am. A 18, 253–264 (2001).
[CrossRef]

J. Hernández-Andrés, J. L. Nieves, J. Romero, R. L. Lee, “Color and spectral analysis of daylight in southern europe,” J. Opt. Soc. Am. A 18, 1325–1335 (2001).
[CrossRef]

2000 (1)

1998 (1)

E. Valero, J. A. Garcı́a, J. L. Nieves, J. Romero, “Measurements of sensitivity to simulated chromatic frequencies for normal and dichromatic observers,” J. Opt. (Paris) 29, 339–344 (1998).
[CrossRef]

1997 (1)

J. Romero, J. A. Garcı́a, E. Valero, J. L. Nieves, “Measurements of the spectral modulation sensitivity function for two normal observers with CRT monitors,” J. Opt. (Paris) 28, 190–198 (1997).
[CrossRef]

1996 (1)

V. Bonnardel, H. Bellemare, J. D. Mollon, “Measurements of human sensitivity to comb-filtered spectra,” Vision Res. 36, 2713–2720 (1996).
[CrossRef] [PubMed]

1995 (2)

J. Romero, J. L. Nieves, A. Garcı́a-Beltrán, “Human processing of colour information in the chromatic-frequency domain,” Vision Res. 35, 867–871 (1995).
[CrossRef] [PubMed]

J. Romero, J. L. Nieves, A. Garcı́a-Beltrán, E. Hita, “Analysis of color-vision models in the chromatic-frequency domain,” J. Opt. (Paris) 26, 9–15 (1995).
[CrossRef]

1994 (1)

M. J. Vrhel, R. Gershon, L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9 (1994).

1993 (1)

J. H. Van Hateren, “Spatial, temporal and spectral pre-processing for colour vision,” Proc. R. Soc. London Ser. B 251, 61–68 (1993).
[CrossRef]

1992 (1)

1991 (2)

P. Lennie, “Color vision,” Opt. Photon. News, August1991, pp. 10–16.

V. Bonnardel, F. J. Varela, “A frequency view of colour: Measuring the human sensitivity to square-wave spectral power distribution,” Proc. R. Soc. London Ser. B 245, 165–171 (1991).
[CrossRef]

1989 (1)

1987 (1)

B. Wandell, “The synthesis and analysis of color images,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-9, 2–13 (1987).
[CrossRef]

1986 (2)

1984 (1)

1982 (1)

H. B. Barlow, “What causes trichromacy? A theoretical analysis using comb-filtered spectra,” Vision Res. 22, 635–643 (1982).
[CrossRef] [PubMed]

1977 (1)

1964 (1)

Barlow, H. B.

H. B. Barlow, “What causes trichromacy? A theoretical analysis using comb-filtered spectra,” Vision Res. 22, 635–643 (1982).
[CrossRef] [PubMed]

V. Bonnardel, D. L. Ruderman, H. B. Barlow, “Fast determination of the spectral modulation sensitivity function: a comparison between trichromats and deuteranopes,” in Color Vision Deficiencies XIII, C. R. Cavonius, ed., Vol. 59 of Documenta Ophthalmology Proceedings Series (Kluwer Academic, Dordrecht, The Netherlands, 1997), pp. 415–424.
[CrossRef]

Bellemare, H.

V. Bonnardel, H. Bellemare, J. D. Mollon, “Measurements of human sensitivity to comb-filtered spectra,” Vision Res. 36, 2713–2720 (1996).
[CrossRef] [PubMed]

Benzschawel, T.

Berns, R. S.

F. H. Imai, M. R. Rosen, R. S. Berns, “Comparative study of metrics for spectral match quality,” in Proceedings of the First European Conference on Color in Graphics, Imaging and Vision (Society for Imaging Science and Technology, Springfield, Va., 2002), pp. 492–496.

Bonnardel, V.

V. Bonnardel, E. Valero, “Study of colour discrimination with comb-filtered spectra,” Vision Res. 41, 541–548 (2001).
[CrossRef] [PubMed]

V. Bonnardel, L. T. Maloney, “Daylight, biochrome surfaces, and human chromatic response in the Fourier domain,” J. Opt. Soc. Am. A 17, 677–686 (2000).
[CrossRef]

V. Bonnardel, H. Bellemare, J. D. Mollon, “Measurements of human sensitivity to comb-filtered spectra,” Vision Res. 36, 2713–2720 (1996).
[CrossRef] [PubMed]

V. Bonnardel, F. J. Varela, “A frequency view of colour: Measuring the human sensitivity to square-wave spectral power distribution,” Proc. R. Soc. London Ser. B 245, 165–171 (1991).
[CrossRef]

V. Bonnardel, D. L. Ruderman, H. B. Barlow, “Fast determination of the spectral modulation sensitivity function: a comparison between trichromats and deuteranopes,” in Color Vision Deficiencies XIII, C. R. Cavonius, ed., Vol. 59 of Documenta Ophthalmology Proceedings Series (Kluwer Academic, Dordrecht, The Netherlands, 1997), pp. 415–424.
[CrossRef]

Bracewell, R.

R. Bracewell, The Fourier Transform and its Application (McGraw-Hill, New York, 1965).

Brill, M. H.

Buchsbaum, G.

Cohn, T. E.

Finlayson, G.

G. Finlayson, S. D. Hordley, “Color constancy at a pixel,” J. Opt. Soc. Am. A 18, 253–264 (2001).
[CrossRef]

G. Finlayson, “Spectral sharpening: what is it and why is it important?” in Proceedings of the First European Conference on Color in Graphics, Imaging and Vision (Society for Imaging Science and Technology, Springfield, Va., 2002), pp. 230–235.

Garci´a, J. A.

J. Romero, J. Hernández-Andrés, J. L. Nieves, J. A. Garcı́a, “Color coordinates of objects with daylight changes,” Color Res. Appl. 28, 25–35 (2003).
[CrossRef]

E. Valero, J. A. Garcı́a, J. L. Nieves, J. Romero, “Measurements of sensitivity to simulated chromatic frequencies for normal and dichromatic observers,” J. Opt. (Paris) 29, 339–344 (1998).
[CrossRef]

J. Romero, J. A. Garcı́a, E. Valero, J. L. Nieves, “Measurements of the spectral modulation sensitivity function for two normal observers with CRT monitors,” J. Opt. (Paris) 28, 190–198 (1997).
[CrossRef]

Garci´a-Beltrán, A.

J. Romero, J. L. Nieves, A. Garcı́a-Beltrán, E. Hita, “Analysis of color-vision models in the chromatic-frequency domain,” J. Opt. (Paris) 26, 9–15 (1995).
[CrossRef]

J. Romero, J. L. Nieves, A. Garcı́a-Beltrán, “Human processing of colour information in the chromatic-frequency domain,” Vision Res. 35, 867–871 (1995).
[CrossRef] [PubMed]

Gershon, R.

M. J. Vrhel, R. Gershon, L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9 (1994).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).

Gottschalk, A.

Hallikanen, J.

Hernández-Andrés, J.

J. Romero, J. Hernández-Andrés, J. L. Nieves, J. A. Garcı́a, “Color coordinates of objects with daylight changes,” Color Res. Appl. 28, 25–35 (2003).
[CrossRef]

J. Hernández-Andrés, J. L. Nieves, J. Romero, R. L. Lee, “Color and spectral analysis of daylight in southern europe,” J. Opt. Soc. Am. A 18, 1325–1335 (2001).
[CrossRef]

Hita, E.

J. Romero, J. L. Nieves, A. Garcı́a-Beltrán, E. Hita, “Analysis of color-vision models in the chromatic-frequency domain,” J. Opt. (Paris) 26, 9–15 (1995).
[CrossRef]

J. Romero, L. Jiménez del Barco, E. Hita, “Mathematical reconstruction of color-matching functions,” J. Opt. Soc. Am. A 9, 25–29 (1992).
[CrossRef]

Hordley, S. D.

Imai, F. H.

F. H. Imai, M. R. Rosen, R. S. Berns, “Comparative study of metrics for spectral match quality,” in Proceedings of the First European Conference on Color in Graphics, Imaging and Vision (Society for Imaging Science and Technology, Springfield, Va., 2002), pp. 492–496.

Iwan, L. S.

M. J. Vrhel, R. Gershon, L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9 (1994).

Jaaskelainen, T.

Jiménez del Barco, L.

Judd, D. B.

Lee, R. L.

Lennie, P.

P. Lennie, “Color vision,” Opt. Photon. News, August1991, pp. 10–16.

MacAdam, D. L.

Maloney, L. T.

Mollon, J. D.

V. Bonnardel, H. Bellemare, J. D. Mollon, “Measurements of human sensitivity to comb-filtered spectra,” Vision Res. 36, 2713–2720 (1996).
[CrossRef] [PubMed]

Nieves, J. L.

J. Romero, J. Hernández-Andrés, J. L. Nieves, J. A. Garcı́a, “Color coordinates of objects with daylight changes,” Color Res. Appl. 28, 25–35 (2003).
[CrossRef]

J. Hernández-Andrés, J. L. Nieves, J. Romero, R. L. Lee, “Color and spectral analysis of daylight in southern europe,” J. Opt. Soc. Am. A 18, 1325–1335 (2001).
[CrossRef]

E. Valero, J. A. Garcı́a, J. L. Nieves, J. Romero, “Measurements of sensitivity to simulated chromatic frequencies for normal and dichromatic observers,” J. Opt. (Paris) 29, 339–344 (1998).
[CrossRef]

J. Romero, J. A. Garcı́a, E. Valero, J. L. Nieves, “Measurements of the spectral modulation sensitivity function for two normal observers with CRT monitors,” J. Opt. (Paris) 28, 190–198 (1997).
[CrossRef]

J. Romero, J. L. Nieves, A. Garcı́a-Beltrán, E. Hita, “Analysis of color-vision models in the chromatic-frequency domain,” J. Opt. (Paris) 26, 9–15 (1995).
[CrossRef]

J. Romero, J. L. Nieves, A. Garcı́a-Beltrán, “Human processing of colour information in the chromatic-frequency domain,” Vision Res. 35, 867–871 (1995).
[CrossRef] [PubMed]

Ohta, N.

Parkinnen, J. P. S.

Romero, J.

J. Romero, J. Hernández-Andrés, J. L. Nieves, J. A. Garcı́a, “Color coordinates of objects with daylight changes,” Color Res. Appl. 28, 25–35 (2003).
[CrossRef]

J. Hernández-Andrés, J. L. Nieves, J. Romero, R. L. Lee, “Color and spectral analysis of daylight in southern europe,” J. Opt. Soc. Am. A 18, 1325–1335 (2001).
[CrossRef]

E. Valero, J. A. Garcı́a, J. L. Nieves, J. Romero, “Measurements of sensitivity to simulated chromatic frequencies for normal and dichromatic observers,” J. Opt. (Paris) 29, 339–344 (1998).
[CrossRef]

J. Romero, J. A. Garcı́a, E. Valero, J. L. Nieves, “Measurements of the spectral modulation sensitivity function for two normal observers with CRT monitors,” J. Opt. (Paris) 28, 190–198 (1997).
[CrossRef]

J. Romero, J. L. Nieves, A. Garcı́a-Beltrán, E. Hita, “Analysis of color-vision models in the chromatic-frequency domain,” J. Opt. (Paris) 26, 9–15 (1995).
[CrossRef]

J. Romero, J. L. Nieves, A. Garcı́a-Beltrán, “Human processing of colour information in the chromatic-frequency domain,” Vision Res. 35, 867–871 (1995).
[CrossRef] [PubMed]

J. Romero, L. Jiménez del Barco, E. Hita, “Mathematical reconstruction of color-matching functions,” J. Opt. Soc. Am. A 9, 25–29 (1992).
[CrossRef]

Rosen, M. R.

F. H. Imai, M. R. Rosen, R. S. Berns, “Comparative study of metrics for spectral match quality,” in Proceedings of the First European Conference on Color in Graphics, Imaging and Vision (Society for Imaging Science and Technology, Springfield, Va., 2002), pp. 492–496.

Ruderman, D. L.

V. Bonnardel, D. L. Ruderman, H. B. Barlow, “Fast determination of the spectral modulation sensitivity function: a comparison between trichromats and deuteranopes,” in Color Vision Deficiencies XIII, C. R. Cavonius, ed., Vol. 59 of Documenta Ophthalmology Proceedings Series (Kluwer Academic, Dordrecht, The Netherlands, 1997), pp. 415–424.
[CrossRef]

Stiles, W. S.

Thomson, M.

M. Thomson, S. Westland, “Colour-imager characterization by parametric fitting of sensor responses,” Color Res. Appl. 26, 442–449 (2001).
[CrossRef]

Valero, E.

V. Bonnardel, E. Valero, “Study of colour discrimination with comb-filtered spectra,” Vision Res. 41, 541–548 (2001).
[CrossRef] [PubMed]

E. Valero, J. A. Garcı́a, J. L. Nieves, J. Romero, “Measurements of sensitivity to simulated chromatic frequencies for normal and dichromatic observers,” J. Opt. (Paris) 29, 339–344 (1998).
[CrossRef]

J. Romero, J. A. Garcı́a, E. Valero, J. L. Nieves, “Measurements of the spectral modulation sensitivity function for two normal observers with CRT monitors,” J. Opt. (Paris) 28, 190–198 (1997).
[CrossRef]

Van Hateren, J. H.

J. H. Van Hateren, “Spatial, temporal and spectral pre-processing for colour vision,” Proc. R. Soc. London Ser. B 251, 61–68 (1993).
[CrossRef]

Varela, F. J.

V. Bonnardel, F. J. Varela, “A frequency view of colour: Measuring the human sensitivity to square-wave spectral power distribution,” Proc. R. Soc. London Ser. B 245, 165–171 (1991).
[CrossRef]

Vrhel, M. J.

M. J. Vrhel, R. Gershon, L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9 (1994).

Wandell, B.

B. Wandell, “The synthesis and analysis of color images,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-9, 2–13 (1987).
[CrossRef]

Westland, S.

M. Thomson, S. Westland, “Colour-imager characterization by parametric fitting of sensor responses,” Color Res. Appl. 26, 442–449 (2001).
[CrossRef]

Wyszecki, G.

Wyszecki, G. W.

Color Res. Appl. (4)

M. H. Brill, “A non-PC look at principal components,” Color Res. Appl. 28, 69–71 (2003).
[CrossRef]

M. J. Vrhel, R. Gershon, L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9 (1994).

J. Romero, J. Hernández-Andrés, J. L. Nieves, J. A. Garcı́a, “Color coordinates of objects with daylight changes,” Color Res. Appl. 28, 25–35 (2003).
[CrossRef]

M. Thomson, S. Westland, “Colour-imager characterization by parametric fitting of sensor responses,” Color Res. Appl. 26, 442–449 (2001).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

B. Wandell, “The synthesis and analysis of color images,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-9, 2–13 (1987).
[CrossRef]

J. Opt. (Paris) (3)

J. Romero, J. A. Garcı́a, E. Valero, J. L. Nieves, “Measurements of the spectral modulation sensitivity function for two normal observers with CRT monitors,” J. Opt. (Paris) 28, 190–198 (1997).
[CrossRef]

E. Valero, J. A. Garcı́a, J. L. Nieves, J. Romero, “Measurements of sensitivity to simulated chromatic frequencies for normal and dichromatic observers,” J. Opt. (Paris) 29, 339–344 (1998).
[CrossRef]

J. Romero, J. L. Nieves, A. Garcı́a-Beltrán, E. Hita, “Analysis of color-vision models in the chromatic-frequency domain,” J. Opt. (Paris) 26, 9–15 (1995).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (8)

Opt. Photon. News (1)

P. Lennie, “Color vision,” Opt. Photon. News, August1991, pp. 10–16.

Proc. R. Soc. London Ser. B (2)

J. H. Van Hateren, “Spatial, temporal and spectral pre-processing for colour vision,” Proc. R. Soc. London Ser. B 251, 61–68 (1993).
[CrossRef]

V. Bonnardel, F. J. Varela, “A frequency view of colour: Measuring the human sensitivity to square-wave spectral power distribution,” Proc. R. Soc. London Ser. B 245, 165–171 (1991).
[CrossRef]

Vision Res. (4)

V. Bonnardel, H. Bellemare, J. D. Mollon, “Measurements of human sensitivity to comb-filtered spectra,” Vision Res. 36, 2713–2720 (1996).
[CrossRef] [PubMed]

V. Bonnardel, E. Valero, “Study of colour discrimination with comb-filtered spectra,” Vision Res. 41, 541–548 (2001).
[CrossRef] [PubMed]

J. Romero, J. L. Nieves, A. Garcı́a-Beltrán, “Human processing of colour information in the chromatic-frequency domain,” Vision Res. 35, 867–871 (1995).
[CrossRef] [PubMed]

H. B. Barlow, “What causes trichromacy? A theoretical analysis using comb-filtered spectra,” Vision Res. 22, 635–643 (1982).
[CrossRef] [PubMed]

Other (7)

V. Bonnardel, D. L. Ruderman, H. B. Barlow, “Fast determination of the spectral modulation sensitivity function: a comparison between trichromats and deuteranopes,” in Color Vision Deficiencies XIII, C. R. Cavonius, ed., Vol. 59 of Documenta Ophthalmology Proceedings Series (Kluwer Academic, Dordrecht, The Netherlands, 1997), pp. 415–424.
[CrossRef]

CIE Publ. 15.2, Colorimetry, 2nd ed. (Central Bureau of the CIE, Vienna, 1986), pp. 70–72.

G. Finlayson, “Spectral sharpening: what is it and why is it important?” in Proceedings of the First European Conference on Color in Graphics, Imaging and Vision (Society for Imaging Science and Technology, Springfield, Va., 2002), pp. 230–235.

National Institute of Standards and Technology (NIST), http://physics.nist.gov/Divisions/Div844/Newrad/abstracts/NadalPoster.htm .

R. Bracewell, The Fourier Transform and its Application (McGraw-Hill, New York, 1965).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).

F. H. Imai, M. R. Rosen, R. S. Berns, “Comparative study of metrics for spectral match quality,” in Proceedings of the First European Conference on Color in Graphics, Imaging and Vision (Society for Imaging Science and Technology, Springfield, Va., 2002), pp. 492–496.

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Figures (7)

Fig. 1
Fig. 1

Example of sinusoidal SPD for m=1, ϕ0=0, and f=1 c/300 nm (defined between 400 and 700 nm).

Fig. 2
Fig. 2

(a) SPDs of the fluorescent illuminants used: solid curve, F2; dashed curve, F7; dotted curve, F11; dotted-dashed curve, commercial fluorescent. (b) Two examples of daylight SPD and CIE illuminant A: solid curve, daylight 1; dashed curve, daylight 2; dotted curve, A.

Fig. 3
Fig. 3

(a) FFT of daylight SPD and parabolic filter of 0.02 c/nm: solid curve, SPD; dotted curve, parabolic filter. (b) Daylight SPD and three filtered signals obtained with a parabolic filter with three different cutoff frequencies: solid curve, original; dotted-dashed curve, f=0.04 c/nm; dotted curve, f=0.016c/nm; dashed curve, f=0.013 c/nm.

Fig. 4
Fig. 4

SPD of the illuminant F2 and three filtered signals obtained with a parabolic filter with three different cutoff frequencies: solid curve, original; dotted-dashed curve, f=0.04 c/nm; dashed curve, f=0.016 c/nm; dotted curve, f=0.013 c/nm.

Fig. 5
Fig. 5

Original (solid curve) and filtered (dashed curve) signals obtained with the SMSF filter: (a) daylight; upper panel, normalized SMSF filter (see Ref. 10); (b) F2 fluorescent; (c) illuminant A.

Fig. 6
Fig. 6

Normalized SMSF-filtered signals for object v142 (see Ref. 23) and five different illuminants: solid curve, daylight; long dashed, commercial fluorescent; short dashed, F1; heavy dotted-dashed, F10; light dotted-dashed, A.

Fig. 7
Fig. 7

Original and reconstructed daylight signals: (a) linear model of varying number of vectors, (b) Eq. (2) with different sampling intervals, (c) parabolic filter of three different cutoff frequencies.

Tables (7)

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Table 1 PSE below a Frequency Limit for Color Signals Corresponding to SPDs of the Different Illuminants a

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Table 2 CIELAB Color-Difference (ΔECIELAB) Values on Comparing Original and Filtered Color Signals by Use of Parabolic Filters with Different Cutoff Frequencies a

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Table 3 Mean Values of PSE below a Frequency Limit for 96 Biochrome Surfaces with Three Illuminants a

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Table 4 Mean Values of the PSE below a Frequency Limit for 74 Nonbiochrome Surfaces with Three Illuminants a

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Table 5 Mean CIELAB Color-Difference (ΔECIELAB) Values on Comparing Original and Filtered Color Signals by Use of Parabolic Filters with Different Cutoff Frequencies for 96 Biochrome Surfaces with Three Illuminants a

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Table 6 Mean CIELAB Color-Difference (ΔECIELAB) Values on Comparing Original and Filtered Color Signals by Use of Parabolic Filters with Different Cutoff Frequencies for 74 Nonbiochrome Surfaces with Three Illuminants a

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Table 7 PSE on Comparing Original and Filtered Color Signals by Use of SMSF Filter a

Equations (2)

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E(λ)=E0[1+m sin(2πfλ+ϕ0)],
E(λ)=n=0NEn+m2flsinc2flλ-n+m2fl,

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