Abstract

A positive column He–Se+ laser with cataphoretic vapor transport can be employed as a three-color laser which emits two blue lines at 460.4 and 464.9 nm, a green line at 522.8 nm, and two red lines at 644.4 and 649 nm, if a special resonator is used. For these three colors and for three individual tubes with different diameters of the fused silica capillary measurements were performed of the TEM00 mode spot size in the capillary and of the output mirror transmission by which a maximum output power is obtained. A laser with long lifetime has been made which emits 4-mW power per color.

© 1986 Optical Society of America

Full Article  |  PDF Article

Corrections

Eberhard Schmidt, Juergen Mentel, and Karl-Heinz Krahn, "Three-color He–Se+ laser with optimized output power: erratum," Appl. Opt. 25, 2995-2995 (1986)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-25-17-2995

References

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  1. M. Richter, Einfuehrung in die Farbmetrik (Walter de Gruyter, Berlin, 1981);G. Wyszecki, W. S. Stiles, Color Science (Wiley, New York, 1967).
    [CrossRef]
  2. S. C. Wang, A. E. Siegman, “Hollow-Cathode Transverse Discharge He–Ne and He–Cd Lasers,” Appl. Phys. 2, 143 (1973).
    [CrossRef]
  3. M. Otaka, T. Oshima, M. Takeuchi, T. Oikawa, K. Fujii, “He–Cd White Light Laser by a Novel Tube Structure,” IEEE J. Quantum Electron. QE-17, 414 (1981).
    [CrossRef]
  4. K.-H. Wong, C. G. Morgan, “White Light Laser,” J. Phys. D 16, L1 (1983).
    [CrossRef]
  5. J. Mizeraczyk, M. Neiger, J. Steffen, “Comparison of He–Cd White-Light Laser Oscillations in Longitudinal and Transverse Hollow-Cathode Tubes,” IEEE J. Quantum Electron. QE-20, 1233 (1984).
    [CrossRef]
  6. K. G. Hernqvist, D. C. Pultorak, “Study of He–Se Laser Performance,” Rev. Sci. Instrum. 43, 290 (1972).
    [CrossRef]
  7. H.-P. Popp, E. Schmidt, “A White-Light He–Se Laser,” IEEE J. Quantum Electron. QE-15, 840 (1979).
    [CrossRef]
  8. W. T. Silfvast, M. B. Klein, “cw Laser Action on 24 Visible Wavelengths in Sell,” Appl. Phys. Lett. 17, 400 (1970).
    [CrossRef]
  9. T. Goto, H. Kano, S. Hattori, “Plasma Parameters in Gas Discharges for Positive Column HeSe-Lasers,” J. Appl. Phys. 43, 5064 (1972).
    [CrossRef]
  10. M. B. Klein, W. T. Silfvast, “New cw Laser Transitions in Sell,” Appl. Phys. Lett. 18, 482 (1971).
    [CrossRef]
  11. H.-P. Popp, E. Schmidt, M. Neiger, F. Pfeil, “Construction, Operation and Output Characteristics of a Small, Long-Life, Cataphoretic HeSe-Laser,” Opt. Laser Technol. 13, 321 (1981).
    [CrossRef]
  12. G. Roll, “Ein spektroskopisches Vielkanalsystem zur schnellen Messung optischer Verstärkungen in Entladungen,” Ph.D. thesis, Fakultaet für Elektrotechnik an der Ruhr-Universitaet Bochum (1984).
  13. T. Arai, A. Morikuri, T. Yabumoto, “Plasma Parameters in a Positive Column He–Se and He–I Laser Discharge,” Jpn. J. Appl. Phys. 15, 1153 (1976).
    [CrossRef]
  14. A. Ferrario, “Measurements of the Upper and Lower Level Lifetime in He–Se Lasers,” Opt. Commun. 8, 333 (1973).
    [CrossRef]
  15. J. Ebert, E. Schmidt, “Resonator-Spiegelanordnung fuer einen Laser,” Patentschrift DE 3007 271 C2 (1980).
  16. M. Neiger, H.-P. Popp, E. Schmidt, “Origin of Laser-Output Noise of Cataphoretic HeSe-Lasers,” Appl. Phys. B 28, 373 (1982).
    [CrossRef]
  17. A. E. Siegman, An Introduction to Lasers and Masers (McGraw-Hill, New York, 1971), Chap. 8-2.
  18. H.-P. Braendli, “Method for Measuring Small Optical Losses Using a He–Ne Laser,” Rev. Sci. Instrum. 39, 583 (1968).
    [CrossRef]
  19. H. P. Huber, G. Herzberg, Molecular Spectra and Molecular Structure: IV Constants of Diatomic Molecules (Van Nostrand-Reinhold, New York, 1979).
  20. B. Wellegehausen, A. Topouzkhanian, C. Effantin, J. D. Incan, “Optically Pumped Continuous Multiline Se2-Laser,” Opt. Commun. 41, 437 (1982).
    [CrossRef]

1984 (1)

J. Mizeraczyk, M. Neiger, J. Steffen, “Comparison of He–Cd White-Light Laser Oscillations in Longitudinal and Transverse Hollow-Cathode Tubes,” IEEE J. Quantum Electron. QE-20, 1233 (1984).
[CrossRef]

1983 (1)

K.-H. Wong, C. G. Morgan, “White Light Laser,” J. Phys. D 16, L1 (1983).
[CrossRef]

1982 (2)

M. Neiger, H.-P. Popp, E. Schmidt, “Origin of Laser-Output Noise of Cataphoretic HeSe-Lasers,” Appl. Phys. B 28, 373 (1982).
[CrossRef]

B. Wellegehausen, A. Topouzkhanian, C. Effantin, J. D. Incan, “Optically Pumped Continuous Multiline Se2-Laser,” Opt. Commun. 41, 437 (1982).
[CrossRef]

1981 (2)

H.-P. Popp, E. Schmidt, M. Neiger, F. Pfeil, “Construction, Operation and Output Characteristics of a Small, Long-Life, Cataphoretic HeSe-Laser,” Opt. Laser Technol. 13, 321 (1981).
[CrossRef]

M. Otaka, T. Oshima, M. Takeuchi, T. Oikawa, K. Fujii, “He–Cd White Light Laser by a Novel Tube Structure,” IEEE J. Quantum Electron. QE-17, 414 (1981).
[CrossRef]

1980 (1)

J. Ebert, E. Schmidt, “Resonator-Spiegelanordnung fuer einen Laser,” Patentschrift DE 3007 271 C2 (1980).

1979 (1)

H.-P. Popp, E. Schmidt, “A White-Light He–Se Laser,” IEEE J. Quantum Electron. QE-15, 840 (1979).
[CrossRef]

1976 (1)

T. Arai, A. Morikuri, T. Yabumoto, “Plasma Parameters in a Positive Column He–Se and He–I Laser Discharge,” Jpn. J. Appl. Phys. 15, 1153 (1976).
[CrossRef]

1973 (2)

A. Ferrario, “Measurements of the Upper and Lower Level Lifetime in He–Se Lasers,” Opt. Commun. 8, 333 (1973).
[CrossRef]

S. C. Wang, A. E. Siegman, “Hollow-Cathode Transverse Discharge He–Ne and He–Cd Lasers,” Appl. Phys. 2, 143 (1973).
[CrossRef]

1972 (2)

K. G. Hernqvist, D. C. Pultorak, “Study of He–Se Laser Performance,” Rev. Sci. Instrum. 43, 290 (1972).
[CrossRef]

T. Goto, H. Kano, S. Hattori, “Plasma Parameters in Gas Discharges for Positive Column HeSe-Lasers,” J. Appl. Phys. 43, 5064 (1972).
[CrossRef]

1971 (1)

M. B. Klein, W. T. Silfvast, “New cw Laser Transitions in Sell,” Appl. Phys. Lett. 18, 482 (1971).
[CrossRef]

1970 (1)

W. T. Silfvast, M. B. Klein, “cw Laser Action on 24 Visible Wavelengths in Sell,” Appl. Phys. Lett. 17, 400 (1970).
[CrossRef]

1968 (1)

H.-P. Braendli, “Method for Measuring Small Optical Losses Using a He–Ne Laser,” Rev. Sci. Instrum. 39, 583 (1968).
[CrossRef]

Arai, T.

T. Arai, A. Morikuri, T. Yabumoto, “Plasma Parameters in a Positive Column He–Se and He–I Laser Discharge,” Jpn. J. Appl. Phys. 15, 1153 (1976).
[CrossRef]

Braendli, H.-P.

H.-P. Braendli, “Method for Measuring Small Optical Losses Using a He–Ne Laser,” Rev. Sci. Instrum. 39, 583 (1968).
[CrossRef]

Ebert, J.

J. Ebert, E. Schmidt, “Resonator-Spiegelanordnung fuer einen Laser,” Patentschrift DE 3007 271 C2 (1980).

Effantin, C.

B. Wellegehausen, A. Topouzkhanian, C. Effantin, J. D. Incan, “Optically Pumped Continuous Multiline Se2-Laser,” Opt. Commun. 41, 437 (1982).
[CrossRef]

Ferrario, A.

A. Ferrario, “Measurements of the Upper and Lower Level Lifetime in He–Se Lasers,” Opt. Commun. 8, 333 (1973).
[CrossRef]

Fujii, K.

M. Otaka, T. Oshima, M. Takeuchi, T. Oikawa, K. Fujii, “He–Cd White Light Laser by a Novel Tube Structure,” IEEE J. Quantum Electron. QE-17, 414 (1981).
[CrossRef]

Goto, T.

T. Goto, H. Kano, S. Hattori, “Plasma Parameters in Gas Discharges for Positive Column HeSe-Lasers,” J. Appl. Phys. 43, 5064 (1972).
[CrossRef]

Hattori, S.

T. Goto, H. Kano, S. Hattori, “Plasma Parameters in Gas Discharges for Positive Column HeSe-Lasers,” J. Appl. Phys. 43, 5064 (1972).
[CrossRef]

Hernqvist, K. G.

K. G. Hernqvist, D. C. Pultorak, “Study of He–Se Laser Performance,” Rev. Sci. Instrum. 43, 290 (1972).
[CrossRef]

Herzberg, G.

H. P. Huber, G. Herzberg, Molecular Spectra and Molecular Structure: IV Constants of Diatomic Molecules (Van Nostrand-Reinhold, New York, 1979).

Huber, H. P.

H. P. Huber, G. Herzberg, Molecular Spectra and Molecular Structure: IV Constants of Diatomic Molecules (Van Nostrand-Reinhold, New York, 1979).

Incan, J. D.

B. Wellegehausen, A. Topouzkhanian, C. Effantin, J. D. Incan, “Optically Pumped Continuous Multiline Se2-Laser,” Opt. Commun. 41, 437 (1982).
[CrossRef]

Kano, H.

T. Goto, H. Kano, S. Hattori, “Plasma Parameters in Gas Discharges for Positive Column HeSe-Lasers,” J. Appl. Phys. 43, 5064 (1972).
[CrossRef]

Klein, M. B.

M. B. Klein, W. T. Silfvast, “New cw Laser Transitions in Sell,” Appl. Phys. Lett. 18, 482 (1971).
[CrossRef]

W. T. Silfvast, M. B. Klein, “cw Laser Action on 24 Visible Wavelengths in Sell,” Appl. Phys. Lett. 17, 400 (1970).
[CrossRef]

Mizeraczyk, J.

J. Mizeraczyk, M. Neiger, J. Steffen, “Comparison of He–Cd White-Light Laser Oscillations in Longitudinal and Transverse Hollow-Cathode Tubes,” IEEE J. Quantum Electron. QE-20, 1233 (1984).
[CrossRef]

Morgan, C. G.

K.-H. Wong, C. G. Morgan, “White Light Laser,” J. Phys. D 16, L1 (1983).
[CrossRef]

Morikuri, A.

T. Arai, A. Morikuri, T. Yabumoto, “Plasma Parameters in a Positive Column He–Se and He–I Laser Discharge,” Jpn. J. Appl. Phys. 15, 1153 (1976).
[CrossRef]

Neiger, M.

J. Mizeraczyk, M. Neiger, J. Steffen, “Comparison of He–Cd White-Light Laser Oscillations in Longitudinal and Transverse Hollow-Cathode Tubes,” IEEE J. Quantum Electron. QE-20, 1233 (1984).
[CrossRef]

M. Neiger, H.-P. Popp, E. Schmidt, “Origin of Laser-Output Noise of Cataphoretic HeSe-Lasers,” Appl. Phys. B 28, 373 (1982).
[CrossRef]

H.-P. Popp, E. Schmidt, M. Neiger, F. Pfeil, “Construction, Operation and Output Characteristics of a Small, Long-Life, Cataphoretic HeSe-Laser,” Opt. Laser Technol. 13, 321 (1981).
[CrossRef]

Oikawa, T.

M. Otaka, T. Oshima, M. Takeuchi, T. Oikawa, K. Fujii, “He–Cd White Light Laser by a Novel Tube Structure,” IEEE J. Quantum Electron. QE-17, 414 (1981).
[CrossRef]

Oshima, T.

M. Otaka, T. Oshima, M. Takeuchi, T. Oikawa, K. Fujii, “He–Cd White Light Laser by a Novel Tube Structure,” IEEE J. Quantum Electron. QE-17, 414 (1981).
[CrossRef]

Otaka, M.

M. Otaka, T. Oshima, M. Takeuchi, T. Oikawa, K. Fujii, “He–Cd White Light Laser by a Novel Tube Structure,” IEEE J. Quantum Electron. QE-17, 414 (1981).
[CrossRef]

Pfeil, F.

H.-P. Popp, E. Schmidt, M. Neiger, F. Pfeil, “Construction, Operation and Output Characteristics of a Small, Long-Life, Cataphoretic HeSe-Laser,” Opt. Laser Technol. 13, 321 (1981).
[CrossRef]

Popp, H.-P.

M. Neiger, H.-P. Popp, E. Schmidt, “Origin of Laser-Output Noise of Cataphoretic HeSe-Lasers,” Appl. Phys. B 28, 373 (1982).
[CrossRef]

H.-P. Popp, E. Schmidt, M. Neiger, F. Pfeil, “Construction, Operation and Output Characteristics of a Small, Long-Life, Cataphoretic HeSe-Laser,” Opt. Laser Technol. 13, 321 (1981).
[CrossRef]

H.-P. Popp, E. Schmidt, “A White-Light He–Se Laser,” IEEE J. Quantum Electron. QE-15, 840 (1979).
[CrossRef]

Pultorak, D. C.

K. G. Hernqvist, D. C. Pultorak, “Study of He–Se Laser Performance,” Rev. Sci. Instrum. 43, 290 (1972).
[CrossRef]

Richter, M.

M. Richter, Einfuehrung in die Farbmetrik (Walter de Gruyter, Berlin, 1981);G. Wyszecki, W. S. Stiles, Color Science (Wiley, New York, 1967).
[CrossRef]

Roll, G.

G. Roll, “Ein spektroskopisches Vielkanalsystem zur schnellen Messung optischer Verstärkungen in Entladungen,” Ph.D. thesis, Fakultaet für Elektrotechnik an der Ruhr-Universitaet Bochum (1984).

Schmidt, E.

M. Neiger, H.-P. Popp, E. Schmidt, “Origin of Laser-Output Noise of Cataphoretic HeSe-Lasers,” Appl. Phys. B 28, 373 (1982).
[CrossRef]

H.-P. Popp, E. Schmidt, M. Neiger, F. Pfeil, “Construction, Operation and Output Characteristics of a Small, Long-Life, Cataphoretic HeSe-Laser,” Opt. Laser Technol. 13, 321 (1981).
[CrossRef]

J. Ebert, E. Schmidt, “Resonator-Spiegelanordnung fuer einen Laser,” Patentschrift DE 3007 271 C2 (1980).

H.-P. Popp, E. Schmidt, “A White-Light He–Se Laser,” IEEE J. Quantum Electron. QE-15, 840 (1979).
[CrossRef]

Siegman, A. E.

S. C. Wang, A. E. Siegman, “Hollow-Cathode Transverse Discharge He–Ne and He–Cd Lasers,” Appl. Phys. 2, 143 (1973).
[CrossRef]

A. E. Siegman, An Introduction to Lasers and Masers (McGraw-Hill, New York, 1971), Chap. 8-2.

Silfvast, W. T.

M. B. Klein, W. T. Silfvast, “New cw Laser Transitions in Sell,” Appl. Phys. Lett. 18, 482 (1971).
[CrossRef]

W. T. Silfvast, M. B. Klein, “cw Laser Action on 24 Visible Wavelengths in Sell,” Appl. Phys. Lett. 17, 400 (1970).
[CrossRef]

Steffen, J.

J. Mizeraczyk, M. Neiger, J. Steffen, “Comparison of He–Cd White-Light Laser Oscillations in Longitudinal and Transverse Hollow-Cathode Tubes,” IEEE J. Quantum Electron. QE-20, 1233 (1984).
[CrossRef]

Takeuchi, M.

M. Otaka, T. Oshima, M. Takeuchi, T. Oikawa, K. Fujii, “He–Cd White Light Laser by a Novel Tube Structure,” IEEE J. Quantum Electron. QE-17, 414 (1981).
[CrossRef]

Topouzkhanian, A.

B. Wellegehausen, A. Topouzkhanian, C. Effantin, J. D. Incan, “Optically Pumped Continuous Multiline Se2-Laser,” Opt. Commun. 41, 437 (1982).
[CrossRef]

Wang, S. C.

S. C. Wang, A. E. Siegman, “Hollow-Cathode Transverse Discharge He–Ne and He–Cd Lasers,” Appl. Phys. 2, 143 (1973).
[CrossRef]

Wellegehausen, B.

B. Wellegehausen, A. Topouzkhanian, C. Effantin, J. D. Incan, “Optically Pumped Continuous Multiline Se2-Laser,” Opt. Commun. 41, 437 (1982).
[CrossRef]

Wong, K.-H.

K.-H. Wong, C. G. Morgan, “White Light Laser,” J. Phys. D 16, L1 (1983).
[CrossRef]

Yabumoto, T.

T. Arai, A. Morikuri, T. Yabumoto, “Plasma Parameters in a Positive Column He–Se and He–I Laser Discharge,” Jpn. J. Appl. Phys. 15, 1153 (1976).
[CrossRef]

Appl. Phys. (1)

S. C. Wang, A. E. Siegman, “Hollow-Cathode Transverse Discharge He–Ne and He–Cd Lasers,” Appl. Phys. 2, 143 (1973).
[CrossRef]

Appl. Phys. B (1)

M. Neiger, H.-P. Popp, E. Schmidt, “Origin of Laser-Output Noise of Cataphoretic HeSe-Lasers,” Appl. Phys. B 28, 373 (1982).
[CrossRef]

Appl. Phys. Lett. (2)

M. B. Klein, W. T. Silfvast, “New cw Laser Transitions in Sell,” Appl. Phys. Lett. 18, 482 (1971).
[CrossRef]

W. T. Silfvast, M. B. Klein, “cw Laser Action on 24 Visible Wavelengths in Sell,” Appl. Phys. Lett. 17, 400 (1970).
[CrossRef]

IEEE J. Quantum Electron. (3)

H.-P. Popp, E. Schmidt, “A White-Light He–Se Laser,” IEEE J. Quantum Electron. QE-15, 840 (1979).
[CrossRef]

M. Otaka, T. Oshima, M. Takeuchi, T. Oikawa, K. Fujii, “He–Cd White Light Laser by a Novel Tube Structure,” IEEE J. Quantum Electron. QE-17, 414 (1981).
[CrossRef]

J. Mizeraczyk, M. Neiger, J. Steffen, “Comparison of He–Cd White-Light Laser Oscillations in Longitudinal and Transverse Hollow-Cathode Tubes,” IEEE J. Quantum Electron. QE-20, 1233 (1984).
[CrossRef]

J. Appl. Phys. (1)

T. Goto, H. Kano, S. Hattori, “Plasma Parameters in Gas Discharges for Positive Column HeSe-Lasers,” J. Appl. Phys. 43, 5064 (1972).
[CrossRef]

J. Phys. D (1)

K.-H. Wong, C. G. Morgan, “White Light Laser,” J. Phys. D 16, L1 (1983).
[CrossRef]

Jpn. J. Appl. Phys. (1)

T. Arai, A. Morikuri, T. Yabumoto, “Plasma Parameters in a Positive Column He–Se and He–I Laser Discharge,” Jpn. J. Appl. Phys. 15, 1153 (1976).
[CrossRef]

Opt. Commun. (2)

A. Ferrario, “Measurements of the Upper and Lower Level Lifetime in He–Se Lasers,” Opt. Commun. 8, 333 (1973).
[CrossRef]

B. Wellegehausen, A. Topouzkhanian, C. Effantin, J. D. Incan, “Optically Pumped Continuous Multiline Se2-Laser,” Opt. Commun. 41, 437 (1982).
[CrossRef]

Opt. Laser Technol. (1)

H.-P. Popp, E. Schmidt, M. Neiger, F. Pfeil, “Construction, Operation and Output Characteristics of a Small, Long-Life, Cataphoretic HeSe-Laser,” Opt. Laser Technol. 13, 321 (1981).
[CrossRef]

Patentschrift DE 3007 271 C2 (1)

J. Ebert, E. Schmidt, “Resonator-Spiegelanordnung fuer einen Laser,” Patentschrift DE 3007 271 C2 (1980).

Rev. Sci. Instrum. (2)

H.-P. Braendli, “Method for Measuring Small Optical Losses Using a He–Ne Laser,” Rev. Sci. Instrum. 39, 583 (1968).
[CrossRef]

K. G. Hernqvist, D. C. Pultorak, “Study of He–Se Laser Performance,” Rev. Sci. Instrum. 43, 290 (1972).
[CrossRef]

Other (4)

M. Richter, Einfuehrung in die Farbmetrik (Walter de Gruyter, Berlin, 1981);G. Wyszecki, W. S. Stiles, Color Science (Wiley, New York, 1967).
[CrossRef]

H. P. Huber, G. Herzberg, Molecular Spectra and Molecular Structure: IV Constants of Diatomic Molecules (Van Nostrand-Reinhold, New York, 1979).

A. E. Siegman, An Introduction to Lasers and Masers (McGraw-Hill, New York, 1971), Chap. 8-2.

G. Roll, “Ein spektroskopisches Vielkanalsystem zur schnellen Messung optischer Verstärkungen in Entladungen,” Ph.D. thesis, Fakultaet für Elektrotechnik an der Ruhr-Universitaet Bochum (1984).

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Figures (6)

Fig. 1
Fig. 1

Double resonator for the He–Se+ three-color laser with output mirror M1, intermediate mirror M2, and back mirror M3. The Pellin-Broca prism P is cut under the Brewster, angle.

Fig. 2
Fig. 2

He–Se+ laser tube with a fused silica capillary and a double-walled water-cooling glass mantle.

Fig. 3
Fig. 3

Laser output P of a resonator formed by mirrors with R1 = R2 = 2 m dependent on mirror distance Lm for a tube with Lc = 500 mm; d = 1.3 mm (tube I).

Fig. 4
Fig. 4

Laser output P of a resonator formed by mirrors with R1 = R2 = 2 m dependent on coupling T for a tube with Lc = 500 mm; d = 1.3 mm (tube I).

Fig. 5
Fig. 5

Transmission of intermediate mirror M2 dependent on wavelength λ.

Fig. 6
Fig. 6

Transmission of output mirror M1 dependent on wavelength λ.

Tables (5)

Tables Icon

Table I Parameters of the Investigated Laser Tubes

Tables Icon

Table II Ratio of Tube Radius to Spot Size k

Tables Icon

Table III Data of the Output Coupling Curves

Tables Icon

Table IV Parameters of the TEM00 Mode In Tube II

Tables Icon

Table V Color Matching Functions of a Three-Color He–Se+ Laser

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

Δ ν h = 1 2 π ( 1 τ lower + 1 τ upper ) > 100 MHz ,
w 0 2 = w e 2 / 2 [ 1 ± 1 λ L c π w e 2 ] .
R min = 2 π λ w 0 2 .
z m = R / 2 [ 1 ± 1 ( R min / R ) 2 ] .
R L t 2 + ( π w 0 2 λ ) 2 2 L t ;
d 2 kw e 2 k λ L c π
Δ ν = c 2 L m < 150 MHz Δ ν D = 1.75 GHz .
R opt = z m + ( R min 2 ) 2 1 z m .
1 R o = n 1 R 2 + 1 R i .
λ π w 2 = 1 R i R i z m z m = 1 R o R o z 0 z 0 .
R o min = 2 ( R o z 0 ) z 0
0.46 μ m T = 1.5 2 % 0.52 μ m T = 5 8 % , 0.65 μ m T = 1.0 1.1 % .
P r : P g : P b = | x x ̅ g x ̅ b y y ̅ g y ̅ b z z ̅ g z ̅ b | : | x ̅ r x x ̅ b y ̅ r y y ̅ b z ̅ r z z ̅ b | : | x ̅ r x ̅ g x y ̅ r y ̅ g y z ̅ r z ̅ g z | ,
P opt c l 1 ( mW m 1 )
x ̅
y ̅
z ̅

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