Abstract

We describe a new alexandrite laser source arrangement designed to measure atmospheric water vapor using the differential absorption lidar technique. This laser is capable of emitting two pulses at two appropriately selected wavelengths within a single flash lamp discharge. A narrow spectral linewidth of Δλ < 1 pm is obtained for each pulse by intracavity filtering with a birefringent filter and two Fabry–Perot interferometers. Wavelength commutation between the two pulses is performed by electro-optically tuning the birefringent filter. The temporal separation between the two pulses can be chosen between 50 and 70 μs and each pulse duration is <250-ns (full width at half-maximum). Typical output energies of 50 mJ/pulse at each wavelength are obtained with this laser system at a 10-Hz repetition rate for a 1.3-kW input electrical power.

© 1991 Optical Society of America

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References

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  1. R. M. Schotland, “Some observations of the vertical profile of water vapor by a laser optical radar,” in Proceedings of the Fourth International Symposium on Remote Sensing of the Environment (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1966), pp. 273 and 283.
  2. E. V. Browell, T. D. Wilkerson, T. J. McIrath, “Water vapor differential absorption lidar development and evaluation,” Appl. Opt. 18, 3474–3483 (1979).
    [CrossRef] [PubMed]
  3. J. C. Walling, “Tunable parametric-ions solid-state lasers,” in Tunable Lasers, L. F. Mollenauer, J. C. White, eds. (Springer-Verlag, New York, 1987), pp. 331–398.
  4. G. K. Schwemmer, M. Dombrovski, C. L. Korb, J. Milrod, H. Walden, R. H. Kagan, “A lidar for measuring atmospheric pressure and temperature,” Rev. Sci. Instrum. 58, 2226–2237 (1987).
    [CrossRef]
  5. BEST, Tropical System Energy Budget, Scientific objectives and preliminary definition of a satellite mission dedicated to GEWEX and GLOBAL CHANGE, CNES Publication (Centre National d'Etudes Spatiales, Paris, 1988).
  6. J. Pelon, G. Mégie, C. Loth, P. Flamant, “Narrow bandwidth Q-switch alexandrite laser for atmospheric applications,” Opt. Commun. 59, 213–218 (1986).
    [CrossRef]
  7. J. Pelon, P. Flamant, G. Mégie, M. Meissonnier, “The leandre Project: a French airborne lidar system for meteorological studies,” presented at the Fourteenth International Laser Radar Conference, San Candido, Italy.
  8. C. Cahen, G. Mégie, P. Flamant, “Lidar monitoring of the water vapor cycle in the troposphere,” J. Appl. Meteorol. 21, 1506–1515 (1982).
    [CrossRef]
  9. J. Bösenberg, “Measurements of the pressure shift of water vapor absorption lines by simultaneous photoacoustic spectroscopy,” Appl. Opt. 24, 3531–3536 (1985).
    [CrossRef] [PubMed]
  10. S. Ismail, E. V. Browell, “Airborne and spaceborne lidar measurements of water vapor profiles: a sensitivity analysis,” Appl. Opt. 28, 3603–3615 (1989).
    [CrossRef] [PubMed]
  11. G. Mégie, R. T. Menzies, “Complementarity of UV and IR differential absorption lidar for global measurements of atmospheric species,” Appl. Opt. 19, 1173–1182 (1980).
    [CrossRef] [PubMed]
  12. J.-Y. Mandin, J.-P. Chevillard, C. Camy-Peyret, J.-M. Flaud, “The high resolution spectrum of water vapor between 13200 and 16500 cm−1,” J. Mol. Spectrosc. 116, 167–190 (1986).
    [CrossRef]
  13. C. Cahen, B. E. Grossmann, J. L. Lesne, J. Benard, G. Leboudec, “Intensities and atmospheric broadening coefficients measured for O2 and H2O absorption lines selected for DIAL monitoring of both temperature and humidity. 2: H2O,” Appl. Opt. 25, 4268–4271 (1986).
    [CrossRef] [PubMed]
  14. B. E. Grossmann, E. V. Browell, “Spectroscopy of the water vapor in the 720 nm wavelength region: Line strengths, self induced pressure broadenings and temperature dependence of linewidths and shifts,” J. Mol. Spectrosc. 136, 264–294 (1989).
    [CrossRef]
  15. C. Cahen, “La vapeur d'eau dans l'atmosphère-mesures par absorption différentielle laser,” thèse (University of Paris VI, Paris, 1981).
  16. H. Cazeneuve, C. Loth, J. Pelon, “Development and modelisation of a dual impulsion alexandrite laser source for meteorological application,” presented at the Fourteenth International Laser Radar Conference, San Candido, Italy.
  17. U. N. Singh, P. H. Flamant, C. Cahen, G. Mégie, “Lidar water vapor measurements in the lower atmosphere,” presented at the Twelfth International Laser Radar Conference, Aix en Provence, France.
  18. H. Cazeneuve, “Etude theorique et experimentale de sources laser vibroniques appliquées à la mesure de variables météorologiques par lidar embarque,” thèse (Université Pierre et Marie Curie, Paris, Dec.1990).
  19. R. Chabbal, “Finesse limite d'un Fabry-Perot formé de lames imparfaites,” J. Phys. Radium 19, 295–299 (1958).
    [CrossRef]
  20. A. Kastler, “Atomes à l'intérieur d'un interféromètre Pérot-Fabry,” Appl. Opt. 1, 17–24 (1962).
    [CrossRef]
  21. L. Delbouille, G. Roland, L. Neven, “Atlas photométrique du spectre solaire de λ 3000 à λ 10000” (Institut Astrophysique de l'Université de Liège, Liège, Belgium, 1973).
  22. D. R. Preuss, J. L. Gole, “Three-stage birefringent filter tuning smoothly over the visible region: theoretical treatment and experimental design,” Appl. Opt. 19, 702–710 (1980).
    [CrossRef] [PubMed]
  23. O. Blanchard, “Conception et développement d'un mesureur de longueur d'onde haute résolution pour des expériences lidar embarquées sur avion,” Thèse (University of Paris VI, Paris, 1990).

1989 (2)

S. Ismail, E. V. Browell, “Airborne and spaceborne lidar measurements of water vapor profiles: a sensitivity analysis,” Appl. Opt. 28, 3603–3615 (1989).
[CrossRef] [PubMed]

B. E. Grossmann, E. V. Browell, “Spectroscopy of the water vapor in the 720 nm wavelength region: Line strengths, self induced pressure broadenings and temperature dependence of linewidths and shifts,” J. Mol. Spectrosc. 136, 264–294 (1989).
[CrossRef]

1987 (1)

G. K. Schwemmer, M. Dombrovski, C. L. Korb, J. Milrod, H. Walden, R. H. Kagan, “A lidar for measuring atmospheric pressure and temperature,” Rev. Sci. Instrum. 58, 2226–2237 (1987).
[CrossRef]

1986 (3)

J. Pelon, G. Mégie, C. Loth, P. Flamant, “Narrow bandwidth Q-switch alexandrite laser for atmospheric applications,” Opt. Commun. 59, 213–218 (1986).
[CrossRef]

J.-Y. Mandin, J.-P. Chevillard, C. Camy-Peyret, J.-M. Flaud, “The high resolution spectrum of water vapor between 13200 and 16500 cm−1,” J. Mol. Spectrosc. 116, 167–190 (1986).
[CrossRef]

C. Cahen, B. E. Grossmann, J. L. Lesne, J. Benard, G. Leboudec, “Intensities and atmospheric broadening coefficients measured for O2 and H2O absorption lines selected for DIAL monitoring of both temperature and humidity. 2: H2O,” Appl. Opt. 25, 4268–4271 (1986).
[CrossRef] [PubMed]

1985 (1)

1982 (1)

C. Cahen, G. Mégie, P. Flamant, “Lidar monitoring of the water vapor cycle in the troposphere,” J. Appl. Meteorol. 21, 1506–1515 (1982).
[CrossRef]

1980 (2)

1979 (1)

1962 (1)

1958 (1)

R. Chabbal, “Finesse limite d'un Fabry-Perot formé de lames imparfaites,” J. Phys. Radium 19, 295–299 (1958).
[CrossRef]

Benard, J.

Blanchard, O.

O. Blanchard, “Conception et développement d'un mesureur de longueur d'onde haute résolution pour des expériences lidar embarquées sur avion,” Thèse (University of Paris VI, Paris, 1990).

Bösenberg, J.

Browell, E. V.

S. Ismail, E. V. Browell, “Airborne and spaceborne lidar measurements of water vapor profiles: a sensitivity analysis,” Appl. Opt. 28, 3603–3615 (1989).
[CrossRef] [PubMed]

B. E. Grossmann, E. V. Browell, “Spectroscopy of the water vapor in the 720 nm wavelength region: Line strengths, self induced pressure broadenings and temperature dependence of linewidths and shifts,” J. Mol. Spectrosc. 136, 264–294 (1989).
[CrossRef]

E. V. Browell, T. D. Wilkerson, T. J. McIrath, “Water vapor differential absorption lidar development and evaluation,” Appl. Opt. 18, 3474–3483 (1979).
[CrossRef] [PubMed]

Cahen, C.

C. Cahen, B. E. Grossmann, J. L. Lesne, J. Benard, G. Leboudec, “Intensities and atmospheric broadening coefficients measured for O2 and H2O absorption lines selected for DIAL monitoring of both temperature and humidity. 2: H2O,” Appl. Opt. 25, 4268–4271 (1986).
[CrossRef] [PubMed]

C. Cahen, G. Mégie, P. Flamant, “Lidar monitoring of the water vapor cycle in the troposphere,” J. Appl. Meteorol. 21, 1506–1515 (1982).
[CrossRef]

C. Cahen, “La vapeur d'eau dans l'atmosphère-mesures par absorption différentielle laser,” thèse (University of Paris VI, Paris, 1981).

U. N. Singh, P. H. Flamant, C. Cahen, G. Mégie, “Lidar water vapor measurements in the lower atmosphere,” presented at the Twelfth International Laser Radar Conference, Aix en Provence, France.

Camy-Peyret, C.

J.-Y. Mandin, J.-P. Chevillard, C. Camy-Peyret, J.-M. Flaud, “The high resolution spectrum of water vapor between 13200 and 16500 cm−1,” J. Mol. Spectrosc. 116, 167–190 (1986).
[CrossRef]

Cazeneuve, H.

H. Cazeneuve, C. Loth, J. Pelon, “Development and modelisation of a dual impulsion alexandrite laser source for meteorological application,” presented at the Fourteenth International Laser Radar Conference, San Candido, Italy.

H. Cazeneuve, “Etude theorique et experimentale de sources laser vibroniques appliquées à la mesure de variables météorologiques par lidar embarque,” thèse (Université Pierre et Marie Curie, Paris, Dec.1990).

Chabbal, R.

R. Chabbal, “Finesse limite d'un Fabry-Perot formé de lames imparfaites,” J. Phys. Radium 19, 295–299 (1958).
[CrossRef]

Chevillard, J.-P.

J.-Y. Mandin, J.-P. Chevillard, C. Camy-Peyret, J.-M. Flaud, “The high resolution spectrum of water vapor between 13200 and 16500 cm−1,” J. Mol. Spectrosc. 116, 167–190 (1986).
[CrossRef]

Delbouille, L.

L. Delbouille, G. Roland, L. Neven, “Atlas photométrique du spectre solaire de λ 3000 à λ 10000” (Institut Astrophysique de l'Université de Liège, Liège, Belgium, 1973).

Dombrovski, M.

G. K. Schwemmer, M. Dombrovski, C. L. Korb, J. Milrod, H. Walden, R. H. Kagan, “A lidar for measuring atmospheric pressure and temperature,” Rev. Sci. Instrum. 58, 2226–2237 (1987).
[CrossRef]

Flamant, P.

J. Pelon, G. Mégie, C. Loth, P. Flamant, “Narrow bandwidth Q-switch alexandrite laser for atmospheric applications,” Opt. Commun. 59, 213–218 (1986).
[CrossRef]

C. Cahen, G. Mégie, P. Flamant, “Lidar monitoring of the water vapor cycle in the troposphere,” J. Appl. Meteorol. 21, 1506–1515 (1982).
[CrossRef]

J. Pelon, P. Flamant, G. Mégie, M. Meissonnier, “The leandre Project: a French airborne lidar system for meteorological studies,” presented at the Fourteenth International Laser Radar Conference, San Candido, Italy.

Flamant, P. H.

U. N. Singh, P. H. Flamant, C. Cahen, G. Mégie, “Lidar water vapor measurements in the lower atmosphere,” presented at the Twelfth International Laser Radar Conference, Aix en Provence, France.

Flaud, J.-M.

J.-Y. Mandin, J.-P. Chevillard, C. Camy-Peyret, J.-M. Flaud, “The high resolution spectrum of water vapor between 13200 and 16500 cm−1,” J. Mol. Spectrosc. 116, 167–190 (1986).
[CrossRef]

Gole, J. L.

Grossmann, B. E.

B. E. Grossmann, E. V. Browell, “Spectroscopy of the water vapor in the 720 nm wavelength region: Line strengths, self induced pressure broadenings and temperature dependence of linewidths and shifts,” J. Mol. Spectrosc. 136, 264–294 (1989).
[CrossRef]

C. Cahen, B. E. Grossmann, J. L. Lesne, J. Benard, G. Leboudec, “Intensities and atmospheric broadening coefficients measured for O2 and H2O absorption lines selected for DIAL monitoring of both temperature and humidity. 2: H2O,” Appl. Opt. 25, 4268–4271 (1986).
[CrossRef] [PubMed]

Ismail, S.

Kagan, R. H.

G. K. Schwemmer, M. Dombrovski, C. L. Korb, J. Milrod, H. Walden, R. H. Kagan, “A lidar for measuring atmospheric pressure and temperature,” Rev. Sci. Instrum. 58, 2226–2237 (1987).
[CrossRef]

Kastler, A.

Korb, C. L.

G. K. Schwemmer, M. Dombrovski, C. L. Korb, J. Milrod, H. Walden, R. H. Kagan, “A lidar for measuring atmospheric pressure and temperature,” Rev. Sci. Instrum. 58, 2226–2237 (1987).
[CrossRef]

Leboudec, G.

Lesne, J. L.

Loth, C.

J. Pelon, G. Mégie, C. Loth, P. Flamant, “Narrow bandwidth Q-switch alexandrite laser for atmospheric applications,” Opt. Commun. 59, 213–218 (1986).
[CrossRef]

H. Cazeneuve, C. Loth, J. Pelon, “Development and modelisation of a dual impulsion alexandrite laser source for meteorological application,” presented at the Fourteenth International Laser Radar Conference, San Candido, Italy.

Mandin, J.-Y.

J.-Y. Mandin, J.-P. Chevillard, C. Camy-Peyret, J.-M. Flaud, “The high resolution spectrum of water vapor between 13200 and 16500 cm−1,” J. Mol. Spectrosc. 116, 167–190 (1986).
[CrossRef]

McIrath, T. J.

Mégie, G.

J. Pelon, G. Mégie, C. Loth, P. Flamant, “Narrow bandwidth Q-switch alexandrite laser for atmospheric applications,” Opt. Commun. 59, 213–218 (1986).
[CrossRef]

C. Cahen, G. Mégie, P. Flamant, “Lidar monitoring of the water vapor cycle in the troposphere,” J. Appl. Meteorol. 21, 1506–1515 (1982).
[CrossRef]

G. Mégie, R. T. Menzies, “Complementarity of UV and IR differential absorption lidar for global measurements of atmospheric species,” Appl. Opt. 19, 1173–1182 (1980).
[CrossRef] [PubMed]

J. Pelon, P. Flamant, G. Mégie, M. Meissonnier, “The leandre Project: a French airborne lidar system for meteorological studies,” presented at the Fourteenth International Laser Radar Conference, San Candido, Italy.

U. N. Singh, P. H. Flamant, C. Cahen, G. Mégie, “Lidar water vapor measurements in the lower atmosphere,” presented at the Twelfth International Laser Radar Conference, Aix en Provence, France.

Meissonnier, M.

J. Pelon, P. Flamant, G. Mégie, M. Meissonnier, “The leandre Project: a French airborne lidar system for meteorological studies,” presented at the Fourteenth International Laser Radar Conference, San Candido, Italy.

Menzies, R. T.

Milrod, J.

G. K. Schwemmer, M. Dombrovski, C. L. Korb, J. Milrod, H. Walden, R. H. Kagan, “A lidar for measuring atmospheric pressure and temperature,” Rev. Sci. Instrum. 58, 2226–2237 (1987).
[CrossRef]

Neven, L.

L. Delbouille, G. Roland, L. Neven, “Atlas photométrique du spectre solaire de λ 3000 à λ 10000” (Institut Astrophysique de l'Université de Liège, Liège, Belgium, 1973).

Pelon, J.

J. Pelon, G. Mégie, C. Loth, P. Flamant, “Narrow bandwidth Q-switch alexandrite laser for atmospheric applications,” Opt. Commun. 59, 213–218 (1986).
[CrossRef]

J. Pelon, P. Flamant, G. Mégie, M. Meissonnier, “The leandre Project: a French airborne lidar system for meteorological studies,” presented at the Fourteenth International Laser Radar Conference, San Candido, Italy.

H. Cazeneuve, C. Loth, J. Pelon, “Development and modelisation of a dual impulsion alexandrite laser source for meteorological application,” presented at the Fourteenth International Laser Radar Conference, San Candido, Italy.

Preuss, D. R.

Roland, G.

L. Delbouille, G. Roland, L. Neven, “Atlas photométrique du spectre solaire de λ 3000 à λ 10000” (Institut Astrophysique de l'Université de Liège, Liège, Belgium, 1973).

Schotland, R. M.

R. M. Schotland, “Some observations of the vertical profile of water vapor by a laser optical radar,” in Proceedings of the Fourth International Symposium on Remote Sensing of the Environment (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1966), pp. 273 and 283.

Schwemmer, G. K.

G. K. Schwemmer, M. Dombrovski, C. L. Korb, J. Milrod, H. Walden, R. H. Kagan, “A lidar for measuring atmospheric pressure and temperature,” Rev. Sci. Instrum. 58, 2226–2237 (1987).
[CrossRef]

Singh, U. N.

U. N. Singh, P. H. Flamant, C. Cahen, G. Mégie, “Lidar water vapor measurements in the lower atmosphere,” presented at the Twelfth International Laser Radar Conference, Aix en Provence, France.

Walden, H.

G. K. Schwemmer, M. Dombrovski, C. L. Korb, J. Milrod, H. Walden, R. H. Kagan, “A lidar for measuring atmospheric pressure and temperature,” Rev. Sci. Instrum. 58, 2226–2237 (1987).
[CrossRef]

Walling, J. C.

J. C. Walling, “Tunable parametric-ions solid-state lasers,” in Tunable Lasers, L. F. Mollenauer, J. C. White, eds. (Springer-Verlag, New York, 1987), pp. 331–398.

Wilkerson, T. D.

Appl. Opt. (7)

J. Appl. Meteorol. (1)

C. Cahen, G. Mégie, P. Flamant, “Lidar monitoring of the water vapor cycle in the troposphere,” J. Appl. Meteorol. 21, 1506–1515 (1982).
[CrossRef]

J. Mol. Spectrosc. (2)

B. E. Grossmann, E. V. Browell, “Spectroscopy of the water vapor in the 720 nm wavelength region: Line strengths, self induced pressure broadenings and temperature dependence of linewidths and shifts,” J. Mol. Spectrosc. 136, 264–294 (1989).
[CrossRef]

J.-Y. Mandin, J.-P. Chevillard, C. Camy-Peyret, J.-M. Flaud, “The high resolution spectrum of water vapor between 13200 and 16500 cm−1,” J. Mol. Spectrosc. 116, 167–190 (1986).
[CrossRef]

J. Phys. Radium (1)

R. Chabbal, “Finesse limite d'un Fabry-Perot formé de lames imparfaites,” J. Phys. Radium 19, 295–299 (1958).
[CrossRef]

Opt. Commun. (1)

J. Pelon, G. Mégie, C. Loth, P. Flamant, “Narrow bandwidth Q-switch alexandrite laser for atmospheric applications,” Opt. Commun. 59, 213–218 (1986).
[CrossRef]

Rev. Sci. Instrum. (1)

G. K. Schwemmer, M. Dombrovski, C. L. Korb, J. Milrod, H. Walden, R. H. Kagan, “A lidar for measuring atmospheric pressure and temperature,” Rev. Sci. Instrum. 58, 2226–2237 (1987).
[CrossRef]

Other (10)

BEST, Tropical System Energy Budget, Scientific objectives and preliminary definition of a satellite mission dedicated to GEWEX and GLOBAL CHANGE, CNES Publication (Centre National d'Etudes Spatiales, Paris, 1988).

J. C. Walling, “Tunable parametric-ions solid-state lasers,” in Tunable Lasers, L. F. Mollenauer, J. C. White, eds. (Springer-Verlag, New York, 1987), pp. 331–398.

J. Pelon, P. Flamant, G. Mégie, M. Meissonnier, “The leandre Project: a French airborne lidar system for meteorological studies,” presented at the Fourteenth International Laser Radar Conference, San Candido, Italy.

R. M. Schotland, “Some observations of the vertical profile of water vapor by a laser optical radar,” in Proceedings of the Fourth International Symposium on Remote Sensing of the Environment (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1966), pp. 273 and 283.

C. Cahen, “La vapeur d'eau dans l'atmosphère-mesures par absorption différentielle laser,” thèse (University of Paris VI, Paris, 1981).

H. Cazeneuve, C. Loth, J. Pelon, “Development and modelisation of a dual impulsion alexandrite laser source for meteorological application,” presented at the Fourteenth International Laser Radar Conference, San Candido, Italy.

U. N. Singh, P. H. Flamant, C. Cahen, G. Mégie, “Lidar water vapor measurements in the lower atmosphere,” presented at the Twelfth International Laser Radar Conference, Aix en Provence, France.

H. Cazeneuve, “Etude theorique et experimentale de sources laser vibroniques appliquées à la mesure de variables météorologiques par lidar embarque,” thèse (Université Pierre et Marie Curie, Paris, Dec.1990).

O. Blanchard, “Conception et développement d'un mesureur de longueur d'onde haute résolution pour des expériences lidar embarquées sur avion,” Thèse (University of Paris VI, Paris, 1990).

L. Delbouille, G. Roland, L. Neven, “Atlas photométrique du spectre solaire de λ 3000 à λ 10000” (Institut Astrophysique de l'Université de Liège, Liège, Belgium, 1973).

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Figures (9)

Fig. 1
Fig. 1

Diagram of the double-pass spectral transmissions of the intracavity filters showing the adjacent transmission Tad requirement and FPI transmission coincidence (thickness ratio not taken into consideration).

Fig. 2
Fig. 2

Orientation of propagation vectors and the optical axis of a quartz plate element of the BRF. Laser emission is polarized along the b axis; θ is the Brewster angle; and φ is the BRF tuning angle

Fig. 3
Fig. 3

BRF selection: (a) maximum transmitted wavelength vs tuning angle φ and (b) double-pass spectral transmission for φ = 37.75°.

Fig. 4
Fig. 4

Double-pass spectral transmission of the BRF and PC for various continuous voltages (kV).

Fig. 5
Fig. 5

Evolution of the PC plus BRF transmission with voltage: (a) maximum transmission (continuous voltage). (b) Shift of the maximum transmitted wavelength: (1) is the calculated curve and ▲ represent experimental points for a continuous voltage; (2) is the calculated curve and ● represent experimental points for the 50-μs pulsed voltage.

Fig. 6
Fig. 6

Cavity arrangement.

Fig. 7
Fig. 7

Stability of pulse-to-pulse emitted energy: (a) at λon, (b) at λoff, and (c) of the total energy.

Fig. 8
Fig. 8

Spectral profiles recorded with the 25-mm Fizeau interferometer: (a) single shot at λon, (b) single shot at λoff, and (c) impulse response of the interferometer.

Fig. 9
Fig. 9

Short-term position accuracy at λon: (a) shot-to-shot spectral position record and (b) averaged spectral profile.

Tables (1)

Tables Icon

Table I Optimal Laser Source Parameters for DIAL Airborne Humidity Measurementsa

Equations (9)

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

I N ( λ ) = [ T 2 ( λ ) g ( λ ) T 2 ( λ 0 ) g ( λ 0 ) ] N for λ such as T 2 g > 1 ,
T ( λ ) = [ 1 + 4 R ( 1 R ) 2 sin 2 φ 2 ] 1 ,
φ 2 = 2 π λ n 1 e 1 cos θ 1 .
I N ( λ ) = T ( λ ) 2 N .
d λ = λ 2 π n 1 e 1 cos θ 1 * arcsin [ 1 R 2 R ( 2 1 / 2 N 1 ) 1 / 2 ] .
( n 1 e 1 cos θ 1 ) min = 7 mm .
n 2 e 2 cos θ 2 > arcsin ( m ad ) π n 1 e 1 cos θ 1 ,
m ad = { ( 1 R ) 2 4 R [ ( 1 T ad ) 1 / 2 1 ] } 1 / 2
n 2 e 2 cos θ 2 > ( n 1 e 1 cos θ 1 ) / 27 .

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