Abstract

Recently developed rigorous theories have been used to investigate the diffraction efficiency behavior of both blazed and holographic gratings. In order to assist designers of spectrometric systems we have covered a complete range of blaze angles for triangular grooves and modulations for sinusoidal groove shape in first and second orders. Several types of mountings are included together with the role played by finite conductivity of aluminum. Useful classifications of both types of gratings are given, as they apply from the near uv to ir regions. Comparisons showing the close agreement between theory and experiment are presented.

© 1977 Optical Society of America

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References

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  1. W. C. Meecham, J. Appl. Phys. 27, 361 (1956).
    [CrossRef]
  2. G. W. Stroke, Rev. Opt. 39, 350 (1960).
  3. P. Bousquet, C. R. Acad. Sci. (Paris) 256, 3422 (1963).
  4. R. Petit, M. Cadilhac, C. R. Acad. Sci. (Paris) 259, 2077 (1964).
  5. A. Wirgin, C. R. Acad. Sci. (Paris) 259, 259 (1964).
  6. J. L. Uretsky, Ann. Phys. 33, 400 (1965).
    [CrossRef]
  7. J. Pavageau, J. Bousquet, Opt. Acta 17, 469 (1970).
    [CrossRef]
  8. D. Maystre, R. Petit, Opt. Commun. 4, 25 (1971); D. Maystre, R. Petit, Nouv. Rev. Opt. 2, 115 (1971).
    [CrossRef]
  9. R. McPhedran, M. Waterworth, Opt. Acta, 20, 177 (1973); R. McPhedran, I. Wilson, M. Waterworth, Opt. Commun. 7, 4 (1973).
    [CrossRef]
  10. M. Nevière, M. Cadilhac, Opt. Commun. 3, 349 (1971); IEEE Trans. Antennas Propag. AP-21, 37 (1973).
    [CrossRef]
  11. A. R. Neureuther, K. Zaki, Alta Freq. 38, 282 (1969).
  12. D. Maystre, Opt. Commun. 6, 50 (1972).
    [CrossRef]
  13. M. Nevière, P. Vincent, R. Petit, Nouv. Rev. Opt. 5, 65 (1974).
    [CrossRef]
  14. M. Nevière, R. Petit, M. Cadilhac, Opt. Commun. 8, 113 (1973).
    [CrossRef]
  15. E. Loewen, D. Maystre, R. McPhedran, I. Wilson, Jpn. J. Appl. Phys. 14, 143 (1975).
    [CrossRef]
  16. W. Liller, Appl. Opt. 2, 187 (1963).
    [CrossRef]
  17. R. Petit, Rev. Opt., 6, 249 (1966).
  18. J. Strong, Concepts of Classical Optics (W. H. Freeman, San Francisco, 1958).
  19. A. Marèchal, G. W. Stroke, C. R. Acad. Sci. (Paris) 249, 2032 (1959).
  20. R. N. Einhorn, Electron. Des. 2, 36 (1969).
  21. I. J. Wilson, L. C. Botten, R. C. McPhedran, Report DGRG 7611, U. Tasmania (1976).
  22. D. Maystre, R. Petit, J. Spectrosc. Soc. Jpn. 23, Suppl. 1, 61, (1974).
  23. D. Maystre, R. Petit, M. Duban, J. Gilewicz, Nouv. Rev. Opt. 5, 79 (1974).
    [CrossRef]
  24. G. Pieuchard, J. Flamand, Jpn. J. Appl. Phys. 14, 153 (1975).
    [CrossRef]
  25. M. C. Hutley, J. P. Verrill, R. C. McPhedran, M. Nevière, P. Vincent, Nouv Rev. Opt. 6, 87 (1975).
    [CrossRef]
  26. R. C. McPhedran, D. Maystre, J. Spectrosc. Soc. Jpn. 23, Suppl. 1, 13 (1974).

1975 (3)

E. Loewen, D. Maystre, R. McPhedran, I. Wilson, Jpn. J. Appl. Phys. 14, 143 (1975).
[CrossRef]

G. Pieuchard, J. Flamand, Jpn. J. Appl. Phys. 14, 153 (1975).
[CrossRef]

M. C. Hutley, J. P. Verrill, R. C. McPhedran, M. Nevière, P. Vincent, Nouv Rev. Opt. 6, 87 (1975).
[CrossRef]

1974 (4)

R. C. McPhedran, D. Maystre, J. Spectrosc. Soc. Jpn. 23, Suppl. 1, 13 (1974).

D. Maystre, R. Petit, J. Spectrosc. Soc. Jpn. 23, Suppl. 1, 61, (1974).

D. Maystre, R. Petit, M. Duban, J. Gilewicz, Nouv. Rev. Opt. 5, 79 (1974).
[CrossRef]

M. Nevière, P. Vincent, R. Petit, Nouv. Rev. Opt. 5, 65 (1974).
[CrossRef]

1973 (2)

M. Nevière, R. Petit, M. Cadilhac, Opt. Commun. 8, 113 (1973).
[CrossRef]

R. McPhedran, M. Waterworth, Opt. Acta, 20, 177 (1973); R. McPhedran, I. Wilson, M. Waterworth, Opt. Commun. 7, 4 (1973).
[CrossRef]

1972 (1)

D. Maystre, Opt. Commun. 6, 50 (1972).
[CrossRef]

1971 (2)

M. Nevière, M. Cadilhac, Opt. Commun. 3, 349 (1971); IEEE Trans. Antennas Propag. AP-21, 37 (1973).
[CrossRef]

D. Maystre, R. Petit, Opt. Commun. 4, 25 (1971); D. Maystre, R. Petit, Nouv. Rev. Opt. 2, 115 (1971).
[CrossRef]

1970 (1)

J. Pavageau, J. Bousquet, Opt. Acta 17, 469 (1970).
[CrossRef]

1969 (2)

A. R. Neureuther, K. Zaki, Alta Freq. 38, 282 (1969).

R. N. Einhorn, Electron. Des. 2, 36 (1969).

1966 (1)

R. Petit, Rev. Opt., 6, 249 (1966).

1965 (1)

J. L. Uretsky, Ann. Phys. 33, 400 (1965).
[CrossRef]

1964 (2)

R. Petit, M. Cadilhac, C. R. Acad. Sci. (Paris) 259, 2077 (1964).

A. Wirgin, C. R. Acad. Sci. (Paris) 259, 259 (1964).

1963 (2)

P. Bousquet, C. R. Acad. Sci. (Paris) 256, 3422 (1963).

W. Liller, Appl. Opt. 2, 187 (1963).
[CrossRef]

1960 (1)

G. W. Stroke, Rev. Opt. 39, 350 (1960).

1959 (1)

A. Marèchal, G. W. Stroke, C. R. Acad. Sci. (Paris) 249, 2032 (1959).

1956 (1)

W. C. Meecham, J. Appl. Phys. 27, 361 (1956).
[CrossRef]

Botten, L. C.

I. J. Wilson, L. C. Botten, R. C. McPhedran, Report DGRG 7611, U. Tasmania (1976).

Bousquet, J.

J. Pavageau, J. Bousquet, Opt. Acta 17, 469 (1970).
[CrossRef]

Bousquet, P.

P. Bousquet, C. R. Acad. Sci. (Paris) 256, 3422 (1963).

Cadilhac, M.

M. Nevière, R. Petit, M. Cadilhac, Opt. Commun. 8, 113 (1973).
[CrossRef]

M. Nevière, M. Cadilhac, Opt. Commun. 3, 349 (1971); IEEE Trans. Antennas Propag. AP-21, 37 (1973).
[CrossRef]

R. Petit, M. Cadilhac, C. R. Acad. Sci. (Paris) 259, 2077 (1964).

Duban, M.

D. Maystre, R. Petit, M. Duban, J. Gilewicz, Nouv. Rev. Opt. 5, 79 (1974).
[CrossRef]

Einhorn, R. N.

R. N. Einhorn, Electron. Des. 2, 36 (1969).

Flamand, J.

G. Pieuchard, J. Flamand, Jpn. J. Appl. Phys. 14, 153 (1975).
[CrossRef]

Gilewicz, J.

D. Maystre, R. Petit, M. Duban, J. Gilewicz, Nouv. Rev. Opt. 5, 79 (1974).
[CrossRef]

Hutley, M. C.

M. C. Hutley, J. P. Verrill, R. C. McPhedran, M. Nevière, P. Vincent, Nouv Rev. Opt. 6, 87 (1975).
[CrossRef]

Liller, W.

Loewen, E.

E. Loewen, D. Maystre, R. McPhedran, I. Wilson, Jpn. J. Appl. Phys. 14, 143 (1975).
[CrossRef]

Marèchal, A.

A. Marèchal, G. W. Stroke, C. R. Acad. Sci. (Paris) 249, 2032 (1959).

Maystre, D.

E. Loewen, D. Maystre, R. McPhedran, I. Wilson, Jpn. J. Appl. Phys. 14, 143 (1975).
[CrossRef]

D. Maystre, R. Petit, J. Spectrosc. Soc. Jpn. 23, Suppl. 1, 61, (1974).

R. C. McPhedran, D. Maystre, J. Spectrosc. Soc. Jpn. 23, Suppl. 1, 13 (1974).

D. Maystre, R. Petit, M. Duban, J. Gilewicz, Nouv. Rev. Opt. 5, 79 (1974).
[CrossRef]

D. Maystre, Opt. Commun. 6, 50 (1972).
[CrossRef]

D. Maystre, R. Petit, Opt. Commun. 4, 25 (1971); D. Maystre, R. Petit, Nouv. Rev. Opt. 2, 115 (1971).
[CrossRef]

McPhedran, R.

E. Loewen, D. Maystre, R. McPhedran, I. Wilson, Jpn. J. Appl. Phys. 14, 143 (1975).
[CrossRef]

R. McPhedran, M. Waterworth, Opt. Acta, 20, 177 (1973); R. McPhedran, I. Wilson, M. Waterworth, Opt. Commun. 7, 4 (1973).
[CrossRef]

McPhedran, R. C.

M. C. Hutley, J. P. Verrill, R. C. McPhedran, M. Nevière, P. Vincent, Nouv Rev. Opt. 6, 87 (1975).
[CrossRef]

R. C. McPhedran, D. Maystre, J. Spectrosc. Soc. Jpn. 23, Suppl. 1, 13 (1974).

I. J. Wilson, L. C. Botten, R. C. McPhedran, Report DGRG 7611, U. Tasmania (1976).

Meecham, W. C.

W. C. Meecham, J. Appl. Phys. 27, 361 (1956).
[CrossRef]

Neureuther, A. R.

A. R. Neureuther, K. Zaki, Alta Freq. 38, 282 (1969).

Nevière, M.

M. C. Hutley, J. P. Verrill, R. C. McPhedran, M. Nevière, P. Vincent, Nouv Rev. Opt. 6, 87 (1975).
[CrossRef]

M. Nevière, P. Vincent, R. Petit, Nouv. Rev. Opt. 5, 65 (1974).
[CrossRef]

M. Nevière, R. Petit, M. Cadilhac, Opt. Commun. 8, 113 (1973).
[CrossRef]

M. Nevière, M. Cadilhac, Opt. Commun. 3, 349 (1971); IEEE Trans. Antennas Propag. AP-21, 37 (1973).
[CrossRef]

Pavageau, J.

J. Pavageau, J. Bousquet, Opt. Acta 17, 469 (1970).
[CrossRef]

Petit, R.

D. Maystre, R. Petit, J. Spectrosc. Soc. Jpn. 23, Suppl. 1, 61, (1974).

M. Nevière, P. Vincent, R. Petit, Nouv. Rev. Opt. 5, 65 (1974).
[CrossRef]

D. Maystre, R. Petit, M. Duban, J. Gilewicz, Nouv. Rev. Opt. 5, 79 (1974).
[CrossRef]

M. Nevière, R. Petit, M. Cadilhac, Opt. Commun. 8, 113 (1973).
[CrossRef]

D. Maystre, R. Petit, Opt. Commun. 4, 25 (1971); D. Maystre, R. Petit, Nouv. Rev. Opt. 2, 115 (1971).
[CrossRef]

R. Petit, Rev. Opt., 6, 249 (1966).

R. Petit, M. Cadilhac, C. R. Acad. Sci. (Paris) 259, 2077 (1964).

Pieuchard, G.

G. Pieuchard, J. Flamand, Jpn. J. Appl. Phys. 14, 153 (1975).
[CrossRef]

Stroke, G. W.

G. W. Stroke, Rev. Opt. 39, 350 (1960).

A. Marèchal, G. W. Stroke, C. R. Acad. Sci. (Paris) 249, 2032 (1959).

Strong, J.

J. Strong, Concepts of Classical Optics (W. H. Freeman, San Francisco, 1958).

Uretsky, J. L.

J. L. Uretsky, Ann. Phys. 33, 400 (1965).
[CrossRef]

Verrill, J. P.

M. C. Hutley, J. P. Verrill, R. C. McPhedran, M. Nevière, P. Vincent, Nouv Rev. Opt. 6, 87 (1975).
[CrossRef]

Vincent, P.

M. C. Hutley, J. P. Verrill, R. C. McPhedran, M. Nevière, P. Vincent, Nouv Rev. Opt. 6, 87 (1975).
[CrossRef]

M. Nevière, P. Vincent, R. Petit, Nouv. Rev. Opt. 5, 65 (1974).
[CrossRef]

Waterworth, M.

R. McPhedran, M. Waterworth, Opt. Acta, 20, 177 (1973); R. McPhedran, I. Wilson, M. Waterworth, Opt. Commun. 7, 4 (1973).
[CrossRef]

Wilson, I.

E. Loewen, D. Maystre, R. McPhedran, I. Wilson, Jpn. J. Appl. Phys. 14, 143 (1975).
[CrossRef]

Wilson, I. J.

I. J. Wilson, L. C. Botten, R. C. McPhedran, Report DGRG 7611, U. Tasmania (1976).

Wirgin, A.

A. Wirgin, C. R. Acad. Sci. (Paris) 259, 259 (1964).

Zaki, K.

A. R. Neureuther, K. Zaki, Alta Freq. 38, 282 (1969).

Alta Freq. (1)

A. R. Neureuther, K. Zaki, Alta Freq. 38, 282 (1969).

Ann. Phys. (1)

J. L. Uretsky, Ann. Phys. 33, 400 (1965).
[CrossRef]

Appl. Opt. (1)

C. R. Acad. Sci. (Paris) (4)

P. Bousquet, C. R. Acad. Sci. (Paris) 256, 3422 (1963).

R. Petit, M. Cadilhac, C. R. Acad. Sci. (Paris) 259, 2077 (1964).

A. Wirgin, C. R. Acad. Sci. (Paris) 259, 259 (1964).

A. Marèchal, G. W. Stroke, C. R. Acad. Sci. (Paris) 249, 2032 (1959).

Electron. Des. (1)

R. N. Einhorn, Electron. Des. 2, 36 (1969).

J. Appl. Phys. (1)

W. C. Meecham, J. Appl. Phys. 27, 361 (1956).
[CrossRef]

J. Spectrosc. Soc. Jpn. (2)

R. C. McPhedran, D. Maystre, J. Spectrosc. Soc. Jpn. 23, Suppl. 1, 13 (1974).

D. Maystre, R. Petit, J. Spectrosc. Soc. Jpn. 23, Suppl. 1, 61, (1974).

Jpn. J. Appl. Phys. (2)

G. Pieuchard, J. Flamand, Jpn. J. Appl. Phys. 14, 153 (1975).
[CrossRef]

E. Loewen, D. Maystre, R. McPhedran, I. Wilson, Jpn. J. Appl. Phys. 14, 143 (1975).
[CrossRef]

Nouv Rev. Opt. (1)

M. C. Hutley, J. P. Verrill, R. C. McPhedran, M. Nevière, P. Vincent, Nouv Rev. Opt. 6, 87 (1975).
[CrossRef]

Nouv. Rev. Opt. (2)

D. Maystre, R. Petit, M. Duban, J. Gilewicz, Nouv. Rev. Opt. 5, 79 (1974).
[CrossRef]

M. Nevière, P. Vincent, R. Petit, Nouv. Rev. Opt. 5, 65 (1974).
[CrossRef]

Opt. Acta (2)

J. Pavageau, J. Bousquet, Opt. Acta 17, 469 (1970).
[CrossRef]

R. McPhedran, M. Waterworth, Opt. Acta, 20, 177 (1973); R. McPhedran, I. Wilson, M. Waterworth, Opt. Commun. 7, 4 (1973).
[CrossRef]

Opt. Commun. (4)

M. Nevière, M. Cadilhac, Opt. Commun. 3, 349 (1971); IEEE Trans. Antennas Propag. AP-21, 37 (1973).
[CrossRef]

D. Maystre, R. Petit, Opt. Commun. 4, 25 (1971); D. Maystre, R. Petit, Nouv. Rev. Opt. 2, 115 (1971).
[CrossRef]

M. Nevière, R. Petit, M. Cadilhac, Opt. Commun. 8, 113 (1973).
[CrossRef]

D. Maystre, Opt. Commun. 6, 50 (1972).
[CrossRef]

Rev. Opt. (2)

R. Petit, Rev. Opt., 6, 249 (1966).

G. W. Stroke, Rev. Opt. 39, 350 (1960).

Other (2)

J. Strong, Concepts of Classical Optics (W. H. Freeman, San Francisco, 1958).

I. J. Wilson, L. C. Botten, R. C. McPhedran, Report DGRG 7611, U. Tasmania (1976).

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Figures (49)

Fig. 1
Fig. 1

First order efficiency curves for a 2° blaze angle echelette grating and Littrow mounting in the case of infinite conductivity. Solid line, S plane; dashed line, P plane.

Fig. 2
Fig. 2

Same as Fig. 1, except θB = 9°.

Fig. 3
Fig. 3

Same as Fig. 1, except θB = 14°; the curve for unpolarized light is also given.

Fig. 4
Fig. 4

Same as Fig. 1, except θB = 19°.

Fig. 5
Fig. 5

Same as Fig. 1, except θB = 26.75°.

Fig. 6
Fig. 6

Same as Fig. 1, except θB = 46°.

Fig. 7
Fig. 7

First order efficiency curves for an 8° 38′ blaze angle echelette grating, perfectly conducting, used with 45° between incident and diffracted beams. Solid curve, S plane; dashed curve, P plane. The light lines give the results for Littrow mount as reference.

Fig. 8
Fig. 8

Same as Fig. 7 except θB = 21° 6′.

Fig. 9
Fig. 9

First order efficiency curves for a 26°45′ blaze angle echelette grating, perfectly conducting. Solid curve, S plane; dashed curve, P plane. Heavy lines 45 deviation between incident and diffracted beams, light lines 8° between beams.

Fig. 10
Fig. 10

Same as Fig. 9 with 46° blaze angle.

Fig. 11
Fig. 11

First order efficiency curves for a 5°10′ blaze angle 1200-groove/mm aluminum grating used in Littrow mount. Solid curve, S plane; dashed curve, P plane.

Fig. 12
Fig. 12

First order efficiency curves for a 26°45′ blaze angle, 1800-groove/mm aluminum grating, used in Littrow mount. Solid curve, S plane; dashed curve, P plane. For reference the infinite conductivity curves are shown lightly.

Fig. 13
Fig. 13

First order efficiency curve for a 10° blaze angle, 1200-groove/mm aluminum grating, 8° between incident and diffracted beams. Solid curve, S plane; dashed curve, P plane. For reference the infinite conductivity curves are shown lightly.

Fig. 14
Fig. 14

Same as Fig. 13 except 1800 grooves/mm.

Fig. 15
Fig. 15

Same as Fig. 12 except 8° deviation between incident and diffracted beams.

Fig. 16
Fig. 16

Same as Fig. 12 except 25° deviation between beams.

Fig. 17
Fig. 17

Same as Fig. 12 except 45° deviation between beams.

Fig. 18
Fig. 18

First order efficiency curves for a 17° 27′ blaze angle, 1200-groove/mm aluminum grating used with 8° deviation between incident and diffracted beams. Solid curves, S plane; dashed curve P plane. For reference the infinite conductivity curves are shown lightly.

Fig. 19
Fig. 19

Same as Fig. 18 except θB = 26° 45′.

Fig. 20
Fig. 20

Same as Fig. 18 except θB = 46° 4′.

Fig. 21
Fig. 21

First order efficiency curve for a perfectly conducting sinusoidal grating used in the scalar domain and Littrow mounting, h/d = 0.05. Solid curve, S plane; dashed curve, P plane.

Fig. 22
Fig. 22

First order efficiency curves for a perfectly conducting sinusoidal grating used in Littrow mount, h/d = 0.14. Solid curve, S plane; dashed curve, P plane.

Fig. 23
Fig. 23

Same as Fig. 22 except h/d = 0.29.

Fig. 24
Fig. 24

Same as Fig. 22 except h/d = 0.36.

Fig. 25
Fig. 25

Same as Fig. 22 except 45° deviation between incident and diffracted beams. Light lines are curves of Fig. 22 as reference.

Fig. 26
Fig. 26

First order efficiency curves for a perfectly conducting sinusoidal grating used with 45° deviations between beams, h/d = 0.25. Solid curve, S plane; dashed curve, P plane. Light lines are the same curve for Littrow mounting as reference.

Fig. 27
Fig. 27

Same as Fig. 26 except h/d = 0.36.

Fig. 28
Fig. 28

First order efficiency curves for a 1800-groove/mm sinusoidal grating with aluminum surface and Littrow mount; h/d = 0.14. Solid curves, S plane; dashed curves, P plane. For reference, light curves are for perfectly conducting surface.

Fig. 29
Fig. 29

Same as Fig. 28 except 8° deviation between beams.

Fig. 30
Fig. 30

Same as Fig. 28 except 45° deviation between beams.

Fig. 31
Fig. 31

First order efficiency curves for a 1800-groove/mm sinusoidal grating with aluminum surface, used with 8° deviation between incident and diffracted beams, h/d = 0.22. Solid curve S plane; dashed curves, P plane. The light curves show the efficiencies for infinite conductivity as reference.

Fig. 32
Fig. 32

Same as Fig. 31 except Littrow mount and h/d = 0.29.

Fig. 33
Fig. 33

Same as Fig. 31 except h/d = 0.29.

Fig. 34
Fig. 34

Same as Fig. 31 except 45° deviation between beams and h/d = 0.29.

Fig. 35
Fig. 35

Same as Fig. 31 except Littrow mount and h/d = 0.36.

Fig. 36
Fig. 36

Same as Fig. 31 except h/d = 0.36.

Fig. 37
Fig. 37

Same as Fig. 31 except 45° deviation between beams and h/d = 0.36.

Fig. 38
Fig. 38

Second order efficiency curves for a 10° blaze angle echelette grating perfectly conducting used with 8° deviation between incident and diffracted beams. Note that abscissa is plotted as mλ/d, where in this case m = 2. Solid curve, S plane; dashed curve, P plane.

Fig. 39
Fig. 39

Same as Fig. 38 for a sinusoidal grating with h/d = 0.14.

Fig. 40
Fig. 40

Same as Fig. 38 except blaze angle is 26° 45′.

Fig. 41
Fig. 41

Same as Fig. 38 but for a sinusoidal grating with h/d = 0.22.

Fig. 42
Fig. 42

Same as. Fig. 38 but for a sinusoidal grating with h/d = 0.36. Also shown in this case drawn lightly are the efficiencies for an aluminum surface and 1800/mm groove frequency together with the corresponding wavelengths.

Fig. 43
Fig. 43

Theoretical infinite conductivity curves for 26° 45′ blaze angle, 90° apex angle, 3.5° between incident and diffracted beams. Solid line, S plane; dashed line, P plane. Measured values of relative efficiency for a 150-groove/mm grating (●, S plane; ○, P-plane) over a wavelength range of 3.75–12.5 μm.

Fig. 44
Fig. 44

Comparison between theoretical and measured absolute efficiencies of a 1200-groove/mm aluminum grating, 26° 45′ blaze angle, 8° between incident and diffracted beams, 90° apex angle. Solid line, S plane; dashed line, P plane. Measured values: ●, S plane; ○, P plane. Wavelength scale added for reference.

Fig. 45
Fig. 45

Same as Fig. 44 except 1800 grooves/mm and apex angle taken as 105°, in accordance with electron micrograph.

Fig. 46
Fig. 46

Same as Fig. 45, except angular deviation between incident and diffracted beams 25°.

Fig. 47
Fig. 47

Same as Fig. 45 except angular deviation between beams 45°.

Fig. 48
Fig. 48

Comparison between Littrow efficiency curves calculated for perfectly conducting gratings with 26° 45′ blaze angle, 90° apex angle, 3.5° A.D., orders m = 1, 2,3, and measurements of relative efficiency of a 150/mm aluminum ruled grating of the same blaze angle. Points are shown, ●, ○, ▲ for orders 1, 2, 3, respectively. Note the curves are plotted against mλ/d: (a) in P plane; (b) in S plane.

Fig. 49
Fig. 49

Wavelengths for several standard gratings groove frequencies plotted with the same λ/d scale used throughout this paper. Copies can be used as overlays to convert the dimensionless scales to wavelength.

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