Abstract

Comparisons of theoretical calculations and experimental measurements of echelle grating efficiencies are given for R2 echelles used in three possible configurations: α > β; α < β; and the quasi-Littrow mode. The throughput-resolution products for these various cases are also compared.

© 1980 Optical Society of America

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References

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  1. D. J. Schroeder, Publ. Astron. Soc. Pac. 82, 1253 (1970).
    [CrossRef]
  2. D. J. Schroeder, Appl. Opt. 6, 1976 (1967).
    [CrossRef] [PubMed]
  3. D. J. Schroeder, Publ. Astron. Soc. Pac. 83, 438 (1971).
    [CrossRef]
  4. F. H. Chaffee, D. J. Schroeder, Ann. Rev. Astron. Astrophy. 14, 23 (1976).
    [CrossRef]
  5. W. M. Burton, N. K. Reay, Appl. Opt. 9, 1227 (1970).
    [CrossRef] [PubMed]
  6. R. L. Hilliard, SPIE Proc. 196, 172 (1979).
    [CrossRef]
  7. Diffraction Grating Handbook (Bausch & Lomb, Rochester, N.Y., 1970).
  8. D. J. Schroeder, Methods of Experimental Physics, Vol. 12, N. Carleton, Ed., (Academic, New York, 1974), Part A, pp. 463–489.
    [CrossRef]

1979 (1)

R. L. Hilliard, SPIE Proc. 196, 172 (1979).
[CrossRef]

1976 (1)

F. H. Chaffee, D. J. Schroeder, Ann. Rev. Astron. Astrophy. 14, 23 (1976).
[CrossRef]

1971 (1)

D. J. Schroeder, Publ. Astron. Soc. Pac. 83, 438 (1971).
[CrossRef]

1970 (2)

D. J. Schroeder, Publ. Astron. Soc. Pac. 82, 1253 (1970).
[CrossRef]

W. M. Burton, N. K. Reay, Appl. Opt. 9, 1227 (1970).
[CrossRef] [PubMed]

1967 (1)

Burton, W. M.

Chaffee, F. H.

F. H. Chaffee, D. J. Schroeder, Ann. Rev. Astron. Astrophy. 14, 23 (1976).
[CrossRef]

Hilliard, R. L.

R. L. Hilliard, SPIE Proc. 196, 172 (1979).
[CrossRef]

Reay, N. K.

Schroeder, D. J.

F. H. Chaffee, D. J. Schroeder, Ann. Rev. Astron. Astrophy. 14, 23 (1976).
[CrossRef]

D. J. Schroeder, Publ. Astron. Soc. Pac. 83, 438 (1971).
[CrossRef]

D. J. Schroeder, Publ. Astron. Soc. Pac. 82, 1253 (1970).
[CrossRef]

D. J. Schroeder, Appl. Opt. 6, 1976 (1967).
[CrossRef] [PubMed]

D. J. Schroeder, Methods of Experimental Physics, Vol. 12, N. Carleton, Ed., (Academic, New York, 1974), Part A, pp. 463–489.
[CrossRef]

Ann. Rev. Astron. Astrophy. (1)

F. H. Chaffee, D. J. Schroeder, Ann. Rev. Astron. Astrophy. 14, 23 (1976).
[CrossRef]

Appl. Opt. (2)

Publ. Astron. Soc. Pac. (2)

D. J. Schroeder, Publ. Astron. Soc. Pac. 82, 1253 (1970).
[CrossRef]

D. J. Schroeder, Publ. Astron. Soc. Pac. 83, 438 (1971).
[CrossRef]

SPIE Proc. (1)

R. L. Hilliard, SPIE Proc. 196, 172 (1979).
[CrossRef]

Other (2)

Diffraction Grating Handbook (Bausch & Lomb, Rochester, N.Y., 1970).

D. J. Schroeder, Methods of Experimental Physics, Vol. 12, N. Carleton, Ed., (Academic, New York, 1974), Part A, pp. 463–489.
[CrossRef]

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Figures (15)

Fig. 1
Fig. 1

(a) Local coordinate system for incident ray on echelle facet with z axis perpendicular to facet. N denotes the echelle normal, and σ is the groove spacing. (b) Range of diffracted light for light incident on narrow face of groove.

Fig. 2
Fig. 2

Orientation of incident beam relative to echelle normal for cases A and B.

Fig. 3
Fig. 3

Positions of interference maxima and blaze function for echelle with tanθB = 2.0, θ = 0, m ̅ = 40.

Fig. 4
Fig. 4

Calculated peak efficiencies for three values of m ̅ as a function of θ for case A orientation (upper figure).

Fig. 5
Fig. 5

Calculated peak efficiency for Littrow mode as function of m ̅ (lower figure).

Fig. 6
Fig. 6

Calculated peak efficiencies for cases A and B orientations with m ̅ = 40 and θB = 63.°435. Curve for case B labeled shadowed includes back reflection of incident light.

Fig. 7
Fig. 7

Calculated peak efficiencies for cases A and B orientations with m ̅ = 100 and θB = 63.°435. Back reflection is included in case B curve labeled shadowed.

Fig. 8
Fig. 8

Blaze functions for cases A (θ = 6°) and C (γ = 6°). Extent of free spectral range is indicated by double-headed arrow for each curve.

Fig. 9
Fig. 9

Apparatus used to obtain measurements of echelle efficiency: (a) grating oriented for case A; (b) for case C.

Fig. 10
Fig. 10

Measured efficiency curves in the 86th order of an echelle with 31.6 grooves/mm.

Fig. 11
Fig. 11

Peak efficiencies measured for echelle with 79 g/mm near λ6500 for m ̅ = 34 in each of three modes. Points for cases A and B are fitted with scaled curves taken from Fig. 6 and case C data with a straight line (upper figure).

Fig. 12
Fig. 12

Peak efficiencies measured for echelle with 31.6 grooves/mm near λ6500 for m ̅ = 86 in each of three modes. Data points are fitted with scaled curves taken from Fig. 7 and case C data with straight line (lower figure).

Fig. 13
Fig. 13

Throughput and throughput–resolution product for cases A and B with m ̅ = 40. Quantities are normalized to peak efficiency at θ = 0.

Fig. 14
Fig. 14

Throughput–resolution product for cases A and C with m ¯ = 40 [see text following Eq. (13) for discussion of effect of slit orientation on LR].

Fig. 15
Fig. 15

Throughput–resolution product across blaze functions for cases A (θ = 6°) and C (γ = 6°).

Tables (1)

Tables Icon

Table I Peak Efficiencies in Different Echelle Orientations

Equations (14)

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( m λ ) / σ = cos γ ( sin α + sin β ) ,
d β d λ = m σ cos γ cos β .
δ β = λ / ( σ cos γ cos β ̅ ) .
case A : α > β ̅ , γ = 0 ; case B : α < β ̅ , γ = 0 ; case C : α = θ B = β ̅ , γ 0 .
I ( δ ) = ( sin δ δ ) 2 ,
δ = 2 π λ s sin ( ψ 2 ) cos ( θ ψ 2 ) ,
sin β = sin β ̅ 2 ( Δ m m ̅ ) sin θ B cos θ .
R = λ / Δ λ = K 1 ( w ) 1 λ d β / d λ ,
L = K 2 w ,
w = rw ( f 2 / f 1 ) ,
L = K 3 w ( / r ) ,
L R = K ( / r ) λ d β / d λ ,
λ d β / d λ = 2 sin θ B cos θ / cos β ̅ .
tan χ = ( λ d β / d λ ) tan γ .

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