Abstract

It was first shown by Pierre Connes (1956) that the resolution–luminosity product of a Michelson spectrometer could be substantially improved by the technique of field compensation. In the present paper various systems of field compensation are discussed, and an account is given of the tolerances allowed in their operation, together with their areas of usefulness.

© 1972 Optical Society of America

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References

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  1. P. Jacquinot, J. Opt. Soc. Am. 44, 761 (1954).
    [CrossRef]
  2. L. Mertz, Transforms in Optics (Wiley, New York, 1965), p. 18.
  3. P. Bouchareine, P. Connes, J. Phys. Rad. 24, 134 (1963).
  4. P. Bouchareine, Thesis, Université de Paris (1962).
  5. P. Connes, Rev. Opt. 35, 37 (1956).
  6. M. Cuisenier, J. Pinard, J. Phys. 28,C2, 97 (1967).
  7. L. Mertz, J. Opt. Soc. Am. 57, advertisement Feb. (1967).
  8. J. F. James, R. S. Sternberg, J. Phys. E. 1, 972 (1968).
  9. G. C. Shepherd, Center for Experimental Space Science, York University, Toronto, private communication.
  10. The Abbe number is defined to be (nd− 1)/(nf− nc) = (n− 1)/δn.
  11. R. S. Sternberg, J. F. James, J. Sci. Instrum. 41, 225 (1964).
    [CrossRef]
  12. R. L. Hillard, G. C. Shepherd, J. Opt. Soc. Am. 56, 362 (1966).
    [CrossRef]
  13. L. Duboin, private communication.
  14. G. W. Stroke, J. Opt. Soc. Am. 47, 1097 (1957).
    [CrossRef]
  15. J. W. Cooley, J. W. Tukey, Math. Comput. 19, 297 (1965).
    [CrossRef]

1968 (1)

J. F. James, R. S. Sternberg, J. Phys. E. 1, 972 (1968).

1967 (2)

M. Cuisenier, J. Pinard, J. Phys. 28,C2, 97 (1967).

L. Mertz, J. Opt. Soc. Am. 57, advertisement Feb. (1967).

1966 (1)

1965 (1)

J. W. Cooley, J. W. Tukey, Math. Comput. 19, 297 (1965).
[CrossRef]

1964 (1)

R. S. Sternberg, J. F. James, J. Sci. Instrum. 41, 225 (1964).
[CrossRef]

1963 (1)

P. Bouchareine, P. Connes, J. Phys. Rad. 24, 134 (1963).

1957 (1)

1956 (1)

P. Connes, Rev. Opt. 35, 37 (1956).

1954 (1)

Bouchareine, P.

P. Bouchareine, P. Connes, J. Phys. Rad. 24, 134 (1963).

P. Bouchareine, Thesis, Université de Paris (1962).

Connes, P.

P. Bouchareine, P. Connes, J. Phys. Rad. 24, 134 (1963).

P. Connes, Rev. Opt. 35, 37 (1956).

Cooley, J. W.

J. W. Cooley, J. W. Tukey, Math. Comput. 19, 297 (1965).
[CrossRef]

Cuisenier, M.

M. Cuisenier, J. Pinard, J. Phys. 28,C2, 97 (1967).

Duboin, L.

L. Duboin, private communication.

Hillard, R. L.

Jacquinot, P.

James, J. F.

J. F. James, R. S. Sternberg, J. Phys. E. 1, 972 (1968).

R. S. Sternberg, J. F. James, J. Sci. Instrum. 41, 225 (1964).
[CrossRef]

Mertz, L.

L. Mertz, J. Opt. Soc. Am. 57, advertisement Feb. (1967).

L. Mertz, Transforms in Optics (Wiley, New York, 1965), p. 18.

Pinard, J.

M. Cuisenier, J. Pinard, J. Phys. 28,C2, 97 (1967).

Shepherd, G. C.

R. L. Hillard, G. C. Shepherd, J. Opt. Soc. Am. 56, 362 (1966).
[CrossRef]

G. C. Shepherd, Center for Experimental Space Science, York University, Toronto, private communication.

Sternberg, R. S.

J. F. James, R. S. Sternberg, J. Phys. E. 1, 972 (1968).

R. S. Sternberg, J. F. James, J. Sci. Instrum. 41, 225 (1964).
[CrossRef]

Stroke, G. W.

Tukey, J. W.

J. W. Cooley, J. W. Tukey, Math. Comput. 19, 297 (1965).
[CrossRef]

J. Opt. Soc. Am. (4)

J. Phys. (1)

M. Cuisenier, J. Pinard, J. Phys. 28,C2, 97 (1967).

J. Phys. E. (1)

J. F. James, R. S. Sternberg, J. Phys. E. 1, 972 (1968).

J. Phys. Rad. (1)

P. Bouchareine, P. Connes, J. Phys. Rad. 24, 134 (1963).

J. Sci. Instrum. (1)

R. S. Sternberg, J. F. James, J. Sci. Instrum. 41, 225 (1964).
[CrossRef]

Math. Comput. (1)

J. W. Cooley, J. W. Tukey, Math. Comput. 19, 297 (1965).
[CrossRef]

Rev. Opt. (1)

P. Connes, Rev. Opt. 35, 37 (1956).

Other (5)

L. Duboin, private communication.

P. Bouchareine, Thesis, Université de Paris (1962).

L. Mertz, Transforms in Optics (Wiley, New York, 1965), p. 18.

G. C. Shepherd, Center for Experimental Space Science, York University, Toronto, private communication.

The Abbe number is defined to be (nd− 1)/(nf− nc) = (n− 1)/δn.

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Figures (14)

Fig. 1
Fig. 1

Resolution–luminosity products of spectrometers with common aperture 1/(2π) cm2. The curve for the field-compensated Michelson is conservative. (A) Grating. (B) Classical Michelson. (C) Field-compensated Michelson. (D) Spherical Fabry-Perot.

Fig. 2
Fig. 2

Partial removal of spherical aberration: (A) classical Michelson; (B) total removal of the i2 term; (C) removal of all terms at i ≐ 8.5° by changing the ratio of displacements by 1%.

Fig. 3
Fig. 3

Mertz’s first system. The plane parallel glass block is to give a large field at zero path difference, since the two wedge prisms cannot be reduced to zero thickness.

Fig. 4
Fig. 4

Ray trace for Mertz’s first system.

Fig. 5
Fig. 5

Connes’s afocal system.

Fig. 6
Fig. 6

Mertz’s second system.

Fig. 7
Fig. 7

Gas pressure system.

Fig. 8
Fig. 8

Shepherd’s systems.

Fig. 9
Fig. 9

The four-prism systems.

Fig. 10
Fig. 10

Bouchareine and Connes’s system.

Fig. 11
Fig. 11

The modified tilting interferometer.

Fig. 12
Fig. 12

The two-mirror prism system.

Fig. 13
Fig. 13

Modification of the two-mirror prism system.

Fig. 14
Fig. 14

Effect on a computed monochromatic line spectrum of an error in synchronization, well removed from the central maximum, with triangular apodization. The height of the main maximum is a 3 × 106.

Tables (2)

Tables Icon

Table I Properties of the Four-Prism Systems

Tables Icon

Table II Comparison of Field Compensation Systems

Equations (40)

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Δ = 2 D [ 1 ( i 2 / 2 ! ) + ( i 4 / 4 ! ) ] .
Δ = n A B + B C + C D + n D H A G G K K L L I I F ,
2 [ e ( n cos r cos i ) + D cos i ] .
D = e [ ( n 1 ) / n ] , Δ 0 = 2 [ e ( n 1 ) + D ] ,
Δ = Δ 0 [ 1 + ( i 4 / 8 n 2 ) ] .
Δ = Δ 0 [ 1 + n δ n n 2 1 + δ n i 2 2 n ( n 2 1 ) ] .
l 1 l 2 = Δ / 2 { [ n ( 1 / n ) ] } ,
Δ = 2 d cos i cos α 2 d n cos r sin α ,
Δ = 2 d cos β cos i + 2 d sin β ( n cos r cos i ) ,
tan β = n / ( n 1 ) , β 80 ° ,
Δ = 2 x [ ( n a cos r a cos i ) sin α ( n b cos r b cos i ) sin β ] .
sin i / sin r a , b = n a , b .
sin α / sin β = [ n a ( n b 1 ) ] / [ n b ( n a 1 ) ] .
cos i = 1 ( i 2 / 2 ! ) + ( i 4 / 4 ! ) , cos r a , b = 1 i 2 2 n 2 a , b + i 4 2 n 2 a , b ( 1 3 1 4 n 2 a , b ) ,
Δ 0 i 4 8 · ( n a + 1 ) / n a 2 ( n b + 1 ) / n b 2 n a n b .
Δ = Δ 0 n a , b δ n a , b + ( x i 2 { [ ( 1 ( 1 / n a ) ] sin α [ 1 ( 1 / n b ) ] sin β } ) δ n a , b n a , b .
x i 2 ( { [ 1 ( 1 / n α ) ] sin α } δ n a n a { [ 1 ( 1 / n b ) ] sin β } δ n b n b ) ,
( / n a , b ) [ 1 ( 1 / n a , b ) ] = ( 1 / n 2 a , b )
= Δ 0 i 2 2 { δ n a / [ n a ( n a 1 ) ] δ n b / [ n b ( n b 1 ) ] n a n b } ,
y + l a n a l b n b = 0 , y + l a / n a l b / n b = 0 ,
y : l a : l b = 1 : n b 2 n a 2 n a ( n b 2 1 ) : n a 2 n b 2 n b ( n a 2 1 ) ,
Δ = 2 D cos i ,
Δ = 2 ( D D 0 ) cos i ,
I = 4 a 2 cos 2 ( i / 2 ) = 2 a 2 ( 1 + cos i ) ,
F = 16 π a 2 0 R max cos 2 ( i / 2 ) R d R ,
F = 4 π a 2 R max { 1 + sin [ ( π Δ / 2 λ ) i max 2 ] ( π Δ / 2 λ ) i max 2 · cos [ π Δ ( 1 i max 2 / 4 ) λ / 2 ] } .
Δ = 2 e ( n cos r cos i ) + 2 D cos i .
cos i = 1 ( i 2 / 2 ! ) + ( i 4 / 4 ! ) , cos r = 1 ( i 2 / 2 n 2 ) + ( i 4 / 2 n 2 ) [ ( 1 / 3 ) ( 1 / 4 n 2 ) ] ,
Δ = 2 { n ( e + δ e ) [ 1 i 2 2 n 2 + i 4 2 n 2 ( 1 3 1 4 n 2 ) ] + [ D ( e + δ e ) ] ( 1 i 2 2 ! + i 4 4 ! ) } .
2 [ e c ( n 1 ) + D c ] = Δ 0 = 2 [ ( e c + δ e ) ( n 1 ) + D ] , D = D c δ e ( n 1 ) ,
Δ 0 = e c { 2 ( n 1 ) [ 1 + ( 1 / n ) ] } .
Δ = Δ 0 { 1 + i 2 δ e Δ 0 ( n 1 n ) + i 4 8 n 2 [ 1 + δ e e c ( 1 n 2 3 ) ] } ,
Δ = Δ 0 { 1 + i 2 δ e Δ 0 ( n 1 n ) + i 4 [ 1 8 n 2 δ e Δ 0 ( n 2 1 ) ( n 2 3 ) 12 n 3 ] } .
f ( i ) = 1 + i 2 δ e Δ 0 ( n 2 1 n ) + i 4 8 n 2 .
F = 8 π a 2 0 R ( 1 + cos { 2 π Δ λ · [ 1 + R 2 f 2 δ e Δ ( n 2 1 n ) + R 4 8 n 2 f 4 ] } ) R d R ,
C 1 = 1 / ( 8 n 2 f 4 ) , C 2 = 2 π Δ / λ , C 3 = ( δ e / f 2 Δ ) [ ( n 2 1 ) / n ] ,
F = R 1 2 2 + 0 R 1 cos [ C 2 ( 1 + C 3 R 2 + C 1 R 4 ) ] R d R .
F { X 1 + 0 x 1 2 cos [ C 2 ( 1 + C 3 X + C 1 X 2 ) d X } / 2 .
α = C 2 C 1 , β = ( 1 / C 1 ) ( C 3 / 2 C 1 ) 2 , p = ( D 3 / C 1 ) , q = 2 X 1 1 2 + C 3 / C 1 ,
F = X 1 + cos α β p q cos α y 2 d y sin α β p q sin α y 2 d y .

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