Abstract

Our method of matrix synthesis of optical components and instruments is applied to the derivation of Jones’s matrices appropriate for fourier interferometers (spectrometers and spectropolarimeters). These matrices are obtained for both the source beam and the detector beam. In the course of synthesis, Jones’s matrices of the various reflectors (plane mirrors; retroreflectors: roofed mirror, trihedral and prism cube corner, cat’s eye) used by these interferometers are also obtained.

© 1971 Optical Society of America

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References

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  1. A. L. Fymat, Appl. Opt. 10, 2499 (1971).
    [CrossRef] [PubMed]
  2. W. A. Shurcliff, Polarized Light (Harvard U. P., Cambridge, 1962), Appendix 2.
  3. E. R. Peck, J. Opt. Soc. Am. 38, 66, 1015 (1948); J. Opt. Soc. Am. 47, 250 (1957).
    [CrossRef] [PubMed]
  4. J. Terrien, Rev. Opt. 38, 29 (1957).
  5. M. V. R. K. Murty, J. Opt. Soc. Am. 50, 83 (1960).
    [CrossRef]
  6. J. Connes, P. Connes, J. Opt. Soc. Am. 56, 896 (1966).
    [CrossRef]
  7. A. L. Fymat, K. D. Abhyankar, Appl. Opt. 9, 1075 (1970); NASA Technical Brief 70-10405 (November1970); Proc. Aspen Int. Conf. on Fourier Spectroscopy, 1970, AFCRL 71-0019, Special Report 114, G. A. Vanasse, A. T. Stair, D. J. Baker, Eds. 377 (1971).
    [CrossRef] [PubMed]
  8. A. L. Fymat (submitted for publication).

1971 (1)

1970 (1)

1966 (1)

1960 (1)

1957 (1)

J. Terrien, Rev. Opt. 38, 29 (1957).

1948 (1)

E. R. Peck, J. Opt. Soc. Am. 38, 66, 1015 (1948); J. Opt. Soc. Am. 47, 250 (1957).
[CrossRef] [PubMed]

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Figures (2)

Fig. 1
Fig. 1

Some reflector configurations (a) plane mirror and 0° specular reflector, (b) and (c) retroreflectors: dihedral roofed mirror and cat’s eye, respectively. (The other retroreflectors, trihedral roofed mirror and cubic prism, are not represented.)

Fig. 2
Fig. 2

Combinations of retroreflectors and 0° specular reflectors to increase the path difference between the two arms of the interferometer (a) single combinations, (b) array combinations.

Equations (37)

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R F = ( ρ 0 0 ρ ) ,
ρ = p 1 - p l p 1 + p l ,             ρ = q 1 - q l q 1 + q l ,
M = R F ( ) = ( ν - 1 ν + 1 ) ( - 1 0 0 1 ) ,
cos θ l ( i ) = { 1 - 1 2 [ ν ( i ) ] 2 } 1 2 ,             i = A , B ,
M = R F ( B ) R F ( A ) ,
R F ( i ) = ( ρ ( i ) 0 0 ρ ( i ) ) ,             i = A , B ,
ρ ( i ) = 1 - ( 2 ) 1 2 ν ( i ) cos θ l ( i ) 1 + ( 2 ) 1 2 ν ( i ) cos θ l ( i ) ,             ρ ( i ) = 1 - ( 2 ) 1 2 cos θ l ( i ) / ν ( i ) 1 + ( 2 ) 1 2 cos θ l ( i ) / ν ( i ) ,
M = [ R F ] 2 .
cos θ l ( j ) = { 1 - [ sin θ 1 ( i ) ν ( i ) ] 2 } 1 2 ,             j = A , B , C ,
M = R ( β ) R F ( C ) R ( α ) R F ( B ) R F ( A ) ,
R F ( i ) = ( ρ ( i ) 0 0 ρ ( i ) ) ,
ρ ( i ) = 1 - ν ( i ) cos θ l ( i ) / cos θ 1 ( i ) 1 + ν ( 1 ) cos θ l ( i ) / cos θ 1 ( i ) ,             ρ ( i ) = 1 - cos θ l ( i ) / ν ( i ) cos θ 1 ( i ) 1 + cos θ l ( i ) / ν ( i ) cos θ 1 ( i ) ,
M = R ( β ) R F R ( α ) [ R F ] 2 .
M = T F R ( β ) R F ( C ) R ( α ) R F ( B ) R F ( A ) T F ,
τ = 2 1 + ν ( P ) cos θ l ( P ) / cos θ 1 ( P ) ,             τ = 2 ν ( P ) + cos θ l ( P ) / cos θ 1 ( P ) .
M = T F R ( β ) R F R ( α ) ( R F ) 2 T F .
M = M ¯ [ ( 9 ) or ( 12 ) ] M ( 3 ) M [ ( 9 ) or ( 12 ) ] .
M = R F ( B ) R F ( C ) R F ( A ) ,
M = R F R F ( C ) R F ;
M = ( R F ) 3 .
Q = M R F ( ) M ,
Q = ( π M k k ) R F ( ) ( π ¯ M k k ) ,             k = 1 , 2 , ,
K = n K n ,             n = 1 , 2 , , N ,
R 1 = exp ( - i δ / 2 ) 1 ,             R 2 = exp ( i δ / 2 ) 1 ,
Source beam :             F source = R 1 S 1 ( r ) M 1 S 1 ( r ) + R 2 S 2 ( t ) M 2 S 2 ( t ) ,
Detector beam :             F det = R 1 S 1 ( t ) M 1 S 1 ( r ) + R 2 S 2 ( r ) M 2 S 2 ( t ) .
A ( θ ) = [ A 11 ( θ ) A 12 ( θ ) A 21 ( θ ) A 22 ( θ ) ]
A ( θ ) = L ( θ ) = f ( cos 2 θ cos θ sin θ cos θ sin θ sin 2 θ ) ,
A ( θ ) = C r ( θ ) = f 2 ( 1 - i + i 1 ) r ,             A ( θ ) = C l ( θ ) = f 2 ( 1 + i - i 1 ) i .
Source beam :             P source ( 1 ) = A 3 [ R 1 S 1 ( r ) A 1 M 1 A 1 S 1 ( r ) + R 2 S 2 ( t ) A 2 M 2 A 2 S 2 ( t ) ] ,
Detector beam :             P det ( 1 ) = A 3 [ R 1 S 1 ( t ) A 1 M 1 A 1 S 1 ( r ) + R 2 S 2 ( r ) A 2 M 2 A 2 S 2 ( t ) ] , A 3 L 3 , A i L i , or C i ,             i = 1 , 2 ,
Source beam :             P source ( 2 ) = A 3 F source ,
Detector beam :             P det ( 2 ) = A 3 F det ,             A 3 L 3 .
Source beam :             P source ( 3 ) = F source A 3 ,
Detector beam :             P det ( 3 ) = F det A 3 , A 3 L 3 ,
Source beam :             P source ( 4 ) = A 3 F source A ,
Detector beam :             P det ( 4 ) = A 3 F det A , A L or C , A 3 L 3 .

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