Abstract

A three-objective multipass matrix system has been theoretically analyzed with respect to the aberrations of the third order. An expression has been derived in the three-dimensional coordinate system relating the position of a point in the output slit to that of a point in the input slit, depending on the construction peculiarities of the system given and the parameters of the matrix of intermediate images. Conditions of image focusing upon the input slit and astigmatism compensation have been derived. Relationships to determine the field curvature and distortion have been derived.

© 1992 Optical Society of America

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References

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  1. J. U. White, “Long optical paths of large aperture,” J. Opt. Soc. Am. 32, 285–288 (1942).
    [CrossRef]
  2. T. R. Reesor, “The astigmatism of a multiple path absorption cell,” J. Opt. Soc. Am. 41, 1059–1060 (1951).
    [CrossRef]
  3. T. Y. Edwards, “Multiple-traverse absorption cell design,” J. Opt. Soc. Am. 51, 98–102 (1961).
    [CrossRef]
  4. E. G. Barskaya, “Aberrations of a multipass cell,” Opt. Mekh. Prom. 5, 25–27 (1971).
  5. S. M. Chernin, E. G. Barskaya, “Multipass optical system,” USSR invention brevet 1,082,162 (4February).
  6. S. M. Chernin, E. G. Barskaya, “Multipass matrix system,” USSR invention brevet 1,091,101 (6July1982).
  7. S. M. Chernin, E. G. Barskaya, “Optical multipass matrix systems,” Appl. Opt. 30, 51–58 (1991).
    [CrossRef] [PubMed]
  8. E. G. Barskaya, “Multipass optical cell,” USSR invention brevet 206,857 (22June1966).

1991 (1)

1971 (1)

E. G. Barskaya, “Aberrations of a multipass cell,” Opt. Mekh. Prom. 5, 25–27 (1971).

1961 (1)

1951 (1)

1942 (1)

Barskaya, E. G.

S. M. Chernin, E. G. Barskaya, “Optical multipass matrix systems,” Appl. Opt. 30, 51–58 (1991).
[CrossRef] [PubMed]

E. G. Barskaya, “Aberrations of a multipass cell,” Opt. Mekh. Prom. 5, 25–27 (1971).

S. M. Chernin, E. G. Barskaya, “Multipass optical system,” USSR invention brevet 1,082,162 (4February).

E. G. Barskaya, “Multipass optical cell,” USSR invention brevet 206,857 (22June1966).

S. M. Chernin, E. G. Barskaya, “Multipass matrix system,” USSR invention brevet 1,091,101 (6July1982).

Chernin, S. M.

S. M. Chernin, E. G. Barskaya, “Optical multipass matrix systems,” Appl. Opt. 30, 51–58 (1991).
[CrossRef] [PubMed]

S. M. Chernin, E. G. Barskaya, “Multipass optical system,” USSR invention brevet 1,082,162 (4February).

S. M. Chernin, E. G. Barskaya, “Multipass matrix system,” USSR invention brevet 1,091,101 (6July1982).

Edwards, T. Y.

Reesor, T. R.

White, J. U.

Appl. Opt. (1)

J. Opt. Soc. Am. (3)

Opt. Mekh. Prom. (1)

E. G. Barskaya, “Aberrations of a multipass cell,” Opt. Mekh. Prom. 5, 25–27 (1971).

Other (3)

S. M. Chernin, E. G. Barskaya, “Multipass optical system,” USSR invention brevet 1,082,162 (4February).

S. M. Chernin, E. G. Barskaya, “Multipass matrix system,” USSR invention brevet 1,091,101 (6July1982).

E. G. Barskaya, “Multipass optical cell,” USSR invention brevet 206,857 (22June1966).

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Figures (3)

Fig. 1
Fig. 1

Multipass matrix three-objective system in three-dimensional coordinate systems.

Fig. 2
Fig. 2

Portion of a ray propagating in the multipass system.

Fig. 3
Fig. 3

Focused aberration pattern after 218 passes.

Equations (25)

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N = 2 ( K S 1 ) .
B = 2 c ( K 1 )
H = t ( S 1 ) .
A C ¯ = A C ¯ ( 1 + 2 A C ¯ * C M ¯ C M 2 ) .
y = B y ( 1 + x + x r ) + m x + x r p = 1 S / 2 ( { q = 1 2 K 1 2 r 2 [ y c 2 ( 2 q 1 ) ] { [ y c 2 ( 2 q 1 ) ] × ( m c 2 ) + M [ z ( 2 p 1 ) t ] } q = 1 2 K 2 2 m r [ d 1 + ( y q c ) 2 + [ z ( 2 p 1 ) t ] 2 2 r ] } ) + p = 1 S / 2 1 m y r 2 { ( z 2 p t ) 2 + [ z 2 ( p 1 ) t ] 2 + 4 r d 2 } ,
z = H z ( 1 + x + x r ) + M x + x r p = 1 S / 2 ( q = 1 2 K 1 2 r 2 [ z ( 2 p 1 ) t ] × { [ y c 2 ( 2 q 1 ) ] × ( m c 2 ) + M [ z ( 2 p 1 ) t ] q = 1 2 K 2 2 M r { d 1 + ( y q c ) 2 = [ z ( 2 p 1 ) t ] 2 2 r } ) + 2 p = 1 S / 2 1 ( 2 z 2 M + t ) [ z ( 2 p 1 ) t ] 2 r 2 + p = 1 S / 2 1 M z 2 r 2 × { ( z 2 p t ) 2 + [ z 2 ( p 1 ) t ] 2 + 4 r d 2 } .
y = B y ( 1 + x + x r ) + m x + x r ( m c 2 ) ( 2 K 1 ) S r 2 × [ y 2 y c ( 2 K 1 ) + c 2 12 ( 4 K 1 ) ( 4 K 3 ) M S r 2 ( 2 K 1 ) ] × [ y c 2 ( 2 K 1 ) ] [ z t ( S 2 1 ) ] + m S r 2 ( K 1 ) × [ y 2 y c ( 2 K 1 ) + 2 r d 1 + z 2 + c 2 6 ( 2 K 1 ) × ( 4 K 3 ) z t ( S 2 ) + t 2 3 ( S 1 ) ( S 2 ) ] + m y 2 r 2 × ( S 2 ) [ z 2 z t ( S 2 ) + t 2 3 ( S 2 4 S + 6 ) + 2 r d 2 ] ,
z = H z ( 1 + x + x r ) + M x + x r ( m c 2 ) ( 2 K 1 ) r 2 × [ y c 2 ( 2 K 1 ) ] [ z t ( S 2 1 ) ] M S r 2 ( 2 K 1 ) × [ z 2 z t ( S 2 ) + t 2 3 ( S 1 ) ( S 2 ) ] + M S r 2 ( K 1 ) × [ y 2 y c ( 2 K 1 ) + 2 r d 1 + z 2 + c 2 6 ( 2 K 1 ) × ( 4 K 3 ) z t ( S 2 ) + t 2 3 ( S 1 ) ( S 2 ) ] + ( 2 z 2 M + t ) ( S 2 ) r 2 [ z 2 z t ( S 2 ) + t 2 3 ( S 1 ) ( S 3 ) ] + M z 2 r 2 ( S 2 ) × [ z 2 z t ( S 2 ) + t 2 3 ( S 2 4 S + 6 ) + 2 r d 2 ] .
y = c 2 ( 2 K 1 )
x + x r S K c 2 3 r 2 ( 2 K 1 ) ( K 1 ) + S r 2 ( K 1 ) × [ c 2 12 ( 2 K 1 ) ( 2 K 3 ) + 2 r d 1 + z 2 z t ( S 2 ) + t 2 3 ( S 1 ) ( S 2 ) ] + S 2 r 2 × [ z 2 z t ( S 2 ) + t 2 3 ( S 2 4 S + 6 ) + 4 r d 2 ] = 0 .
d 2 = t 2 24 r ( S 2 4 S + 15 ) .
d 1 = 1 24 r [ c 2 ( 2 K 1 ) ( 2 K 3 ) t 2 ( S 2 1 ) ] .
S 2 1 ( 2 K 1 ) ( 2 K + 3 ) = ( c t ) 2 .
S K 2 c t .
x + x = ( N 2 1 ) 1 r [ ( z z 0 ) 2 t 2 4 ] .
z 0 = t S 2 2 .
ρ x = r N 2 .
Δ y = 0 ,
Δ z = Δ M r 2 N [ z 2 z t ( S 2 ) + t 2 3 ( S 1 ) ( S 2 ) N 1 N c 2 3 ( 2 K 1 ) ( K 1 ) N + 2 2 N ] .
z = z 0 [ c 2 6 ( 2 K 1 ) ( K 1 ) t 2 12 ( S 2 4 ) ] 1 / 2 .
S 2 1 2 ( 2 K 1 ) ( K 1 ) = ( c t ) 2 .
S K 2 c t .
Δ z = Δ M r 2 N [ ( z z 0 ) 2 t 2 4 ] .
Δ y = Δ M S t 2 r 2 ( 2 K 1 ) [ y c 2 ( 2 K 1 ) ] .
ρ y = r 2 2 y 2 ( S 2 ) .

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