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References

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  1. S. Rosin and O. H. Clark, J. Opt. Soc. Am. 31, 198 (1941).
    [Crossref]
  2. M. Herzberger, J. Opt. Soc. Am. 33, 651 (1943).
    [Crossref]

1943 (1)

1941 (1)

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Figures (2)

Fig. 1
Fig. 1

Die Brechkraftkomponenten ϕ1, ϕ2, ⋯, ϕk, die Höhenverhältnisse ω1, ω2, ⋯, ωk und die Dingschnittweite s1.

Fig. 2
Fig. 2

Die Brechkraftkomponenten ϕ1, ϕ2, ⋯, ϕk, die Abstände e1′, e2′, ⋯, ek−1′ und die Dingschnittweite s1.

Equations (29)

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ω k = h k h 1 = i = 2 k s i s i - 1 ,
β = n 1 n k i = 1 k s i s i
f = n 1 n k ( s 1 i = 2 k s i s i ) s 1 = ,
ϕ = 1 f = n k n 1 ( 1 s 1 i = 2 k s i s i ) s 1 = .
ϕ = ( i = 1 k ω i ϕ i - S 1 ) ( 1 - S 1 i = 2 k e i - 1 ω i - 1 ω i ) + S 1 ω k
S 1 = - 1 / s 1
ϕ = i = 1 k ω i ϕ i .
t ϕ = k ,
ω 1 = 1 , ω 2 = 1 - ϕ 1 e 1 , ω 3 = 1 - ϕ 1 ( e 1 + e 2 ) - ϕ 2 e 2 + ϕ 1 ϕ 2 e 1 e 2 , ω 4 = 1 - ϕ 1 ( e 1 + e 2 + e 3 ) - ϕ 2 ( e 2 + e 3 ) - ϕ 3 e 3 + ϕ 1 ϕ 2 ( e 1 e 2 + e 1 e 3 ) + ϕ 1 ϕ 3 ( e 1 e 3 + e 2 e 3 ) + ϕ 2 ϕ 3 e 2 e 3 - ϕ 1 ϕ 2 ϕ 3 e 1 e 2 e 3 ,
ϕ = 1 / f
ϕ = i = 1 k ϕ i ,
ϕ = i = 1 k ω i ϕ i
M = | 0 0 0 0 0 0 0 · 0 0 0 1 ϕ k 0 0 0 0 0 0 0 · 0 0 1 d k - 1 1 0 0 0 0 0 0 0 · 0 1 ϕ k - 1 1 0 0 0 0 0 0 0 0 · 1 d k - 2 1 0 0 0 0 0 0 0 0 0 · ϕ k - 2 1 0 0 0 · · · · · · · · · · · · · 0 0 0 0 0 1 ϕ 3 · 0 0 0 0 0 0 0 0 0 1 d 2 1 · 0 0 0 0 0 0 0 0 1 ϕ 2 1 0 · 0 0 0 0 0 0 0 1 d 1 1 0 0 · 0 0 0 0 0 0 S 1 ϕ 1 1 0 0 0 · 0 0 0 0 0 1 d 0 1 0 0 0 0 · 0 0 0 0 0 ϕ 0 1 0 0 0 0 0 · 0 0 0 0 0 | .
S 1 = - n 1 / s 1 .
im Falle einer Brechfläche : ϕ i = ( n i - n i ) / r i , im Falle einer Spiegelfläche : ϕ i = - 2 n i / r i , im Falle einzelner Linsen : ϕ i = 1 / f i , im Falle von Teilsystemen : ( ϕ i ) i j = 1 / ( f i ) i j .
M I = M / ϕ 0 , M II = - 2 M ϕ 0 d 0 = - M I d 0 , M III = - 2 M ϕ 0 ϕ k = - M I ϕ k , M IV = - 3 M ϕ 0 d 0 ϕ k = M II ϕ k = M III d 0 , M V = - 3 M ϕ 0 d k - 1 ϕ k = M III d k - 1 , M VI = 4 M ϕ 0 d 0 d k - 1 ϕ k = - M IV d k - 1 = - M V d 0 .
| M I 1 M II M III 0 - M IV M V 1 M VI | = 0.
t 2 k = ( 2 k 0 ) + ( 2 k - 1 1 ) + ( 2 k - 2 2 ) + + ( k + 2 k - 2 ) + ( k + 1 k - 1 ) + ( k k ) , t 2 k - 1 = ( 2 k - 1 0 ) + ( 2 k - 2 1 ) + ( 2 k - 3 2 ) + + ( k + 2 k - 3 ) + ( k + 1 k - 2 ) + ( k k - 1 ) , t 2 k - 2 = ( 2 k - 2 0 ) + ( 2 k - 3 1 ) + ( 2 k - 4 2 ) + + ( k + 1 k - 3 ) + ( k k - 2 ) + ( k - 1 k - 1 ) , t 2 k - 3 = ( 2 k - 3 0 ) + ( 2 k - 4 1 ) + ( 2 k - 5 2 ) + + ( k + 1 k - 4 ) + ( k k - 3 ) + ( k - 1 k - 2 ) .
( n m ) + ( n m - 1 ) = ( n + 1 m )
t 2 k = t 2 k - 1 + t 2 k - 2 , t 2 k - 1 = t 2 k - 2 + t 2 k - 3 ,
ω k = M IV , s k / n k = M IV / M VI , s k / n k = M IV / M II , ϕ = M II , z 1 = 1 - M II / ϕ 1 M II , z k = M II / ϕ k - 1 M II = M IV - 1 M II ,
ω k = M III , s k / n k = - M III / M V , s k / n k = - M III / M I , β = S 1 / M I .
ϕ i = M II - ( M II ) ϕ i = 0 M II / ϕ i = ϕ - ( M II ) ϕ i = 0 M II / ϕ i ,
d i = M II - ( M II ) d i = 0 M II / d i = ϕ - ( M II ) d i = 0 M II / d i ,
s 1 = 1 / β - M II / ϕ 1 ϕ .
M I = | 0 0 1 ϕ 2 0 1 d 1 1 S 1 ϕ 1 1 0 1 1 0 0 | = - ( ϕ 1 + ϕ 2 - d 1 ϕ 1 ϕ 2 - S 1 + S 1 d 1 ϕ 2 ) , M II = | 0 1 ϕ 2 1 d 1 1 ϕ 1 1 0 | = ϕ 1 + ϕ 2 - d 1 ϕ 1 ϕ 2 , M III = | 0 1 d 1 S 1 ϕ 1 1 1 1 0 | = 1 - d 1 ϕ 1 + S 1 d 1 , M IV = | 1 d 1 ϕ 1 1 | = 1 - d 1 ϕ 1 , M V = | S 1 ϕ 1 1 1 | = S 1 - ϕ 1 , M VI = | ϕ 1 | = ϕ 1
ω 2 = 1 - d 1 ϕ 1 , s 2 n 2 = 1 - d 1 ϕ 1 ϕ 1 s 2 n 2 = 1 - d 1 ϕ 1 ϕ 1 + ϕ 2 - d 1 ϕ 1 ϕ 2 , ϕ = ϕ 1 + ϕ 2 - d 1 ϕ 1 ϕ 2 , z 1 = d 1 ϕ 2 ϕ 1 + ϕ 2 - d 1 ϕ 1 ϕ 2 , z 2 = - d 1 ϕ 2 ϕ 1 + ϕ 2 - d 1 ϕ 1 ϕ 2 ,
ω 2 = 1 - d 1 ϕ 1 + S 1 d 1 , s 2 n 2 = 1 - d 1 ϕ 1 + S 1 d 1 ϕ 1 - S 1 , s 2 n 2 = 1 - d 1 ϕ 1 + S 1 d 1 ϕ 1 + ϕ 2 - d 1 ϕ 1 ϕ 2 - S 1 + S 1 d 1 ϕ 2 , β = S 1 - ( ϕ 1 + ϕ 2 - d 1 ϕ 1 ϕ 2 - S 1 + S 1 d 1 ϕ 2 ) .
ϕ 1 = ϕ - | 0 1 ϕ 2 1 d 1 1 0 1 0 | | 1 ϕ 2 d 1 1 | = ϕ - ϕ 2 1 - d 1 ϕ 2 , ϕ 2 = ϕ - | 0 1 0 1 d 1 1 ϕ 1 1 0 | | 1 d 1 ϕ 1 1 | = ϕ - ϕ 1 1 - d 1 ϕ 1 , d 1 = ϕ - | 0 1 ϕ 2 1 0 1 ϕ 0 1 0 | | 0 ϕ 2 ϕ 1 0 | = 1 ϕ 1 + 1 ϕ 2 - ϕ ϕ 1 ϕ 2 , s 1 = 1 β - | 1 d 1 ϕ 2 1 | ϕ = 1 β + d 1 ϕ 2 - 1 ϕ .