Abstract

This paper reports the results of a treatment of a differential method for the fine correction of optical systems that is described at length in a Polish publication, which accounts for the extensive bibliography. The method is applied to various problems by deriving formulas for correcting one set of errors and at the same time, if desired, keeping another set of errors below a given tolerance limit.

© 1963 Optical Society of America

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References

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  1. L. Fialovszky, Anwendung einer Differentialmethode und der Ausgleichungsrechnung zur Feinkorrektion optischer Systeme, Compte rendu du premier Symposium international sur les calculs géodésiques Cracovie, 9–15 Septembre 1959, Académie Polonaise des sciences Comité de Géodésia, 1961.
  2. M. Herzberger, Über die Durchrechnung von Strahlen durch optische Systeme, Z. Physik 43, 750 (1927).
    [CrossRef]
  3. F. D. Cruickshank, “A System of Transfer Coefficients for Use in the Design of Lens Systems. VI,” Proc. Phys. Soc. (London) 58, 296 (1946).
    [CrossRef]
  4. A. L. M’Auley and F. D. Cruickshank, “A Differential Method of Adjusting the Aberration of a Lens System,” Proc. Phys. Soc. (London) 57, 302 (1945).
    [CrossRef]
  5. F. D. Cruickshank, “The Paraxial Differential Transfer Coefficients of a Lens System,” J. Opt. Soc. Am. 36, 13 (1946).
    [CrossRef] [PubMed]
  6. W. M. Stempel, “An Empirical Approach to Lens Design,” J. Opt. Soc. Am. 33, 278 (1943).
    [CrossRef]
  7. W. M. Stempel, “A Differential Adjustment Method of Refining Optical Systems,” J. Opt. Soc. Am. 38, 935 (1948).
    [CrossRef] [PubMed]
  8. F. I. Havliček, “Zur Feinkorrektion optischer Systeme,” Optik 9, 333 (1952).
  9. F. I. Havliček, “Über die Verwendung von Differenzen der Seidelschen Koeffizienten bei der Korrektur von optischen Systemen,” Optik 10, 475 (1953).
  10. F. A. Lucy, “Simultaneous Correction of Meridian Aberrations,” J. Opt. Soc. Am. 45, 320, 323, 670 (1955).
    [CrossRef]
  11. S. Rosen and C. Eldert, “Least-Squares Method for Optical Correction,” J. Opt. Soc. Am. 44, 250 (1954).
    [CrossRef]
  12. S. Rosen and An-Min Chung, “Application of the Least-Squares Method,” J. Opt. Soc. Am. 46, 223 (1956).
    [CrossRef]
  13. D. P. Feder, “Calculation of an Optical Merit Function and Its Derivatives with Respect to the System Parameters,” J. Opt. Soc. Am. 47, 913 (1957).
    [CrossRef]
  14. J. Meiron and H. M. Loebenstein, “Automatic Correction of Residual Aberrations,” J. Opt. Soc. Am. 4, 1104 (1957).
    [CrossRef]
  15. J. Meiron, “Automatic Lens Design by the Least Squares Method,” J. Opt. Soc. Am. 49, 293 (1959).
    [CrossRef]
  16. M. Herzberger, “Light Distribution in the Optical Image,” J. Opt. Soc. Am. 37, 485 (1947); reprinted in La théorie des images optiques (Editions de la Revue d’optique, Paris, 1949), p. 108.
    [CrossRef] [PubMed]
  17. J. S. Seress, “Reflection to the Petzval’s Memorials,” Acta Tech. Acad. Sci. Hung. 25, 211 (1959).
  18. J. Petzval, “Bericht über optische Untersuchungen,” Wiener Sitz.-Ber. 24, 50, 92, 129 (1857).

1959 (2)

J. Meiron, “Automatic Lens Design by the Least Squares Method,” J. Opt. Soc. Am. 49, 293 (1959).
[CrossRef]

J. S. Seress, “Reflection to the Petzval’s Memorials,” Acta Tech. Acad. Sci. Hung. 25, 211 (1959).

1957 (2)

D. P. Feder, “Calculation of an Optical Merit Function and Its Derivatives with Respect to the System Parameters,” J. Opt. Soc. Am. 47, 913 (1957).
[CrossRef]

J. Meiron and H. M. Loebenstein, “Automatic Correction of Residual Aberrations,” J. Opt. Soc. Am. 4, 1104 (1957).
[CrossRef]

1956 (1)

1955 (1)

1954 (1)

1953 (1)

F. I. Havliček, “Über die Verwendung von Differenzen der Seidelschen Koeffizienten bei der Korrektur von optischen Systemen,” Optik 10, 475 (1953).

1952 (1)

F. I. Havliček, “Zur Feinkorrektion optischer Systeme,” Optik 9, 333 (1952).

1948 (1)

1947 (1)

1946 (2)

F. D. Cruickshank, “A System of Transfer Coefficients for Use in the Design of Lens Systems. VI,” Proc. Phys. Soc. (London) 58, 296 (1946).
[CrossRef]

F. D. Cruickshank, “The Paraxial Differential Transfer Coefficients of a Lens System,” J. Opt. Soc. Am. 36, 13 (1946).
[CrossRef] [PubMed]

1945 (1)

A. L. M’Auley and F. D. Cruickshank, “A Differential Method of Adjusting the Aberration of a Lens System,” Proc. Phys. Soc. (London) 57, 302 (1945).
[CrossRef]

1943 (1)

1927 (1)

M. Herzberger, Über die Durchrechnung von Strahlen durch optische Systeme, Z. Physik 43, 750 (1927).
[CrossRef]

1857 (1)

J. Petzval, “Bericht über optische Untersuchungen,” Wiener Sitz.-Ber. 24, 50, 92, 129 (1857).

Chung, An-Min

Cruickshank, F. D.

F. D. Cruickshank, “The Paraxial Differential Transfer Coefficients of a Lens System,” J. Opt. Soc. Am. 36, 13 (1946).
[CrossRef] [PubMed]

F. D. Cruickshank, “A System of Transfer Coefficients for Use in the Design of Lens Systems. VI,” Proc. Phys. Soc. (London) 58, 296 (1946).
[CrossRef]

A. L. M’Auley and F. D. Cruickshank, “A Differential Method of Adjusting the Aberration of a Lens System,” Proc. Phys. Soc. (London) 57, 302 (1945).
[CrossRef]

Eldert, C.

Feder, D. P.

Fialovszky, L.

L. Fialovszky, Anwendung einer Differentialmethode und der Ausgleichungsrechnung zur Feinkorrektion optischer Systeme, Compte rendu du premier Symposium international sur les calculs géodésiques Cracovie, 9–15 Septembre 1959, Académie Polonaise des sciences Comité de Géodésia, 1961.

Havlicek, F. I.

F. I. Havliček, “Über die Verwendung von Differenzen der Seidelschen Koeffizienten bei der Korrektur von optischen Systemen,” Optik 10, 475 (1953).

F. I. Havliček, “Zur Feinkorrektion optischer Systeme,” Optik 9, 333 (1952).

Herzberger, M.

Loebenstein, H. M.

J. Meiron and H. M. Loebenstein, “Automatic Correction of Residual Aberrations,” J. Opt. Soc. Am. 4, 1104 (1957).
[CrossRef]

Lucy, F. A.

M’Auley, A. L.

A. L. M’Auley and F. D. Cruickshank, “A Differential Method of Adjusting the Aberration of a Lens System,” Proc. Phys. Soc. (London) 57, 302 (1945).
[CrossRef]

Meiron, J.

J. Meiron, “Automatic Lens Design by the Least Squares Method,” J. Opt. Soc. Am. 49, 293 (1959).
[CrossRef]

J. Meiron and H. M. Loebenstein, “Automatic Correction of Residual Aberrations,” J. Opt. Soc. Am. 4, 1104 (1957).
[CrossRef]

Petzval, J.

J. Petzval, “Bericht über optische Untersuchungen,” Wiener Sitz.-Ber. 24, 50, 92, 129 (1857).

Rosen, S.

Seress, J. S.

J. S. Seress, “Reflection to the Petzval’s Memorials,” Acta Tech. Acad. Sci. Hung. 25, 211 (1959).

Stempel, W. M.

Acta Tech. Acad. Sci. Hung. (1)

J. S. Seress, “Reflection to the Petzval’s Memorials,” Acta Tech. Acad. Sci. Hung. 25, 211 (1959).

J. Opt. Soc. Am. (10)

Optik (2)

F. I. Havliček, “Zur Feinkorrektion optischer Systeme,” Optik 9, 333 (1952).

F. I. Havliček, “Über die Verwendung von Differenzen der Seidelschen Koeffizienten bei der Korrektur von optischen Systemen,” Optik 10, 475 (1953).

Proc. Phys. Soc. (London) (2)

F. D. Cruickshank, “A System of Transfer Coefficients for Use in the Design of Lens Systems. VI,” Proc. Phys. Soc. (London) 58, 296 (1946).
[CrossRef]

A. L. M’Auley and F. D. Cruickshank, “A Differential Method of Adjusting the Aberration of a Lens System,” Proc. Phys. Soc. (London) 57, 302 (1945).
[CrossRef]

Wiener Sitz.-Ber. (1)

J. Petzval, “Bericht über optische Untersuchungen,” Wiener Sitz.-Ber. 24, 50, 92, 129 (1857).

Z. Physik (1)

M. Herzberger, Über die Durchrechnung von Strahlen durch optische Systeme, Z. Physik 43, 750 (1927).
[CrossRef]

Other (1)

L. Fialovszky, Anwendung einer Differentialmethode und der Ausgleichungsrechnung zur Feinkorrektion optischer Systeme, Compte rendu du premier Symposium international sur les calculs géodésiques Cracovie, 9–15 Septembre 1959, Académie Polonaise des sciences Comité de Géodésia, 1961.

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Equations (27)

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z 1 = z 1 ( r 1 , r k , e 2 , e k , n 2 , n k ) , z 2 = z 2 ( r 1 , r k , e 2 , e k , n 2 , n k ) , z m = z m ( r 1 , r k , e 2 , e k , n 2 , n k ) .
i = 1 k z 1 r i Δ r i + i = 2 k z 1 e i Δ e i + i = 2 k z 1 n i Δ n i Δ z 1 = 0 , i = 1 k z 2 r i Δ r i + i = 2 k z 2 e i Δ e i + i = 2 k z 2 n i Δ n i Δ z 2 = 0 , i = 1 k z m r i Δ r i + i = 2 k z m e i Δ e i + i = 2 k z m n i Δ n i Δ z m = 0 ,
X i = ( S i β i )
S i = S i 1 e i , sin φ i = [ ( S i r i ) / r i ] sin β i 1 , sin φ i = [ n i / ( n i + 1 ) ] sin φ i , β i = β i 1 + φ i φ i , S i = r i + ( r i sin φ i / sin β i ) ,
a i = S i / S i 1 = B i ( 1 T i cot β i ) , b i = S i / β i 1 = B i ( S i r i ) [ cot β i 1 cot β i ( 1 + T i cot β i 1 ) ] , c i = β i / S i 1 = T i / ( S i r i ) , d i = β i / β i 1 = 1 + T i cot β i 1 , g i = S i / r i = 1 B i [ 1 ( S i T i / r i ) cot β i ] h i = β i / r 2 = S i T i / r i ( S i r i ) , p i = ( S i / n i ) x = ( 1 + cot β i tg φ i ) × ( r i sin φ i / n i sin β i ) , g i = ( β i / n i ) x = ( 1 / n i ) tg φ i , k i = S i 1 / n i = m i p i 1 , l i = β i 1 / n i = m i q i , t i = S i / n i = a i k i + b i l i + p i , u i = β i / n i = c i k i + d i l i + q i ,
m i = n i / ( n i + 1 ) , T i = tg φ i tg φ i , B i = m i ( sin β i 1 / sin β i ) .
Δ X i ( Δ r i ) = ( g i h i ) Δ r i , Δ X i ( Δ e i ) = ( a i c i ) Δ e i , Δ X i ( Δ n i ) = ( t i u i ) Δ n i .
Δ X k = [ ( M k · M k 1 ) M i + 1 ] = K i + 1 Δ X i ,
M i + 1 = ( a i + 1 b i + 1 c i + 1 d i + 1 )
K i + 1 = [ ( M k · M k 1 ) M i + 1 ]
Δ X k ( Δ r i ) = K i + 1 ( g i h i ) Δ r i , Δ X k ( Δ e i ) = K i + 1 ( a i c i ) Δ e i , Δ X k ( Δ n i ) = K i + 1 ( t i u i ) Δ n i .
n i + 1 S i = n i S i 1 e i + n i + 1 n i r i
( a ) i = S i S i 1 = S i e i = m i S i S i 2 , ( g ) i = S i r i = S i r i 2 ( 1 m i ) , ( p ) i = ( S i n i ) x = S i 2 n i + 1 ( 1 r i 1 S i ) , ( k ) i = S i 1 n i = m i 1 ( p ) i 1 , ( t ) i = S i n i = ( a ) i ( k ) i + ( p ) i .
Δ S k = j = i + 1 k ( a ) j · Δ S i .
Δ S k ( Δ r i ) = Δ r i ( g ) i j = i + 1 k ( a ) j , Δ S k ( Δ e i ) = Δ e i j = i + 1 k ( a ) j , Δ S k ( Δ n i ) = Δ n i ( t ) i j = i + 1 k ( a ) j .
Δ z 1 ( Δ r i ) = [ ( g ) i j = i + 1 k ( a ) j K i + 1 ( g i h i ) ] Δ r i , Δ z 1 ( Δ e i ) = [ j = i + 1 k ( a ) j K i + 1 ( a i c i ) ] Δ e i , Δ z 1 ( Δ n i ) = [ ( t ) i j = i + 1 k ( a ) j K i + 1 ( t i u i ) ] Δ n i .
φ 1 = a 1 x 1 + a 2 x 2 + + a l x l + z 1 = 0 , φ 2 = b 1 x 1 + b 2 x 2 + + b l x l + z 2 = 0 , φ m = m 1 x 1 + m 2 x 2 + + m l x l + z m = 0 ;
A 1 x 1 + B 1 x 2 + + L 1 x l + Z 1 = υ 1 , A 2 x 1 + B 2 x 2 + + L 2 x l + Z 2 = υ 2 , A n x 1 + B n x 2 + + L n x l + Z n = υ n .
[ p x x ] = p 1 x 1 2 + p 2 x 2 2 + + p l x l 2
p i = ( P i a i 2 + P 2 b i 2 + + P m m i 2 ) 1 2 ,
F 3 = [ P υ υ ] 1 n = P 1 υ 1 2 + P 2 υ 2 2 + + P m υ m 2
F 4 = [ P υ υ ] 1 n + [ p x x ] 1 l
x 1 = υ 1 , x 2 = υ 2 , x l = υ l ,
( [ P A A ] 1 n + p 1 ) * x 1 + [ P A B ] x 2 + + [ P A L ] x l + [ P A Z ] = 0 , [ P B A ] x 1 + ( [ P B B ] + p 2 ) * x 2 + + [ P B L ] x l + [ P B Z ] = 0 , [ P L A ] x 1 + [ P L B ] x 2 + + ( [ P L L ] + p l ) * x l + [ P L Z ] = 0
[ P A Z ] x 1 + [ P B Z ] x 2 + + [ P L Z ] x l + [ P Z Z ] = [ P V V ] 1 n + [ p υ υ ] 1 l
F 6 = [ P υ υ ] 1 n + [ p xx ] 1 l + [ Z λ φ ] 1 m
( [ P A A ] + p 1 ) * x 1 + [ P A B ] x 2 + + [ P A Z ] + [ P B A ] x 1 + ( [ P B B ] + p 2 ) * x 2 + + [ P B Z ] + [ P L A ] x 1 + [ P L B ] x 2 + + [ P L Z ] + a 1 λ 1 + b 1 λ 2 + + m 1 λ m a 2 λ 1 + b 2 λ 2 + + m 2 λ m a l λ 1 + b l λ 2 + + m l λ m = 0 , = 0 , = 0.